Skip to main content Accessibility help
×
Hostname: page-component-848d4c4894-nr4z6 Total loading time: 0 Render date: 2024-06-02T04:58:18.723Z Has data issue: false hasContentIssue false

References

Published online by Cambridge University Press:  18 December 2014

Grigory Isaakovich Barenblatt
Affiliation:
University of Cambridge
Get access

Summary

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Scaling, Self-similarity, and Intermediate Asymptotics
Dimensional Analysis and Intermediate Asymptotics
, pp. 366 - 382
Publisher: Cambridge University Press
Print publication year: 1996

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ablowitz, M.J. & Clarkson, P.A. (1991). Solitons, Nonlinear Evolution Equations and Inverse Scattering. Cambridge University Press.CrossRefGoogle Scholar
Abramowitz, M. & Stegun, I.A., eds. (1970). Handbook of Mathematical Functions. Dover Publications, New York.
Adamsky, V.B. (1956). Integration of a system of autosimulating equations for the problem of a short-duration shock in a cold gas. Soviet Phys. Acoustics 2 (1), 1–7.Google Scholar
Aldushin, A.P., Zeldovich, Ya.B. & Khudyaev, S.I. (1979). Flame propagation in a reacting gas mixture. Preprint, Institute of Chemical Physics, Chernogolovka.Google Scholar
Alexandrov, S.E. & Goldstein, R.V. (1993a). On the separated flows in the theory of plasticity. Izvestiya, Russian Ac. Sci. Mech. Solids4, 144–149.Google Scholar
Alexandrov, S.E. & Goldstein, R.V. (1993b). The flow of plastic mass in a converging channel: the singularities of a solution. Doklady, Russian Ac. Sci. 332 (3), 314–316.Google Scholar
Amit, D. (1989). Field Theory, the Renormalization Group and Critical Phenomena, 2nd edition, World Scientific, Singapore etc.Google Scholar
Andrade, E.N. da C. (1910). On the viscous flow of metals and allied phenomena. Proc. Roy. Soc. A84, 1–12.Google Scholar
Anderson, D.M. & Davis, S.H. (1993). Two-fluid viscous flow in a corner. J. Fluid Mech. 257, 1–31.CrossRefGoogle Scholar
Andrianov, I.V. & Kholod, E.G. (1993). Intermediate asymptotics in nonlinear dynamics of shells. Izvestiya, Russian Ac. Sci., Mech. Solids 2, 172–7.Google Scholar
Andrushchenko, V.A., Barenblatt, G.I. & Chudov, L.A. (1975). Self-similar propagation of strong blast waves in the presence of radiation or energy release at the wave front. In Progress in the Mechanics of Deformable Media, collection of papers dedicated to the 100th anniversary of B.G. Galerkin, Shapiro, G.S. (ed.), 35–44, (in Russian) Nauka, Moscow.Google Scholar
Angenent, S.B. & Aronson, D.G. (1993). The focusing problem for the radially symmetric porous medium equation. Euro. J. Appl. Math., (to appear).Google Scholar
Aronson, D.G. & Graveleau, J. (1993). A self-similar solution to the focusing problem for the porous medium equation. Euro. J. Appl. Math. 4, 65–81.CrossRefGoogle Scholar
Aronson, D.G.Vázquez, J.L. (1993). Anomalous exponents in nonlinear diffusion. IMA Preprint No. 1165, University of Minnesota.
Bailey, R.W. (1929). Transactions of Tokyo Sect. Meeting of the World Power Conference, Tokyo.Google Scholar
Baldin, A.M. & Didenko, L.A. (1990). Asymptotic properties of hadron matter in relative four-velocity space. Fortschritte der Physik 38 (4), 261–332.Google Scholar
Barenblatt, G.I. (1952). On some unsteady motions of fluids and gases in a porous medium, Prikl. Mat. Mekh. 16 (1), 67–78.Google Scholar
Barenblatt, G.I. (1953). On the motion of suspended particles in a turbulent flow, Prikl. Mat. Mekh. 17 (3), 261–274.Google Scholar
Barenblatt, G.I. (1954). On limiting self-similar motions in the theory of unsteady filtration of gas in a porous medium and the theory of the boundary layer, Prikl. Mat. Mekh. 18 (4), 409–414.Google Scholar
Barenblatt, G.I. (1955). On the motion of suspended particles in a turbulent flow, occupying a half-space or a plane open channel of finite depth, Prikl. Mat. Mekh. 19 (1), 61–88.Google Scholar
Barenblatt, G.I. (1956). On certain problems of the theory of elasticity, which arise in the theory of the hydraulic fracture of the oil stratum. Appl. Math. Mech. (PMM) 20 (4), 475–486.Google Scholar
Barenblatt, G.I. (1959a). On the equilibrium cracks formed in brittle fracture. Appl. Math. Mech. (PMM) 23: (3), 434-44; (4), 706-21; (5), 893–900.CrossRefGoogle Scholar
Barenblatt, G.I. (1959b). The problem of thermal self-ignition. In: Gelfand, I.M.Some Problems of the Theory of Quasi-Linear Equations, Russian Mathematical Surveys Vol. 14 (2), 137–42.Google Scholar
Barenblatt, G.I. (1962). Mathematical theory of equilibrium cracks in brittle fracture. Adv. Appl. Mech. 7, 55–129.Google Scholar
Barenblatt, G.I. (1964). On certain general concepts of the mathematical theory of brittle fracture. Appl. Math. Mech. (PMM) 28 (4), 630–43.CrossRefGoogle Scholar
Barenblatt, G.I. (1977). Strong interaction of gravity waves and turbulence. Izvestiya, USSR Ac. Sci., Atmos. Oceanic Phys. 13 (8), 581–83.Google Scholar
Barenblatt, G.I. (1978a). Dynamics of turbulent spots and intrusions in a stably stratified fluid. Izvestiya, USSR Ac. Sci., Atmos. Oceanic Phys. 14 (2), 139–45.Google Scholar
Barenblatt, G.I. (1978b). Self-similarity of temperature and salinity distributions in the upper thermocline. Izvestiya, USSR Acad. Sci., Atmos. Oceanic Phys. 14 (11), 820–23.Google Scholar
Barenblatt, G.I. (1979). Similarity, Self-similarity, and Intermediate Asymptotics(1st Russian edition Gidrometeoizdat, Leningrad, 1978; 2nd Russian edition, Gidrometeoizdat, Leningrad, 1982). Plenum, New York, London.CrossRefGoogle Scholar
Barenblatt, G.I. (1983). Self-similar turbulence propagation from an instantaneous plane source. In Non-linear dynamics and turbulence, Barenblatt, G.I., Iooss, G. & Joseph, D.D. (eds.), 48–60, Pitman, Boston.Google Scholar
Barenblatt, G.I. (1987). Dimensional Analysis, Gordon and Breach, New York, London.Google Scholar
Barenblatt, G.I. (1991). On the scaling laws (incomplete self-similarity with respect to Reynolds number) for the developed turbulent flows in tubes. C.R. Acad. Sci. Paris, 313, Sér. II, 107–12.Google Scholar
Barenblatt, G.I. (1993a). Scaling laws for fully developed turbulent shear flows. Part 1. Basic hypotheses and analysis. J. Fluid Mech. 248, 513–20.Google Scholar
Barenblatt, G.I. (1993b). Intermediate asymptotics, scaling laws and renormalization group in continuum mechanics. Meccanica 28, 177–83.CrossRefGoogle Scholar
Barenblatt, G.I. (1993c). Some general aspects of fracture mechanics. In Modelling of Defects and Fracture Mechanics, Herrmann, G. (ed.), pp. 29–50. Springer-Verlag, Vienna, New York.Google Scholar
