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  • Journal of Fluid Mechanics, Volume 571
  • January 2007, pp. 149-175

Katabatic flow along a differentially cooled sloping surface

  • ALAN SHAPIRO (a1) and EVGENI FEDOROVICH (a1)
  • DOI: http://dx.doi.org/10.1017/S0022112006003302
  • Published online: 25 January 2007
Abstract

Buoyancy inhomogeneities on sloping surfaces arise in numerous situations, for example, from variations in snow/ice cover, cloud cover, topographic shading, soil moisture, vegetation type, and land use. In this paper, the classical Prandtl model for one-dimensional flow of a viscous stably stratified fluid along a uniformly cooled sloping planar surface is extended to include the simplest type of surface inhomogeneity – a surface buoyancy that varies linearly down the slope. The inhomogeneity gives rise to acceleration, vertical motions associated with low-level convergence, and horizontal and vertical advection of perturbation buoyancy. Such processes are not accounted for in the classical Prandtl model. A similarity hypothesis appropriate for this inhomogeneous flow removes the along-slope dependence from the problem, and, in the steady state, reduces the Boussinesq equations of motion and thermodynamic energy to a set of coupled nonlinear ordinary differential equations. Asymptotic solutions for the velocity and buoyancy variables in the steady state, valid for large values of the slope-normal coordinate, are obtained for a Prandtl number of unity for pure katabatic flow with no ambient wind or externally imposed pressure gradient. The undetermined parameters in these solutions are adjusted to conform to lower boundary conditions of no-slip, impermeability and specified buoyancy. These solutions yield formulae for the boundary-layer thickness and slope-normal velocity component at the top of the boundary layer, and provide an upper bound of the along-slope surface-buoyancy gradient beyond which steady-state solutions do not exist. Although strictly valid for flow above the boundary layer, the steady asymptotic solutions are found to be in very good agreement with the terminal state of the numerical solution of an initial-value problem (suddenly applied surface buoyancy) throughout the flow domain. The numerical results also show that solution non-existence is associated with self-excitation of growing low-frequency gravity waves.

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B. W. Atkinson 1995 Orographic and stability effects on valley-side drainage flows. Boundary- Layer Met. 75, 403428.

F. K. Ball 1956 The theory of strong katabatic winds. Austral. J. Phys. 9, 373386.

A. J. Brazel , H. J. S. Fernando , J. C. R. Hunt , N. Selover , B. C. Hedquist & E. Pardyjak 2005 Evening transition observations in Phoenix, Arizona. J. Appl. Met. 44, 99112.

D. H. Bromwich , J. J. Cassano , T. Klein , G. Heinemann , K. M. Hines , K. Steffen & J. E. Box 2001 Mesoscale modeling of katabatic winds over Greenland with the Polar MM5. Mon. Weather Rev. 129, 22902309.

B. Cushman-Roisin , W. H. Heil & D. Nof 1985 Oscillations and rotations of elliptical warm-core rings. J. Geophys. Res. 90, 11 75611 764.

F. Defant 1949 Zur Theorie der Hangwinde, nebst Bemerkungen zur Theorie der Berg- und Talwinde. Arch. Met. Geophys. Bioklim. A 1, 421450.

J. C. Doran & T. W. Horst 1981 Velocity and temperature oscillations in drainage winds. J. Appl. Met. 20, 361364.

J. C. Doran & T. W. Horst 1983 Observations and models of simple nocturnal slope flows. J. Atmos. Sci. 40, 708717.

J. W. Elder 1965 Laminar free convection in a vertical slot. J. Fluid Mech. 23, 7798.

J. Egger 1985 Slope winds and the axisymmetric circulation over Antarctica. J. Atmos. Sci. 42, 18591867.

H. J. S. Fernando , S. M. Lee , J. Anderson , M. Princevac , E. Pardyjak & S. Grossman-Clarke 2001 Urban fluid mechanics: air circulation and contaminant dispersion in cities. Environ. Fluid Mech. 1, 107164.

B. H. Fiedler 1999 Thermal convection in a layer bounded by uniform heat flux: application of a strongly nonlinear analytical solution. Geophys. Astrophys. Fluid Dyn. 91, 223250.

D. R. Fitzjarrald 1984 Katabatic wind in opposing flow. J. Atmos. Sci. 41, 11431158.

H. Gallee & G. Schayes 1994 Development of a 3-dimensional meso-γ primitive equation model: katabatic winds simulation in the area of Terra Nova Bay, Antarctica. Mon. Weather Rev. 122, 671685.

