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Holmboe wave fields in simulation and experiment

Published online by Cambridge University Press:  07 April 2010

J. R. CARPENTER ,
E. W. TEDFORD ,
M. RAHMANI  and
G. A. LAWRENCE
J. R. CARPENTER*
Affiliation:
Department of Civil Engineering, University of British Columbia, Vancouver, BC V6T 1Z4, Canada
E. W. TEDFORD
Affiliation:
Department of Civil Engineering, University of British Columbia, Vancouver, BC V6T 1Z4, Canada
M. RAHMANI
Affiliation:
Department of Civil Engineering, University of British Columbia, Vancouver, BC V6T 1Z4, Canada
G. A. LAWRENCE
Affiliation:
Department of Civil Engineering, University of British Columbia, Vancouver, BC V6T 1Z4, Canada
*
†Present address: EAWAG, Swiss Federal Institute of Aquatic Science and Technology, Seestrasse 79, Kastanienbaum, Switzerland. Email address for correspondence: [email protected]
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Abstract

The basic wave field resulting from Holmboe's instability is studied both numerically and experimentally. Comparisons between the direct numerical simulations (DNS) and laboratory experiments result in Holmboe waves that are similar in their appearance and phase speed. However, different boundary conditions result in mean flows that display gradual variations either temporally (in the simulations) or spatially (in the experiments). These differences are found to affect the evolution of the dominant wavenumber and amplitude of the wave field. The simulations exhibit a nonlinear ‘wave coarsening’ effect, whereby the energy is shifted to lower wavenumbers in discrete merging events. This process is typically found to result from either ejections of mixed fluid away from the density interface or vortex pairing. In the experiments, energy is transferred to lower wavenumbers by the ‘stretching’ of the wave field by a gradually varying mean velocity. This stretching results in a reduction of wave amplitude compared with the DNS.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 648 , 10 April 2010 , pp. 205 - 223
Copyright
Copyright © Cambridge University Press 2010