Barenblatt, G.I. (1994). Scaling Phenomena in Fluid Mechanics. Cambridge University Press.Google Scholar
Barenblatt, G.I. & Botvina, L.R. (1981). Incomplete self-similarity of fatigue in the linear range of crack growth. Fatigue of Engineering Materials and Structures 3, 193–212.Google Scholar
Barenblatt, G.I. & Botvina, L.R. (1982). A note concerning power-type constitutive equations of deformation and fracture of solids. Int. J. Eng. Sci., 20 (2), 187–91.CrossRefGoogle Scholar
Barenblatt, G.I. & Botvina, L.R. (1983). The self-similarity of fatigue fracture. The damage accumulation. Izvestiya, USSR Ac. Sci., Mech. Solids 44, 161–5.Google Scholar
Barenblatt, G.I. & Botvina, L.R. (1986). Similarity methods in mechanics and physics of fracture. Physical and Chemical Mechanics of Materials (1), 57–62.Google Scholar
Barenblatt, G.I. & Botvina, L.R. (1993). Self-oscillatory modes of fatigue fracture and the formation of self-similar structures at the fracture surface. Proc. Roy. Soc. London A442, 489–94.Google Scholar
Barenblatt, G.I. & Christianovich, S.A. (1955). On the failure of the roof in mine-workings. Izvestiya, USSR Ac. Sci., Techn. Sci. 11, 73–86.Google Scholar
Barenblatt, G.I., Entov, V.M. & Ryzhik, V.M. (1990). Theory of Fluid Flows Through Natural Rocks. Kluwer Academic Publishers, Dordrecht, Boston, London.CrossRefGoogle Scholar
Barenblatt, G.I., Galerkina, N.L. & Lebedev, I.A. (1992). Mathematical model of lower quasi-homogeneous oceanic layer: general concepts and sealing-off model. Izvestiya, Russian Ac. Sci., Atmos. Oceanic Phys. 28 (1), 68–74.Google Scholar
Barenblatt, G.I., Galerkina, N.L. & Lebedev, I.A. (1993). Mathematical model of lower quasi-homogeneous oceanic layer: effects of temperature and salinity stratification and tidal oscillations. Izvestiya, Russian Ac. Sci., Atmos. Oceanic Phys. 29 (4), 537–42.Google Scholar
Barenblatt, G.I., Galerkina, N.L. & Luneva, M.V. (1987). Evolution of turbulent burst. Inzhenerno-Fizichesky Zh. (Zh. Eng. Phys.) 53, 733–40.Google Scholar
Barenblatt, G.I. & Gavrilov, A.A. (1974). On the theory of self-similar degeneracy of homogeneous isotropic turbulence. Sov. Phys. JETP 38 (2), 399–402.Google Scholar
Barenblatt, G.I. & Goldenfeld, N.D. (1995). Does fully developed turbulence exist? Reynolds number independence versus asymptotic covariance. Phys. Fluids 7 (12), 3078–3082.CrossRefGoogle Scholar
Barenblatt, G.I. & Golitsyn, G.S. (1974). Local structure of mature dust storms. J. Atmos. Sci. 31, 1917–33.2.0.CO;2>CrossRefGoogle Scholar
Barenblatt, G.I., Guirguis, R.H., Kamel, M.M., Kuhl, A.L., Oppenheim, A.K. & Zeldovich, Ya.B. (1980). Self-similar explosion waves of variable energy at the front. J. Fluid Mech. 99 (4), 811–58.CrossRefGoogle Scholar
Barenblatt, G.I. & Krylov, A.P. (1955). On elasto-plastic regime of filtration. Izvestiya, USSR Ac. Sci., Tech. Sci. 2, 14–26.Google Scholar
Barenblatt, G.I. & Monin, A.S. (1976). Similarity Laws for Stratified Turbulent Shear Flows. Report of the Fourth All-Union Congress on Theoretical and Applied Mechanics, 41, Naukova Dumka. Kiev.Google Scholar
Barenblatt, G.I. & Monin, A.S. (1979a). Similarity laws for turbulent stratified shear flows. Arch. Rat. Mech. Anal. 70 (4), 307–17.CrossRefGoogle Scholar
Barenblatt, G.I. & Monin, A.S. (1979b). On a plausible mechanism of the phenomenon of discoidal formations in the atmosphere. Doklady, USSR Ac. Sci., 246 (4) 834–837.Google Scholar
Barenblatt, G.I. & Monin, A.S. (1983). Similarity principles for the biology of pelagic animals. Proc. Natl. Acad. Sci. USA 80 (6), 3540–42.CrossRefGoogle ScholarPubMed
Barenblatt, G.I. & Prostokishin, V.M. (1993). Scaling laws for fully developed turbulent shear flows. Part 2. Processing of experimental data. J. Fluid Mech. 248, 521–9.Google Scholar
Barenblatt, G.I. & Sivashinsky, G.I. (1969). Self-similar solutions of the second kind in nonlinear filtration. Appl. Math. Mech. (PMM) 33 (5), 836–45.CrossRefGoogle Scholar
Barenblatt, G.I. & Sivashinsky, G.I. (1970). Self-similar solutions of the second kind in the problem of propagation of intense shock waves. Appl. Math. Mech. (PMM) 34 (4), 655–62.CrossRefGoogle Scholar
Barenblatt, G.I. & Vishik, M.I. (1956). On the finite speed of propagation in the problems of unsteady filtration of fluid and gas in a porous medium. Appl. Math. Mech. (PMM) 20 (4), 411–17.Google Scholar
Barenblatt, G.I. & Zeldovich, Ya.B. (1957a). On the dipole-type solution in the problem of a polytropic gas flow in a porous medium. Appl. Math. Mech. (PMM), 21 (5), 718–20.Google Scholar
Barenblatt, G.I. & Zeldovich, Ya.B. (1957b). On the stability of flame propagation. Appl. Math. Mech. (PMM) 21 (6), 856–9.Google Scholar
Barenblatt, G.I. & Zeldovich, Ya.B. (1971). Intermediate asymptotics in mathematical physics. Russian Math. Surveys 26 (2), 45–61.CrossRefGoogle Scholar
Barenblatt, G.I. & Zeldovich, Ya.B. (1972). Self-similar solutions as intermediate asymptotics. Ann. Rev. Fluid Mech. 4, 285–312.CrossRefGoogle Scholar
Batchelor, G.K. (1967). An Introduction to Fluid Dynamics. Cambridge University Press.Google Scholar
Batchelor, G.K.Linden, P.F. (1992). Discussion at the Fluid Mechanics Seminar, DAMTP, University of Cambridge.
Bechert, K. (1941). Differentialgleichungen der Wellenausbreitung in Gasen. Ann. Phys. 39 (5), 357–72.Google Scholar
Belyaev, V.S. & Gesentzwei, A.N. (1978). Shear instabilities of internal waves in the ocean. Izvestiya, USSR Ac. Sci., Atmos. Oceanic Phys. 14 (6), 459–63.Google Scholar
Belyaev, V.S., Losovatsky, I.D. & Ozmidov, R.V. (1975). Relationships between small-scale turbulence parameters and local stratification conditions in the ocean. Izvestiya, USSR Ac. Sci., Atmos. Oceanic Phys. 11 (7), 448–52.Google Scholar
Benbow, J.J. (1960). Cone cracks in fused silica. Proc. Phys. Soc. B75, 697–99.Google Scholar
Benilov, A.Yu. (1973). Generation of ocean turbulence by surface waves. Izvestiya, USSR Ac. Sci., Atmos. Oceanic Phys. 9 (3), 160–4.Google Scholar
Beretta, E., Bertsch, M. & Dal Passo, R. (1995). Non-negative solutions of a fourth-order nonlinear degenerate parabolic equation. Arch. Rat. Mech. Anal. 129 (2), 175–200.CrossRefGoogle Scholar
Bernis, F. & Friedman, A. (1990). Higher order nonlinear degenerate parabolic equations. J. Diff. Equations 83 (1), 179–206.CrossRefGoogle Scholar
Bernis, F., Peletier, L.A. & Williams, S.M. (1992). Source type solutions of a fourth order nonlinear degenerate parabolic equation. Nonlinear Anal., Theory, Meth. Applic. 18 (3), 217–34.Google Scholar
Bertozzi, A.L., Brenner, M.P., Dupont, T.F. & Kadanoff, L.P. (1993). Singularities and similarities in Interface Flows. Preprint, Ryerson Laboratory, University of Chicago.
