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Formation of corner waves in the wake of a partially submerged bluff body

Published online by Cambridge University Press:  21 April 2015

P. Martínez-Legazpi
Affiliation:
Fluid Mechanics Group, Universidad Carlos III de Madrid, 28911 Leganés, Spain
J. Rodríguez-Rodríguez*
Affiliation:
Fluid Mechanics Group, Universidad Carlos III de Madrid, 28911 Leganés, Spain
A. Korobkin
Affiliation:
School of Mathematics, University of East Anglia, Norwich NR4 7TJ, UK
J. C. Lasheras
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, CA 92093-0411, USA
*
Email address for correspondence: javier.rodriguez@uc3m.es

Abstract

We study theoretically and numerically the downstream flow near the corner of a bluff body partially submerged at a deadrise depth ${\rm\Delta}h$ into a uniform stream of velocity $U$, in the presence of gravity, $g$. When the Froude number, $\mathit{Fr}=U/\sqrt{g{\rm\Delta}h}$, is large, a three-dimensional steady plunging wave, which is referred to as a corner wave, forms near the corner, developing downstream in a similar way to a two-dimensional plunging wave evolving in time. We have performed an asymptotic analysis of the flow near this corner to describe the wave’s initial evolution and to clarify the physical mechanism that leads to its formation. Using the two-dimensions-plus-time approximation, the problem reduces to one similar to dam-break flow with a wet bed in front of the dam. The analysis shows that, at leading order, the problem admits a self-similar formulation when the size of the wave is small compared with the height difference ${\rm\Delta}h$. The essential feature of the self-similar solution is the formation of a mushroom-shaped jet from which two smaller lateral jets stem. However, numerical simulations show that this self-similar solution is questionable from the physical point of view, as the two lateral jets plunge onto the free surface, leading to a self-intersecting flow. The physical mechanism leading to the formation of the mushroom-shaped structure is discussed.

Type
Papers
Copyright
© 2015 Cambridge University Press 

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References

Bifkhoff, G. & Zarantonello, E. H. 1957 Jets, Wakes and Cavities. Academic.Google Scholar
Drazen, D., Beale, K. L. C., Bhushan, S., Fullerton, A. M., O’Shea, T., Brucker, K., Dommermuth, D., Wyatt, D., Carrica, P., Fu, T. C. & Stern, F. 2010 Comparisons of model-scale experimental measurements and computational predictions for the transom wave of a large-scale transom model. In 28th Symposium on Naval Hydrodynamics, Pasadena, CA, September 12–17, vol. 2, pp. 762790. ISBN: 978-1-61839-299-2.Google Scholar
Faltinsen, O. M., Landrini, M. & Greco, M. 2004 Slamming in marine applications. J. Engng Maths 48, 187217.CrossRefGoogle Scholar
Goater, A. J. N. & Hogg, A. J. 2011 Bounded dam-break flows with tailwaters. J. Fluid Mech. 686, 160186.CrossRefGoogle Scholar
Hager, W. H. & Mazumder, S. K. 1992 Supercritical flow at abrupt expansions. Proc. Inst. Civil Eng. – Water Maritime and Energy 96, 153166.CrossRefGoogle Scholar
Hager, W. H. & Yasuda, Y. 1997 Unconfined expansion of supercritical water flow. J. Engng Mech. ASCE 123, 451457.CrossRefGoogle Scholar
Iafrati, A. & Korobkin, A. A. 2004 Initial stage of flat plate impact onto liquid free surface. Phys. Fluids 16, 22142227.CrossRefGoogle Scholar
Korobkin, A. & Yilmaz, O. 2009 The initial stage of dam-break flow. J. Engng Maths 63, 293308.CrossRefGoogle Scholar
Martínez-Legazpi, P.2011 Corner waves downstream from a partially submerged vertical plate. PhD thesis, Universidad Carlos III de Madrid.Google Scholar
Martínez-Legazpi, P., Rodríguez-Rodríguez, J., Marugán-Cruz, C. & Lasheras, J. C. 2013 Plunging to spilling transition in corner surface waves in the wake of a partially submerged vertical plate. Exp. Fluids 54, 14371447.CrossRefGoogle Scholar
Needham, D. J., Chamberlain, P. G. & Billingham, J. 2008 The initial development of a jet caused by fluid, body and free surface tension. Part 3. An inclined accelerated plate. Q. J. Mech. Appl. Maths 61, 581614.CrossRefGoogle Scholar
Pozrikidis, C. 2002 A Practical Guide to Boundary Element Methods with the Software Library BEMLIB. CRC Press.CrossRefGoogle Scholar
Semenov, Y. A., Wu, G. X. & Olivier, J. M. 2013 Splash jet generated by collision of two liquid wedges. J. Fluid Mech. 737, 132145.CrossRefGoogle Scholar
Shakeri, M., Maxeiner, E., Fu, T. & Duncan, J. H. 2009a An experimental examination of the 2d+t approximation. J. Ship Res. 53, 5967.Google Scholar
Shakeri, M., Tavakolinejad, M. & Duncan, J. H. 2009 b An experimental investigation of divergent bow waves simulated by a two-dimensional plus temporal wave maker technique. J. Fluid Mech. 634, 217243.CrossRefGoogle Scholar
Spalart, P. R., Moser, R. D. & Rogers, M. M. 1991 Spectral method for the Navier–Stokes equations with one infinite and 2 periodic directions. J. Comput. Phys. 96, 297324.CrossRefGoogle Scholar
Stansby, P. K., Chegini, A. & Barnes, T. C. D. 1998 The initial stages of a dam-break flow. J. Fluid Mech. 374, 407424.CrossRefGoogle Scholar
Whitham, G. B. 1974 Linear and Nonlinear Waves. John Wiley and Sons.Google Scholar
Wu, T. Y.-T. 1972 Cavity and wake flows. Annu. Rev. Fluid Mech. 4, 243284.CrossRefGoogle Scholar
Yilmaz, O., Korobkin, A. & Iafrati, A. 2013 The initial stage of dam-break flow of two immiscible fluids. Linear analysis of global flow. Appl. Ocean Res. 42, 6069.CrossRefGoogle Scholar
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