A. E. Gill 1966 The boundary layer regime for convection in a rectangular cavity. J. Fluid Mech. 26, 515536.

B. Grisogono & J. Oerlemans 2001 Analytic solution for gradually varying eddy diffusivities. J. Atmos. Sci. 58, 33493354.

B. Grisogono & J. Oerlemans 2002 Justifying the WKB approximation in pure katabatic flows. Tellus A 54, 453462.

L. N. Gutman & J. W. Melgarejo 1981 On the laws of geostrophic drag and heat transfer over a slightly inclined terrain. J. Atmos. Sci. 38, 17141724.

T. Haiden & C. D. Whiteman 2005 Katabatic flow mechanisms on a low-angle slope. J. Appl. Met. 44, 113126.

G. Heinemann & T. Klein 2002 Modelling and observations of the katabatic flow dynamics over Greenland. Tellus A 54, 542554.

C. G. Helmis & K. H. Papadopoulos 1996 Some aspects of the variation with time of katabatic flow over a simple slope. Q. J. R. Met. Soc. 122, 595610.

J. C. R. Hunt , H. J. S. Fernando & M. Princevac 2003 Unsteady thermally driven flows on gentle slopes. J. Atmos. Sci. 60, 21692182.

J. Imberger & J. C. Patterson 1990 Physical limnology. Adv. Appl. Mech. 27, 303475.

T. Klein , G. Heinemann , D. H. Bromwich , J. J. Cassano & K. M. Hines 2001 Mesoscale modeling of katabatic winds over Greenland and comparisons with AWS and aircraft data. Met. Atmos. Phys. 78, 115132.

R. Lu & R. P. Turco 1994 Air pollutant transport in a coastal environment. Part I: Two-dimensional simulations of sea-breeze and mountain effects. J. Atmos. Sci. 51, 22852308.

O. S. Madsen 1977 A realistic model of the wind-induced Ekman boundary layer. J. Phys. Ocean. 7, 248255.

P. C. Manins & B. L. Sawford 1979 A model of katabatic winds. J. Atmos. Sci. 36, 619630.

P. Monti , H. J. S. Fernando , M. Princevac , W. C. Chan , T. A. Kowalewski & E. R. Pardyjak 2002 Observations of flow and turbulence in the nocturnal boundary layer over a slope. J. Atmos. Sci. 59, 25132534.

K. H. Papadopoulos , C. G. Helmis , A. T. Soilemes , J. Kalogiros , P. G. Papageorgas & D. N. Asimakopoulos 1997 The structure of katabatic flows down a simple slope. Q. J. R. Met. Soc. 123, 15811601.

T. R. Parish 1984 A numerical study of strong katabatic winds over Antarctica. Mon. Weather Rev. 112, 545554.

T. R. Parish & K. T. Waight 1987 The forcing of antarctic katabatic winds. Mon. Weather Rev. 115, 22142226.

T. Peacock , R. Stocker & M. Aristoff 2004 An experimental investigation of the angular dependence of diffusion-driven flow. Phys. Fluids 16, 35033505.

P. Pettré & J.-C. André 1991 Surface-pressure change through Loewe's phenomena and katabatic flow jumps: study of two cases in Adélie Land, Antarctica. J. Atmos. Sci. 48, 557571.

I. A. Renfrew 2004 The dynamics of idealized katabatic flow over a moderate slope and ice shelf. Q. J. R. Met. Soc. 130, 10231045.

A. Shapiro 1996 Nonlinear shallow-water oscillations in a parabolic channel: exact solutions and trajectory analyses. J. Fluid Mech. 318, 4976.

A. Shapiro 2001 A centrifugal wave solution of the Euler and Navier–Stokes equations. Z. Angew. Math. Phys. 52, 913923.

A. Shapiro & E. Fedorovich 2004 Unsteady convectively driven flow along a vertical plate immersed in a stably stratified fluid. J. Fluid Mech. 498, 333352.

E. D. Skyllingstad 2003 Large-eddy simulation of katabatic flows. Boundary-Layer Met. 106, 217243.

G. L. Stone & D. E. Hoard 1989 Low-frequency velocity and temperature fluctuations in katabatic valley flows. J. Appl. Met. 28, 477488.

W. C. Thacker 1981 Some exact solutions to the nonlinear shallow-water wave equations. J. Fluid Mech. 107, 499508.

P. D. Tyson 1968 Velocity fluctuations in the mountain wind. J. Atmos. Sci. 25, 381384.

G. Veronis 1970 The analogy between rotating and stratified fluids. Annu. Rev. Fluid Mech. 2, 3766.

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