Bertozzi, A.L. & Pugh, M. (1995). The lubrication approximation for thin viscous films: regularity and long time behavour of weak solutions. Comm. Pure Appl. Math, (in press).Google Scholar
Bertsch, M., Dal Passo, R. & Kersner, R. (1994). The evolution of turbulent bursts: the b – ε model. Euro. J. Appl. Math. 5 (4), 537–557.CrossRefGoogle Scholar
Birkhoff, G. (1960). Hydrodynamics, a Study in Logic, Fact, and Similitude, 2nd edition. Princeton University Press.Google Scholar
Bluman, G.W. & Cole, J.D. (1974). Similarity Methods for Differential Equations, Springer-Verlag, New York, Heidelberg, Berlin.CrossRefGoogle Scholar
Boatto, S., Kadanoff, L.P. & Olla, P. (1993). Travelling wave solutions to thin film equations. Preprint, Ryerson Laboratory, University of Chicago.
Bogolyubov, N.N. & Shirkov, D.V. (1955). On the renormalization group in quantum electrodynamics. Doklady, USSR Ac. Sci., 103 (2), 203–6.Google Scholar
Bogolubov, N.N. & Shirkov, D.V. (1959). Introduction to the Theory of Quantized Fields. Wiley Interscience, New York, London.Google Scholar
Bose, E. & Bose, M. (1911). Über die Turbulenzreibung verschiedener Flüssigkeiten. Physikalische Zeitschrift 12 (4), 126–35.Google Scholar
Bose, E. & Rauert, D. (1909). Experimentalbeitrag zur Kenntnis der turbulenten Flüssigkeitsreibung. Physikalische Zeitschrift 10 (12), 406–9.Google Scholar
Botvina, L.R. (1989). Kinetics of Fracture of Structural Materials. Nauka, Moscow.Google Scholar
Brailovsky, I. & Sivashinsky, G.I. (1994). Oscillatory propagation of reaction waves sustained by external sources of energy (to appear).
Bricmont, J. & Kupiainen, A. (1992). Renormalization group and the Ginzburg-Landau equation. Comm. Math. Phys. 150, 193–208.CrossRefGoogle Scholar
Bridgman, P.W. (1931). Dimensional Analysis. Yale University Press, New Haven.Google Scholar
Brushlinsky, K.V. & Kazhdan, Ya.M. (1963). On auto-models in the solution of certain problems of gas dynamics. Russian Math. Surveys 18 (2), 1–22.Google Scholar
Budiansky, B. & Carrier, G.F. (1973). The pointless wedge. SI AM J. Appl. Math. 25 (3), 378–87.CrossRefGoogle Scholar
Bui, H.D. (1977). Mécanique de la Rupture Fragile. Masson, Paris.Google Scholar
Cane, B.J. & Greenwood, G.W. (1975). The nucleation and growth of cavities in iron during deformation at elevated temperatures. Metal Sci. 9 (2), 55–60.CrossRefGoogle Scholar
Carothers, S.D. (1912). Plane strain in a wedge. Proc. Roy. Soc. Edinburgh 23, 292–306.Google Scholar
Carrier, G.F. & Pearson, C.E. (1976). Partial Differential Equations, Theory and Technique. Academic Press, New York, San Francisco, London.Google Scholar
Carslaw, H.W. & Jaeger, J.C. (1960). Conduction of Heat in Solids, 2nd edition. Clarendon, Oxford.Google Scholar
Castaing, B., Gagne, Y. & Hopfinger, E.J. (1990). Velocity probability density functions of high Reynolds number turbulence. Physica D. 46 177–200.CrossRefGoogle Scholar
Chen, L.-Y. & Goldenfeld, N. (1992). Renormalization-group theory for the propagation of a turbulent burst. Phys. Rev. A45 (8), 5572–4.Google Scholar
Chen, L.-Y., Goldenfeld, N. & Oono, Y. (1991). Renormalization-group theory for the modified porous-medium equation. Phys. Rev. A44 (10), 6544–50.Google Scholar
Chen, L.-Y., Goldenfeld, N. & Oono, Y. (1994). Renormalization group theory for global asymptotic analysis. Phys. Rev. Lett, (submitted).Google ScholarPubMed
Chernyi, G.G. (1961). Introduction to Hypersonic Flow (trans. R.F. Probstein). Academic Press, New York.Google Scholar
Cole, J.D. (1968). Perturbation Methods in Applied Mathematics. Blaisdell, Toronto, London.Google Scholar
Cole, J.D. & Wagner, B.A. (1995) On self-similar solutions of Barenblatt's non-linear filtration equation. Euro. J. Appl. Math (in press).Google Scholar
Collins, R.E. (1961). Flow of Fluids through Porous Materials. Reinhold, New York.Google Scholar
Corino, E.R. & Brodkey, R.S. (1969). A visual investigation of the wall region in turbulent flow. J. Fluid Mech. 37 (1), 1–30.CrossRefGoogle Scholar
Daniell, P.J. (1930). The theory of flame motion. Proc. Roy. Soc. A126, 393–402.Google Scholar
Dempsey, J.P. (1981). The wedge subjected to tractions: a paradox resolved. J. Elasticity 11, 1–10.CrossRefGoogle Scholar
Diez, J.A., Gratton, R. & Gratton, J. (1992). Self-similar solution of the second kind for a convergent viscous gravity current. Phys. Fluids A4 (6), 1148–55.Google Scholar
Drazin, P.G. & Johnson, R.S. (1989). Solitons: An Introduction. Cambridge University Press.CrossRefGoogle Scholar
Dryden, H.L. (1943). A review of the statistical theory of turbulence. Quart. J. Appl. Math. 1, 7–42.Google Scholar
Dundurs, J. & Markenscoff, X. (1989). The Sternberg-Koifer conclusion and other anomalies of the concentrated couple. ASME J. Appl. Mech. 56, 240–5.CrossRefGoogle Scholar
Dussan, V., E.B. & Davis, S.H. (1986). Stability in systems with moving contact lines. J. Fluid Mech. 173, 115–30.CrossRefGoogle Scholar
Dussan, V., E.B., Ramé, E. & Garoff, S. (1991). On identifying the appropriate boundary conditions at a moving contact line: an experimental investigation. J. Fluid Mech. 230, 97–116.CrossRefGoogle Scholar
Efimov, S.S. & Tsarenko, V.M. (1980). Self-similarity of the temperature distribution in the upper thermocline. Izvestiya, USSR Ac. Sci., Atmos. Oceanic Phys. 16 (6), 429–33.Google Scholar
Eilenberger, G. (1981). Solitons. Mathematical Methods for Physicists. Springer-Verlag, Berlin, Heidelberg, New York.Google Scholar
Einstein, H.A. & Ning, Chen (1955). Effects of Heavy Sediment Concentration Near the Bed on the Velocity and Sediment Distribution. University of California MRD Series Report No. 8.Google Scholar
Entov, V.M. (1994). Private communication.
Fedorov, K.N. (1976). Fine Thermohaline Structure of Ocean Water. Gidrometeoizdat, Leningrad.Google Scholar
Fisher, R.A. (1937). The wave of advance of advantageous genes. Ann. Eugenics, 7, 355–69.CrossRefGoogle Scholar
Fordy, A.P. (ed.) (1990). Soliton Theory: A Survey of Results. Manchester University Press, Manchester, New York.
Forsyth, P.J.E. (1976). Some observations and measurements on mixed fatigue tensile crack growth in aluminium alloys. Scripta Metall. 10, 383–6.CrossRefGoogle Scholar
Fourier, J. (1822). Théorie analytique de la chaleur. Firmin Didot, Paris.Google Scholar
Frankel, M., Roytburd, V. & Sivashinsky, G. (1994). A sequence of period doubling and chaotic pulsations in a free-boundary problem modelling thermal instabilities. SI AM J. Appl. Math, (to appear).Google Scholar
Gad-el-Hak, M. & Corrsin, S. (1974). Measurements of the nearly isotropic turbulence behind a uniform jet grid. J. Fluid Mech. 62 (1), 115–43.CrossRefGoogle Scholar
Gardner, C.S.J., Greene, J.M., Kruskal, M.D. & Miura, R.M. (1967). A method for solving the Korteweg-de-Vries equation. Phys. Rev. Lett. 19, 1095–97.CrossRefGoogle Scholar
Gell-Mann, M. & Low, F.E. (1954). Quantum electrodynamics at small distances. Phys. Rev. 95, 1300–12.CrossRefGoogle Scholar
Germain, P. (1973). Méthodes asymptotiques en mécanique des fluids. In Dynamics of Fluids, R., Balian & J.L., Peube (eds.), 7–147. Gordon and Breach, London, etc.Google Scholar
Germain, P. (1986a). Mécanique, tome I. Ecole Polytechnique, Ellipses, Paris.
