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

  • P. Martínez-Legazpi (a1), J. Rodríguez-Rodríguez (a1), A. Korobkin (a2) and J. C. Lasheras (a3)
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.

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Corresponding author
Email address for correspondence: javier.rodriguez@uc3m.es
References
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Bifkhoff G. & Zarantonello E. H. 1957 Jets, Wakes and Cavities. Academic.
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.
Faltinsen O. M., Landrini M. & Greco M. 2004 Slamming in marine applications. J. Engng Maths 48, 187217.
Goater A. J. N. & Hogg A. J. 2011 Bounded dam-break flows with tailwaters. J. Fluid Mech. 686, 160186.
Hager W. H. & Mazumder S. K. 1992 Supercritical flow at abrupt expansions. Proc. Inst. Civil Eng. – Water Maritime and Energy 96, 153166.
Hager W. H. & Yasuda Y. 1997 Unconfined expansion of supercritical water flow. J. Engng Mech. ASCE 123, 451457.
Iafrati A. & Korobkin A. A. 2004 Initial stage of flat plate impact onto liquid free surface. Phys. Fluids 16, 22142227.
Korobkin A. & Yilmaz O. 2009 The initial stage of dam-break flow. J. Engng Maths 63, 293308.
Martínez-Legazpi P.2011 Corner waves downstream from a partially submerged vertical plate. PhD thesis, Universidad Carlos III de Madrid.
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.
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.
Pozrikidis C. 2002 A Practical Guide to Boundary Element Methods with the Software Library BEMLIB. CRC Press.
Semenov Y. A., Wu G. X. & Olivier J. M. 2013 Splash jet generated by collision of two liquid wedges. J. Fluid Mech. 737, 132145.
Shakeri M., Maxeiner E., Fu T. & Duncan J. H. 2009a An experimental examination of the 2d+t approximation. J. Ship Res. 53, 5967.
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.
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.
Stansby P. K., Chegini A. & Barnes T. C. D. 1998 The initial stages of a dam-break flow. J. Fluid Mech. 374, 407424.
Whitham G. B. 1974 Linear and Nonlinear Waves. John Wiley and Sons.
Wu T. Y.-T. 1972 Cavity and wake flows. Annu. Rev. Fluid Mech. 4, 243284.
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.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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