Germain, P. (1986b). Mécanique, tome II. Ecole Polytechnique, Ellipses, Paris.
Ginzburg, I.S., Entov, V.M. & Theodorovich, E.V. (1992). Renormalization group method for the problem of convective diffusion with irreversible sorption. Appl. Math. Mech. (PMM) 56 (1), 59–96.CrossRefGoogle Scholar
Goldenfeld, N. (1989). The approach to equilibrium: scaling and the renormalization group. Invited lecture at the Conference on Non-linear Phenomena, Moscow, USSR Ac. Sci., 19-22 September.
Goldenfeld, N. (1992). Lectures on Phase Transitions and the Renormalization Group. Addison-Wesley.Google Scholar
Goldenfeld, N., Martin, O. & Oono, Y. (1989). Intermediate asymptotics and renormalization group theory. J. Scient. Comput. 4, 355–72.CrossRefGoogle Scholar
Goldenfeld, N., Martin, O. & Oono, Y. (1991). Asymptotics of partial differential equations and the renormalization group. In Proc. NATO Advanced Research Workshop on Asymptotics Beyond all Orders, La Jolla, S., Tanvera (ed.). Plenum Press.Google Scholar
Goldenfeld, N., Martin, O., Oono, Y. & Liu, F. (1990). Anomalous dimensions and the renormalization group in a non-linear diffusion process. Phys. Rev. Lett. 65 (12), 1361–64.Google Scholar
Goldenfeld, N. & Oono, Y. (1991). Renormalization group theory for two problems in linear continuum mechanics. Physica A. 177, 213–19.CrossRefGoogle Scholar
Goldstein, S. (1939). A note on the boundary layer equations. Proc. Camb. Phil. Soc. 35, 338–40.CrossRefGoogle Scholar
Goldstein, R.V. & Vainshelbaum, V.M. (1978). Material scale length as a measure of fracture toughness in fracture mechanics of plastic materials. Int. J. Fracture, 14 (2), 185–201.Google Scholar
Golitsyn, G.S. (1973). Introduction to the Dynamics of Planetary Atmospheres. Gidrometeoizdat, Leningrad.Google Scholar
Gossard, E.E. & Hooke, W.H. (1975). Waves in the Atmosphere. Elsevier, New York.Google Scholar
Grebenev, V.N. (1992). The dynamic system that arises in the problem of the evolution of a turbulent layer of a homogeneous fluid. Comput. Math, and Math. Phys. 32 (1), 103–13.Google Scholar
Griffith, A.A. (1920). The phenomenon of rupture and flow in solids. Phil. Trans. Roy. Soc. London A221, 163–98.Google Scholar
Guderley, K.G. (1942). Starke kugelige und zylindrische Verdichtungsstösse in der Nähe des Kugelmittelpunktes bzw. der Zylinderachse. Luftfahrtforschung 19 (9), 302–12.Google Scholar
Häfele, W. (1955). Zur analytischen Behandlung ebener, starker, instationarer Stoss-wellen. Z. Naturforschung 10a (9/10), 693–7.Google Scholar
Hahn, H.G. (1976). Bruchmechanik. Teubner, Stuttgart.Google Scholar
Hain, K. & Hörner, S.V. (1954). Instationare starke Stossfronten. Z. Naturforschung 9a (12), 993–1004.Google Scholar
Hanjalic, K. & Launder, B.E. (1972). A Reynolds stress model of turbulence, and its application to thin shear flows. J. Fluid Mech. 52, 609–38.CrossRefGoogle Scholar
Harmon, L.D. (1973). Recognition of faces. Scientific American 229 (5), 70–82.CrossRefGoogle ScholarPubMed
Hastings, S.P. & Peletier, L.A. (1992). On a self-similar solution for the decay of turbulent bursts. Euro. J. Appl. Math. 3, 319–41.CrossRefGoogle Scholar
Heiser, F.A. & Mortimer, W. (1972). Effects of thickness and orientation on fatigue crack growth rate in 4340 steel. Met. Trans. 3, 2119–23.CrossRefGoogle Scholar
Hill, R. (1992). Similarity analysis of creep indentation tests. Proc. Roy. Soc. London A436, 617–30.Google Scholar
Hill, R., Storåkers, B. & Zdunek, A.B. (1989). A theoretical study of the Brinell hardness test. Proc. Roy. Soc. London A423, 301–30.Google Scholar
Hinch, E.J. (1991). Perturbation Methods. Cambridge University Press.CrossRefGoogle Scholar
Hinze, J.O. (1959). Turbulence. An Introduction to its Mechanism and Theory. McGraw-Hill, New York, Toronto, London.Google Scholar
Hinze, J.O. (1962). Turbulent pipe-flow, in Mècanique de la turbulence, 63–76. Edition du Centre Nat. Rech. Sci. Paris.Google Scholar
Hulshof, J. (1993). Self-similar solutions of the κ – ε model for turbulence. Report No. W93-11, Mathematical Institute, University of Leiden.
Hulshof, J. & Vázquez, J.L. (1993). Self-similar solutions of the second kind for the modified porous medium equation. Report No. W93-04, Mathematical Institute, University of Leiden.
Huppert, H.E. (1982). The propagation of two-dimensional and axisymmetric viscous gravity currents over a rigid horizontal surface. J. Fluid Mech. 121, 43–58.CrossRefGoogle Scholar
Inglis, C.E. (1922). Some special cases of two-dimensional stress and strain. Thins. Inst. Naval Arch. 64, 253–8.Google Scholar
Irwin, G.R. (1949). Fracture dynamics, in Fracturing of Metals, 147–66. ASM, Cleveland, OH.Google Scholar
Irwin, G.R. (1957). Analysis of stresses and strains near the end of a crack traversing a plate. J. Appl. Mech. 24, 361–4.Google Scholar
Irwin, G.R. (1958). Fracture, in Handbuch der Physik, Bd VI, pp. 551–90. Springer, Berlin.Google Scholar
Irwin, G.R. (1960). Fracture mode transition for a crack traversing a plate. Trans. ASME, Ser. D 82, 417–25.Google Scholar
Jeffrey, A. & Kakutani, T. (1972). Weak non-linear dispersive waves: a discussion centered around the Korteweg-de-Vries equation. SIAM Review 14 (4), 582–643.CrossRefGoogle Scholar
Johnson, K.L. (1985). Contact Mechanics. Cambridge University Press.CrossRefGoogle Scholar
Kadanoff, L.P. (1966). Scaling laws for Ising model nearTc. Physics 2 (6), 263–72.Google Scholar
Kadanoff, L.P., Götze, W., Hamblen, D., Hecht, R., Lewis, E.A.S., Paleiauskas, V.V.I., Rayl, M., Swift, J., Aspnes, D. & Kane, J. (1967). Static phenomena near critical points: theory and experiment. Rev. Mod. Phys. 39 (2), 395–431.CrossRefGoogle Scholar
Kalashnikov, A.S. (1987). Some problems of qualitative theory of non-linear second-order parabolic equations. Russian Math. Surveys 42, 169–222.CrossRefGoogle Scholar
Kamenomostskaya, S.L. (Kamin) (1957). On a problem of the theory of filtration. Doklady, USSR Ac. Sci., 116 (1), 18–20.Google Scholar
Kamin, S., Peletier, L.A. & Vázquez, J.-L. (1991). On the Barenblatt equation of elasto-plastic filtration. Indiana Univ. Math. J. 40 (4), 1333–62.CrossRefGoogle Scholar
Kamin, S. & Vázquez, J.L. (1992). The propagation of turbulent bursts. Euro. J. Appl. Math. 3, 263–72.CrossRefGoogle Scholar
Kanel', Ya.I. (1962). On the stabilization of solutions of Cauchy problems met within the theory of combustion. Matem. Sb. 59 (101), 245–88.Google Scholar
Kao, T.W. (1976). Principal stage of wake collapse in a stratified fluid: two-dimensional theory. Phys. Fluids 19 (8), 1071–4.CrossRefGoogle Scholar
Kapitza, S.P., (1966). A natural system of units in classical electrodynamics and electronics. Sov. Phys. Uspekhi 9, 184.CrossRefGoogle Scholar
Karpman, V.I. (1975). Non-linear Waves in Dispersive Media. Pergamon, Oxford.
Keller, L.V. & Friedmann, A.A. (1924). Differentialgleichungen für die turbulente Bewegung einer kompressiblen Flüssigkeit. In Proc. First Int. Congress Appl. Mech., pp. 395–405. J. Waltman Jr, Delft.Google Scholar
Kerchman, V.I. (1971). On self-similar solutions of the second kind in the theory of unsteady filtration. Appl. Math. Mech. (PMM) 35 (1), 158–62.CrossRefGoogle Scholar
Kestin, J. & Richardson, P.D. (1963). Heat transfer across turbulent incompressible boundary layers. Int. J. Heat. Mass Transfer 6 (2), 147–89.CrossRefGoogle Scholar
Kevorkian, J. & Cole, J.D. (1980). Perturbation Methods in Applied Mathematics. Springer-Verlag, New York, Heidelberg, Berlin.Google Scholar
Kim, H.T., Kline, S.J. & Reynolds, W.C. (1971). The production of turbulence near a smooth wall in a turbulent boundary layer. J. Fluid Mech. 50 (1), 133–60.CrossRefGoogle Scholar
Kistler, A.L. & Vrebalovich, T. (1966). Grid turbulence at large Reynolds numbers. J. Fluid Mech. 26 (1), 37–47.CrossRefGoogle Scholar
Kitaigorodsky, S.A. & Miropolsky, Yu.Z. (1970). Izvestiya, USSR Ac. Set, Atmos. Oceanic Phys. 6 (2), 97–102.
Kline, S.J., Reynolds, W.C., Schraub, F.A. & Runstadler, P.W. (1967). The structure of turbulent boundary layers. J. Fluid Mech. 30 (4), 741–74.CrossRefGoogle Scholar
Kochin, N.E., Kibel', I.A. & Roze, N.V. (1964). Theoretical Hydromechanics, Vol. 1. Interscience, New York. Vol. 2 available from ASTIA as AD129210.
Kochina, I.N., Mikhailov, N.N. & Filinov, M.V. (1983). Groundwater mound damping. Int. J. Eng. Sci. 21 (4), 413–21.CrossRefGoogle Scholar
Kolmogorov, A.N. (1941). The local structure of turbulence in incompressible fluids at very high Reynolds numbers. Doklady, USSR Ac. Sci. 30 (4), 299–303.Google Scholar
Kolmogorov, A.N. (1942). The equations of turbulent motion of incompressible fluids. Izvestiya, USSR Ac. Sci., Phys. 6 (1-2), 56–8.Google Scholar
Kolmogorov, A.N. (1954). On a new variant of the gravitational theory of motion of suspended sediment. Vestn. MGU 3, 41–5.Google Scholar
Kolmogorov, A.N. (1962). A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number. J. Fluid Mech. 13 (1), 82–5.CrossRefGoogle Scholar
Kolmogorov, A.N., Petrovsky, I.G. & Piskunov, N.S. (1937). Investigation of the diffusion equation connected with an increasing amount of matter and its application to a biological problem. Bull. MGU Al (6), 1–26.Google Scholar
Korotaev, G.K. & Panteleev, N.A. (1977). Experimental investigations of hydrody-namic instability in the oceans. Oceanology USSR 17 (6), 914–53.Google Scholar
Kovasznay, L.S.G., Kilens, V. & Blackwelder, R.F. (1970). Large-scale motion in the intermittent region of a turbulent boundary layer. J. Fluid Mech. 41 (2), 283–325.CrossRefGoogle Scholar
Kulikovsky, A.G. & Lyubimov, G.A. (1965). Magneto-hydrodynamics. Addison-Wesley, Reading MA.Google Scholar
Lagerstrom, P.A. & Casten, R.J. (1972). Some basic concepts underlying singular perturbation techniques. SIAM Review 14 (1), 63–120.CrossRefGoogle Scholar
Landau, L.D. & Lifshitz, E.M. (1986). Theory of Elasticity, 2nd edition. Pergamon Press, London.Google Scholar
Landau, L.D. & Lifshitz, E.M. (1987). Fluid Mechanics, 2nd edition. Pergamon Press, London.Google Scholar
Launder, B.E. & Spalding, D.B. (1972). Mathematical Models of Turbulence. Academic Press, London.Google Scholar
Launder, B.E., Morse, A.P., Rodi, W. & Spalding, D.B. (1972). Prediction of free shear flows – a comparison of six turbulence models. NASA Report SP 321.
Launder, B.E. & Spalding, D.B. (1974). The numerical computation of turbulent flows. Comp. Math. Appl. Mech. Eng. 3, 269–89.CrossRefGoogle Scholar
Lax, P.D. (1968). Integrals of nonlinear equations of evolution and solitary waves. Comm. Pure Appl. Math. 21 (5), 467–90.CrossRefGoogle Scholar
Liebowitz, H. (ed.) (1968a). Fracture. An Advanced Treatise, Vol. I. Academic Press, New York, London.
Liebowitz, H. (ed). (1968b). Fracture. An Advanced Treatise, Vol II. Academic Press, New York, London.
Lighthill, J. (1978). Waves in Fluids. Cambridge University Press.Google Scholar
Linden, P.F. (1975). The deepening of a mixed layer in a stratified fluid. J. Fluid Mech. 71 (2), 385–405.CrossRefGoogle Scholar
Ling, S.C. & Huang, T.T. (1970). Decay of weak turbulence. Phys. Fluids 13 (12), 2912–20.CrossRefGoogle Scholar
Ling, S.C. & Wan, C.A. (1972). Decay of isotropic turbulence generated by a mechanically agitated grid. Phys. Fluids 15 (8), 1363–9.CrossRefGoogle Scholar
Loitsiansky, L.G. (1939). Some basic laws of isotropic turbulent flow. Proc. Central Aero-Hydrodynamic Institute, Moscow 440, 3–23. (In Russian.) Translated as Loitsiansky, L.G. (1945). Some basic laws of isotropic turbulent flow. NACA Technical Memo. No. 1079.Google Scholar
Ma, S.-K. (1976). Modern Theory of Critical Phenomena. Benjamin/Cummings, Reading MA.Google Scholar
Mandelbrot, B. (1975). Les objects fractals: forme, hasard et dimension. Flammarion, Paris.Google Scholar
Mandelbrot, B. (1977). Fractals, Form, Chance and Dimension. W.H. Freeman and Co., San Francisco.Google Scholar
Mandelbrot, B. (1982). The Fractal Geometry of Nature. W.H. Freeman and Co., San Francisco.Google Scholar
Maxworthy, T. (1973). Experimental and theoretical studies of horizontal jets in a stratified fluid. In Proc. Int. Symposium on Stratified Flows, Novosibirsk, 1972, 611–18. Am. Soc. Civ. Eng., New York.Google Scholar
McMahon, T.A. (1971). Rowing: a similarity analysis. Science 173, 23 July 1971, 349–51.CrossRefGoogle ScholarPubMed
Meyer, F. (1955). Zur Darstellung starker Stossfronten durch Homologie-Losungen. Z. Naturforschung 10a (9/10), 693–7.Google Scholar
Migdal, A.B. (1977). Qualitative Methods in Quantum Theory. W.A. Benjamin, Reading, MA.Google Scholar
Miles, J.W. (1961). On the stability of heterogeneous shear flow. J. Fluid Mech. 10 (4), 496–508.CrossRefGoogle Scholar
Miles, J.W. (1963). On the stability of heterogeneous shear flow. J. Fluid Mech. 16 (2), 209–27.CrossRefGoogle Scholar
Millionshchikov, M.D. (1939). Decay of homogeneous turbulence in a viscous incompressible fluid. Doklady, USSR Ac. Sci. 22 (5), 236–40.Google Scholar
Moffatt, H.K. (1964). Viscous and resistive eddies near a sharp corner. J. Fluid Mech. 18 (1), 1–18.CrossRefGoogle Scholar
Moffatt, H.K. & Duffy, B.R. (1980). Local similarity solutions and their limitations. J. Fluid Mech. 96 (2), 299–313.CrossRefGoogle Scholar
Monin, A.S. (1950). Turbulence in the atmospheric surface layer. Coll. Sci. Inform. Hydromet. Science USSR, Moscow (1), 13–27.Google Scholar
Monin, A.S. & Obukhov, A.M. (1953). Dimensionless characteristics of turbulence in the surface layer of the atmosphere. Doklady, USSR Ac. Sci. 93 (2), 223–6.Google Scholar
Monin, A.S. & Obukhov, A.M. (1954). Basic relationships for turbulent mixing in the surface layer of the atmosphere. Proc. Inst. Theor. Geophys., USSR Ac. Sci. 24 (151), 163–87.Google Scholar
Monin, A.S. & Ozmidov, R.V. (1981). Oceanic Turbulence. Gidrometeoizdat, Leningrad.Google Scholar
Monin, A.S. & Yaglom, A.M. (1971). Statistical Fluid Mechanics. Mechanics of Turbulence, Vol. 1. MIT Press, Cambridge, London.Google Scholar
Monin, A.S. & Yaglom, A.M. (1975), Statistical Fluid Mechanics. Mechanics of Turbulence, Vol. 2. MIT Press, Cambridge, London.Google Scholar
Monin, A.S. & Yaglom, A.M. (1992). Statistical Fluid Mechanics: Theory of Turbulence, Vol. 1, 2nd Russian edition. Gidrometeoizdat, St Petersburg.Google Scholar
Munk, W. (1966). Abyssal recipes. Deep Sea Research 13, 707–30.Google Scholar
Murray, J.D. (1977). Lectures on Non-linear Differential Equation Models in Biology. Clarendon Press, Oxford.Google Scholar
Muskhelishvili, N.I. (1963). Some Basic Problems of the Mathematical Theory of Elasticity, 2nd English edition. P. Noordhoff, Groningen.Google Scholar
Muskhelishvili, N.I. (1966). Some Basic Problems of Mathematical Theory of Elasticity, 5th Russian edition. Nauka, Moscow.Google Scholar
Nigmatulin, R.I. (1965). A plane strong explosion on a boundary of two ideal, calor-ically perfect gases. Bulletin MGU, Ser. Matem. Mekh. 1, 83–7.Google Scholar
Nikuradse, J. (1932). Gesetzmässigkeiten der turbulenten Strömung in glatten Röhren. VDI Forschungscheft No. 356.Google Scholar
Nikolaeva, G.G. et al. (1975). Metabolism rate and size-weight characteristics of theRhithropanopeus harrisii tredantatus crab from the Caspian Sea. Oceanology USSR 15, 99–100.Google Scholar
Norton, F.H. (1929). Creep of Steel at High Temperatures. McGraw Hill, New York.Google Scholar
Novikov, S., Manakov, S.V., Pitaevsky, L.P. & Zakharov, V.E. (1984). Theory of Solitions: The Inverse Scattering Method. Consultants Bureau, New York, London.Google Scholar
Nowell, A.R.M. & Hollister, C.D. (1985). The objectives and rationale of HEBBLE. Marine Geology 66, 1–12.CrossRefGoogle Scholar
Obukhov, A.M. (1941). On the distribution of energy in the spectrum of a turbulent flow. Doklady, USSR Ac. Sci. 32 (1), 22–4.Google Scholar
Obukhov, A.M. (1946). Turbulence in thermally inhomogeneous atmosphere. Proc. Inst. Theor. Geophys., USSR Ac. Sci. 1, 95–115.Google Scholar
Obukhov, A.M. (1962). Some specific features of atmospheric turbulence. J. Fluid Mech. 13 (1), 77–81.Google Scholar
Offen, G.R. & Kline, S.J. (1975). A proposed model of the bursting process in turbulent boundary layers. J. Fluid Mech. 70 (2), 209–28.CrossRefGoogle Scholar
Oleinik, O.A. (1957). Discontinuous solutions of nonlinear differential equations. Uspekhi Mat. Nauk 12, 3(75), 3–73.Google Scholar
Oleynik, O.A., Kalashnikov, A.S. & Chzhou, Yui-lin (1958). The Cauchy problem and boundary problems for equations of the type of unsteady filtration. Izvestiya, USSR Ac. Sci., Ser. Mat. 22, 667–704.Google Scholar
Oppenheim, A.K., Kuhl, A.C. & Kamel, M.M. (1972). On self-similar blast waves headed by the Chapman-Jouguet detonation. J. Fluid Mech. 55 (2), 257–70.CrossRefGoogle Scholar
Oppenheim, A.K., Kuhl, A.L., Lundstrom, E.A. & Kamel, M.M. (1971). A systematic exposition of the conservation equations for blast waves. J. Appl. Mech. 38 (4), 783–94.CrossRefGoogle Scholar
Oppenheim, A.K., Lundström, E.A., Kuhl, A.C. & Kamel, M.M. (1972). A parametric study of self-similar blast waves. J. Fluid Mech. 52 (4), 657–82.CrossRefGoogle Scholar
Orowan, E. (1949). Fracture and strength of solids. Rep. Progr. Phys. Soc. London 12, 185–232.Google Scholar
Ovsyannikov, L.V. (1978). Group Analysis of Differential Equations. Nauka, Moscow.Google Scholar
Panasyuk, V.V. (1968). Limiting Equilibrium of Brittle Bodies with Cracks. Naukova Dumka, Kiev.Google Scholar
Paquette, G.C., Chen, L.-Y., Goldenfeld, N. & Oono, Y. (1994). Structural stability and renormalization group for propagating fronts. Phys. Rev. Lett. 72, 76–9.CrossRefGoogle Scholar
Paquette, G.C. & Oono, Y. (1994). Structural stability and selection of propagation fronts in semilinear partial diffferential equations. Phys. Rev. E 49, 2368–88.CrossRefGoogle Scholar
Paris, P.C. & Erdogan, F. (1963). A critical analysis of crack propagation laws. J. Basic Eng. Trans. ASME, Ser. D. 85, 528–34.CrossRefGoogle Scholar
Parkhomenko, V.P., Popov, S.P. & Ryzhov, O.S. (1977a). On the influence of the initial velocity of particles on the unsteady axisymmetric gas motions. Uchenye Zapiski (Research Notes) TSAGI, 8 (3), 32–8.Google Scholar
Parkhomenko, V.P., Popov, S.P. & Ryzhov, O.S. (1977b). On the influence of the initial velocity of particles on the unsteady spherically symmetric gas motions. Comput. Math, and Math. Phys. 15 (5), 1325–9.Google Scholar
Parvin, M. & Williams, J.G. (1975). The effect of temperature on the fracture of polycarbonate. J. Mater. Sci. 10 (11), 1883–6.CrossRefGoogle Scholar
Patashinsky, A.Z. & Pokrovsky, V.L. (1966). On the behaviour of ordering systems near the phase transition point. J. Exp. Theor. Phys. 50 (2), 439–47.Google Scholar
Pattle, R.E. (1959). Diffusion from an instantaneous point source with a concentration-dependent coefficient. Quart. J. Mech. Appl. Math. 12, 407–9.CrossRefGoogle Scholar
Pedlosky, J. (1979). Geophysical Fluid Dynamics. Springer-Verlag, New York, Heidelberg, Berlin.CrossRefGoogle Scholar
Petrovsky, I.G. (1967). Lectures on Partial Differential Equations. Saunders, Philadelphia.Google Scholar
Phillips, O.M. (1967). The generation of clear-air turbulence by the degradation of internal waves. In Atmospheric Turbulence and the Propagation of Radio Waves, 130–8. Nauka, Moscow.Google Scholar
Phillips, O.M. (1976). Energy loss mechanisms from low-mode waves. Report on the Soviet-American Conference on Internal Waves, Novobirsk, December 1976.
Phillips, O.M. (1977). The Dynamics of the Upper Ocean, 2nd edition. Cambridge University Press, Princeton.Google Scholar
Polubarinova-Kochina, P.Ya. (1962). Theory of Groundwater Movement. Princeton University Press.Google Scholar
Prandtl, L. (1932a). Meteorologische Anwendungen der Strömungslehre. Beiträge Phys. Atmos. 19 (3), 188–202.
Prandtl, L. (1932b). Zur turbulenten Strömung in Röhren und längs Platten. Ergebn. Aerodyn. Versuchsanstalt, Göttingen B4, 18–29.
Prandtl, L. (1945). Ueber ein neues Formelsystem für die ausgebildete Turbulenz. Nach. Ges. Wiss. Gottingen, Math.-Phys. Kl, 6–18.Google Scholar
Praskovsky, A. & Oncley, S. (1994). Measurement of Kolmogorov constant and intermittency exponent at very high Reynolds numbers. Physics of Fluids 6 (9), 2886–2889.CrossRefGoogle Scholar
Prostokishin, V.M. (1994). Private communication.
Raizer, Yu.P. (1968). A high-frequency high-pressure gas flow discharge as a slow combustion process. J. Appl. Mech. Tech. Phys. 9 (3), 239–43.Google Scholar
Raizer, Yu.P. (1970). Physical foundations of the theory of cracks in brittle fracture. Soviet Phys. Uspekhi 100 (2), 329–47.Google Scholar
Raizer, Yu.P. (1977). Laser-induced Discharge Phenomena. Consultants Bureau, New York.Google Scholar
Rao, K.N., Narasimha, R. & Badri Narayanan, M.A. (1971). The bursting phenomenon in a turbulent boundary layer. J. Fluid Mech. 48 (2), 339–52.CrossRefGoogle Scholar
Reynolds, O. (1895). On the dynamical theory of incompressible viscous fluids and the determination of the criterion. Phil. Trans. Roy. Soc. London 186, 123–64.Google Scholar
Reynolds, W.C. (1976). Computation of turbulent flows. An. Rev. Fluid Mech. 8, 183–208.CrossRefGoogle Scholar
Richardson, L.F. (1922). Weather Prediction by Numerical Process. Cambridge University Press.Google Scholar
Richardson, L.F. (1961). The problem of contiguity: an appendix of statistics of deadly quarrels. General Systems Year Book 6, 139–87.Google Scholar
Roesler, F. (1956). Brittle fracture near equilibrium. Proc. Phys. Soc. B69, 981–92.Google Scholar
Rosen, J.B. (1954). Theory of laminar flame stability, I, II. J. Chem. Phys. 22 (4), 733–48.Google Scholar
Samarsky, A.A. & Sobol', I.M. (1963). Examples of numerical computation of temperature waves. Comput. Math, and Math. Phys. 3 (4), 702–16.Google Scholar
Sapunkow, Ia.G. (1967). Convergent detonation waves under Chapman-Jouguet conditions in media with variable and constant initial densities. Appl. Math. Mech. (PMM) 31 (5), 945–8.Google Scholar
Schlichting, H. (1968). Boundary Layer Theory, 6th edition. McGraw-Hill, New York.Google Scholar
Sedov, L.I. (1944). Decay of isotropic turbulent motions of an incompressible fluid. Doklady, USSR Ac. Sci. 42 (3), 121–4.Google Scholar
Sedov, L.I. (1945). On some unsteady motions of compressible fluids. Prikl. Mat. Mekh. 9 (4), 293–311.Google Scholar
Sedov, L.I. (1946). Propagation of strong shock waves. Prikl. Mat. Mekh. 10, 241–50, (Pergamon Translations, No. 1223).Google Scholar
Sedov, L.I. (1959). Similarity and Dimensional Methods in Mechanics. Academic Press, New York.Google Scholar
Sedov, L.I. (1971). A Course in Continuum Mechanics. Wolters-Noordhoff, Groningen.Google Scholar
SethuRaman, S. (1980). A case of persistent breaking of internal gravity waves in the atmospheric gravity waves in the atmospheric surface layer over the ocean. Boundary-layer Meteorology 19 (1), 67–80.CrossRefGoogle Scholar
Shchelkachev, V.N. (1959). Development of Oil-water Strata Under Elastic Drive. Gostoptekhizdat, Moscow.Google Scholar
Shkadinsky, K.G., Khaikin, B.I. & Merzhanov, A.G. (1971). Propagation of a pulsating exothermic reaction front in the condensed phase. Comb. Expl. Shock Waves 7, 15–22.Google Scholar
Shushkina, E.A., Kus'micheva, V.I. & Ostapenko, L.A. (1971). Energy equivalent of body mass, respiration, and calorific value of mysids from the Sea of Japan. Oceanology USSR 11 (6), 880–3.Google Scholar
Sobolev, S.L. (1954). On a new problem of mathematical physics. Izvestiya, USSR Ac. Sci., ser. mat. 18 (1), 3–50.Google Scholar
Sneddon, I.N. (1951). Fourier Transforms. McGraw-Hill, New York.Google Scholar
Staniukovich, K.P. (1960). Unsteady Motion of Continuous Media. Pergamon Press, New York.Google Scholar
Sternberg, E. & Koiter, W.T. (1958). The wedge under a concentrated couple: a paradox in the two-dimensional theory of elasticity. J. Appl. Mech. 25 (4), 575–81.Google Scholar
Stewart, R.W. (1951). Triple velocity correlations in isotropic turbulence. Proc. Camb. Phil. Soc. 47, 146–57.CrossRefGoogle Scholar
Stommel, H. (1958). The abyssal circulation. Deep Sea Research 5, 80–2.Google Scholar
Storåkers, B. & Larsson, P.L. (1994). On Brinell and Boussinesq indentation of creeping solids. J. Mech. Phys. Solids (in press).CrossRefGoogle Scholar
Stückelberg, E.C.G. & Peterman, A. (1953). La normalisation des constantes dans la theorie des quanta. Helvetica Physica Acta XXVI, 499–520.Google Scholar
Swift, J. (1992) Gulliver's Travels. Wordsworth Classics (seep. 124).Google Scholar
Tabor, D. (1951). Hardness of Metals. Clarendon Press, Oxford.Google Scholar
Taffanel, M. (1913). Sur la combustion des mélanges gazeux et les vitessesde réaction. C. R. Ac. Sci. Paris 157, 714–7.Google Scholar
Taffanel, M. (1914). Sur la combustion des mélanges gazeux et les vitesses de réaction. C. R. Ac. Sci. Paris 158, 42–5.Google Scholar
Taylor, G.I. (1910). The conditions necessary for discontinuous motion in gases. Proc. Roy. Soc. A84, 371–7.Google Scholar
Taylor, G.I. (1935). Statistical theory of turbulence, I-IV. Proc. Roy. Soc. A151, 421–78.Google Scholar
Taylor, G.I. (1941). The formation of a blast wave by a very intense explosion. Report RC-210, 27 June 1941, Civil Defence Research Committee.
Taylor, G.I. (1950a). The formation of a blast wave by a very intense explosion. I, Theoretical discussion. Proc. Roy. Soc. A201, 159–74.
Taylor, G.I. (1950b). The formation of a blast wave by a very intense explosion. II. The atomic explosion of 1945. Proc. Roy. Soc. A201, 175–86.
Taylor, G.I. (1963). Scientific Papers, G.K., Batchelor (ed.), Vol. 3, Aerodynamics and the Mechanics of Projectiles and Explosions. Cambridge University Press.Google Scholar
Thompson, S.M. & Turner, J.S. (1975). Mixing across an interface due to turbulence generated by an oscillating grid. J. Fluid Mech. 67 (2), 349–68.CrossRefGoogle Scholar
Ting, T.C.T. (1984). The wedge subjected to tractions: a paradox reexamined. J. Elasticity 14, 235–47.CrossRefGoogle Scholar
Townsend, A.A. (1976). Structure of Turbulent Shear Flow, 2nd edition. Cambridge University Press.Google Scholar
Turner, J.S. (1968). The influence of molecular diffusivity on turbulent entrainment across a density interface. J. Fluid Mech. 33 (4), 639–6.CrossRefGoogle Scholar
Turner, J.S. (1973). Buoyancy Effects in Fluids. Cambridge University Press.CrossRefGoogle Scholar
Turner, J.S. (1978). The temperature profile below the surface mixed layer. Ocean Modelling 11, 6–8.Google Scholar
Van den Booghaart, A. (1966). Crazing and characterisation of brittle fracture in polymers. In Proc. Conf. Phys. Basis of Yield and Fracture, Oxford University Press.Google Scholar
Van Dyke, M. (1975). Perturbation Methods in Fluid Mechanics, 2nd edition. Parabolic Press, Stanford.Google Scholar
Van Dyke, M. (1982). An Album of Fluid Motions. Parabolic Press, Stanford.Google Scholar
Vanoni, V. (1946). Transportation of suspended sediment by water. Thins. Am. Soc. Civil Eng. 111, 67–133.Google Scholar
Vavakin, A.S. & Salganik, R.L. (1975). On experimental determination of rate dependence of fracture toughness. Izvestiya, USSR Ac. Sci., Mech. Solids 5, 127–33.Google Scholar
Vlasov, I.O., Derzhavina, A.I. & Ryzhov, O.S. (1974). On an explosion on the boundary of two media. Comput. Math, and Math. Phys. 14 (6), 1544–52.CrossRefGoogle Scholar
von Kármán, Th. (1911). Über die Turbulenzreibung verschiedener Flüssigkeiten. Phys. Zeit. 12 (8), 1071–4.Google Scholar
von Kármán, Th. (1930). Mechanische Ahnlichkeit und Turbulenz. Nachrichten Ges. Wiss. Gottingen, Math-Phys. Kl, 58–76.Google Scholar
von Kármán, Th. (1957). Aerodynamics. Cornell University Press, Ithaca.Google Scholar
von Kármán, Th. & Howarth, L. (1938). On the statistical theory of isotropic turbulence. Proc. Roy. Soc. London A164 (917), 192–215.Google Scholar
von Koch, H. (1904). Sur une courbe continue sans tangente obtenue par une construction geometrique elementaire. Arkiv Mat. Astron. Fys. 2, 681–704.Google Scholar
von Neumann, J. (1941). The point source solution. National Defence Research Committee, Div. B, Report AM-9, June 30, 1941.
von Neumann, J. (1963). The point source solution, in Collected Works, Vol. VI, 219–37. Pergamon Press, Oxford, New York, London, Paris,Google Scholar
von Weizsäcker, C.F. (1954). Genäherte Darstellung starker instationärer Stosswellen durch Homologie-Lösungen. Z. Naturforschung 9a, 269–75.Google Scholar
Weatherly, G.L. & Kelly, E.A. (1982). ‘Too cold’ bottom layer at the bottom of Scotia Rise. J. Marine Res. 40, 985–1012.Google Scholar
Whitham, G.B. (1974). Linear and Nonlinear Waves. Wiley, New York.Google Scholar
Williams, M.L. (1952). Stress singularities resulting from various boundary conditions in angular corners of plates in extension. J. Appl. Mech. 19 (4), 526–8.Google Scholar
Wilson, K. (1971). Renormalization group and critical phenomena, I, II. Phys. Rev. B4 (9), 3174-83, 3184–205.Google Scholar
Woods, J.D. (1968). Wave-induced shear instability in the summer thermocline. J. Fluid Mech. 32 (4), 792–800.CrossRefGoogle Scholar
Wu, J. (1969). Mixed region collapse with internal wave generation in a density stratified medium. J. Fluid Mech. 35 (3), 531–44.CrossRefGoogle Scholar
Yaglom, A.M. (1974). Data on the characteristics of turbulence in the surface layer of the atmosphere. Izvestiya, USSR Ac. Sci., Atmos. Oceanic Phys. 10 (6), 566–86.Google Scholar
Zatsepin, A.G., Fedorov, K.N., Voropayev, S.I. & Pavlov, A.M. (1978). Experimental study of the spreading of a mixed region in a stratified fluid. Izvestiya, USSR Ac. Sci., Atmos. Oceanic Phys. 14 (2), 170–3.Google Scholar
Zeldovich, Ya.B. (1942). On the distribution of pressure and velocity in products of detonation blasts, in particular for spherically propagating detonation waves. Zhurn. Bksper. Teor. Fiz. 12 (9), 389–406.Google Scholar
Zeldovich, Ya.B. (1948). On the theory of flame propagation. Zhurn. Fiz. Khimii 22 (1), 27–48.Google Scholar
Zeldovich, Ya.B. (1956). The motion of a gas under the action of a short term pressure shock. Akust. Zh. 2 (1), 28–38, (Sov. Phys. Acoustics 2, 25-35).Google Scholar
Zeldovich, Ya.B. (1978). The flame propagation in a mixture reacting at the initial temperature. Preprint, Institute of Chemical Physics, Chernogolovka.
Zeldovich, Ya.B. (1992). Selected Works. Volume 1, Chemical Physics and Hydrodynamics. Princeton University Press, Princeton.Google Scholar
Zeldovich, Ya.B. & Barenblatt, G.I. (1958). The asymptotic properties of self-modeling solutions of the nonstationary gas filtration equations. Soviet Phys. Doklady 3 (1), 44–7.Google Scholar
Zeldovich, Ya.B., Barenblatt, G.I., Librovich, V.B. & Makhviladze, G.M. (1985). The Mathematical Theory of Combustion and Explosions. Consultants Bureau, New York, London.CrossRefGoogle Scholar
Zeldovich, Ya.B. & Frank-Kamenetsky, D.A. (1938a). Theory of uniform propagation of flames. Doklady, USSR Ac. Sci. 19 (2), 693–7.Google Scholar
Zeldovich, Ya.B. & Frank-Kamenetsky, D.A. (1938b). Theory of uniform propagation of flames. Zhurn. Fiz. Khimii 12 (1), 100–5.Google Scholar
Zeldovich, Ya.B. & Kompaneets, A.S. (1950). On the theory of propagation of heat with thermal conductivity depending on temperature. In Collection of Papers Dedicated to the 70th Birthday of A.F. Ioffe, 61–71. Izd. Akad. Nauk USSR, Moscow.Google Scholar
Zeldovich, Ya.B. & Kompaneets, A.S. (1960). Theory of Detonation. Academic Press, New York.Google Scholar
Zeldovich, Ya.B. & Raizer, Yu.P. (1966). Physics of Shock Waves and High Temperature Hydrodynamic Phenomena, Vol. I. Academic Press, New York, London.Google Scholar
Zeldovich, Ya.B. & Raizer, Yu.P. (1967). Physics of Shock Waves and High Temperature Hydrodynamic Phenomena, Vol. II, Academic Press, New York, London.Google Scholar
Zheltov, Yu.P. & Christianovich, S.A. (1955). On the hydraulic fracture of the oil stratum. Izvestiya, USSR Ac. Sci. Techn. Sci. 5, 3–41.Google Scholar
Zhukov, A.I. & Kazhdan, Ia.M. (1956). Motion of a gas due to the effect of a brief impulse. Soviet Phys. Acoustics 2 (4), 375–381.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • References
  • Grigory Isaakovich Barenblatt, University of Cambridge
  • Book: Scaling, Self-similarity, and Intermediate Asymptotics
  • Online publication: 18 December 2014
  • Chapter DOI: https://doi.org/10.1017/CBO9781107050242.017
Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • References
  • Grigory Isaakovich Barenblatt, University of Cambridge
  • Book: Scaling, Self-similarity, and Intermediate Asymptotics
  • Online publication: 18 December 2014
  • Chapter DOI: https://doi.org/10.1017/CBO9781107050242.017
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • References
  • Grigory Isaakovich Barenblatt, University of Cambridge
  • Book: Scaling, Self-similarity, and Intermediate Asymptotics
  • Online publication: 18 December 2014
  • Chapter DOI: https://doi.org/10.1017/CBO9781107050242.017
Available formats
×