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References

REFERENCES

Alexakis, A. 2005 On Holmboe's instability for smooth shear and density profiles. Phys. Fluids 17, 084103.Google Scholar
Alexakis, A. 2007 Marginally unstable Holmboe modes. Phys. Fluids 19, 054105.Google Scholar
Alexakis, A. 2009 Stratified shear flow instabilities at large Richardson numbers. Phys. Fluids 21, 054108.Google Scholar
Balmforth, N. J. & Mandre, S. 2004 Dynamics of roll waves. J. Fluid Mech. 514, 1–33.Google Scholar
Bretherton, F. P. & Garrett, C. J. R. 1969 Wavetrains in inhomogeneous moving media. Proc. R. Soc. A 302, 529–554.Google Scholar
Browand, F. K. & Winant, C. D. 1973 Laboratory observations of shear-layer instability in a stratified fluid. Boundary-Layer Meteorol. 5, 67–77.Google Scholar
Carpenter, J. R., Lawrence, G. A. & Smyth, W. D. 2007 Evolution and mixing of asymmetric Holmboe instabilities. J. Fluid Mech. 582, 103–132.Google Scholar
Caulfield, C. P. & Peltier, W. R. 2000 Anatomy of the mixing transition in homogenous and stratified free shear layers. J. Fluid Mech. 413, 1–47.Google Scholar
Haigh, S. P. 1995 Non-symmetric Holmboe waves. PhD thesis, University of British Columbia, Vancouver, BC, Canada.Google Scholar
Hazel, P. 1972 Numerical studies of the stability of inviscid parallel shear flows. J. Fluid Mech. 39, 39–61.Google Scholar
Hogg, A. M. & Ivey, G. N. 2003 The Kelvin–Helmholtz to Holmboe instability transition in stratified exchange flows. J. Fluid Mech. 477, 339–362.Google Scholar
Holmboe, J. 1962 On the behaviour of symmetric waves in stratified shear layers. Geofys. Pub. 24, 67–112.Google Scholar
Huang, N. E., Long, S. R. & Shen, Z. 1996 The mechanism for frequency downshift in nonlinear water wave evolution. Adv. Appl. Mech. 32, 59–117.Google Scholar
Huang, N. E., Shen, Z. & Long, S. R. 1999 A new view of nonlinear water waves: the Hilbert spectrum. Annu. Rev. Fluid Mech. 31, 417–457.Google Scholar
Koppel, D. 1964 On the stability of a thermally stratified fluid under the action of gravity. J. Math. Phys. 5, 963–982.Google Scholar
Lawrence, G. A., Browand, F. K. & Redekopp, L. G. 1991 The stability of a sheared density interface. Phys. Fluids A 3, 2360–2370.Google Scholar
Longuet-Higgins, M. S. & Cokelet, E. D. 1978 The deformation of steep surface waves on water. Part II. Growth of normal-mode instabilities. Proc. R. Soc. Lond. A 364, 1–28.Google Scholar
Longuet-Higgins, M. S. & Dommermuth, D. G. 1997 Crest instabilities of gravity waves. Part 3. Nonlinear development and breaking. J. Fluid Mech. 266, 33–50.Google Scholar
Pawlak, G. & Armi, L. 1996 Stability and mixing of a two-layer exchange flow. Dyn. Atmos. Oceans 24, 139–151.Google Scholar
Peregrine, D. H. 1976 Interaction of water waves and currents. Adv. Appl. Mech. 16, 9–117.Google Scholar
Pouliquen, O., Chomaz, J. M. & Huerre, P. 1994 Propagating Holmboe waves at the interface between two immiscible fluids. J. Fluid Mech. 266, 277–302.Google Scholar
Sargent, F. E. & Jirka, G. H. 1987 Experiments on saline wedge. J. Hydraul. Engng 113, 1307–1324.Google Scholar
Sharples, J., Coates, M. J. & Sherwood, J. E. 2003 Quantifying turbulent mixing and oxygen fluxes in a Mediterranean-type, microtidal estuary. Ocean Dyn. 53, 126–136.Google Scholar
Smyth, W. D. 2006 Secondary circulations in Holmboe waves. Phys. Fluids 37, 064104.Google Scholar
Smyth, W. D., Carpenter, J. R. & Lawrence, G. A. 2007 Mixing in symmetric Holmboe waves. J. Phys. Oceanogr. 37, 1566–1583.Google Scholar
Smyth, W. D., Klaassen, G. P. & Peltier, W. R. 1988 Finite amplitude Holmboe waves. Geophys. Astrophys. Fluid Dyn. 43, 181–222.Google Scholar
Smyth, W. D., Moum, J. N. & Caldwell, D. R. 2001 The efficiency of mixing in turbulent patches: inferences from direct simulations and microstructure observations. J. Phys. Oceanogr. 31, 1969–1992.Google Scholar
Smyth, W. D., Nash, J. D. & Moum, J. N. 2005 Differential diffusion in breaking Kelvin–Helmholtz billows. J. Phys. Oceanogr. 35, 1004–1022.Google Scholar
Smyth, W. D. & Peltier, W. R. 1990 Three-dimensional primary instabilities of a stratified, dissipative, parallel flow. Geophys. Astrophys. Fluid Dyn. 52, 249–261.Google Scholar
Smyth, W. D. & Winters, K. B. 2003 Turbulence and mixing in Holmboe waves. J. Phys. Oceanogr. 33, 694–711.Google Scholar
Tedford, E. W., Carpenter, J. R., Pawlowicz, R., Pieters, R. & Lawrence, G. A. 2009 a Observation and analysis of shear instability in the Fraser River estuary. J. Geophys. Res. 114, C11006. doi:10.1029/2009JC005313.Google Scholar
Tedford, E. W., Pieters, R. & Lawrence, G. A. 2009 b Symmetric Holmboe instabilities in a laboratory exchange flow. J. Fluid Mech. 636, 137–153.Google Scholar
Tulin, M. P. & Waseda, T. 1999 Laboratory observations of wave group evolution, including breaking effects. J. Fluid Mech. 378, 197–232.Google Scholar
Wesson, J. C. & Gregg, M. C. 1994 Mixing at the Camarinal Sill in the Strait of Gibraltar. J. Geophys. Res. 99, 9847–9878.Google Scholar
Winters, K. B., MacKinnon, J. A. & Mills, B. 2004 A spectral model for process studies of rotating, density-stratified flows. J. Atmos. Ocean. Technol. 21, 69–94.Google Scholar
Yonemitsu, N., Swaters, G. E., Rajaratnam, N. & Lawrence, G. A. 1996 Shear instabilities in arrested salt-wedge flows. Dyn. Atmos. Oceans 24, 173–182.Google Scholar
Yoshida, S., Ohtani, M., Nishida, S. & Linden, P. F. 1998 Mixing processes in a highly stratified river. In Physical Processes in Lakes and Oceans (ed. Imberger, J.). Coastal and Estuarine Studies, vol. 54, pp. 389–400. American Geophysical Union.Google Scholar
Zhu, D. Z. & Lawrence, G. A. 2001 Holmboe's instability in exchange flows. J. Fluid Mech. 429, 391–409.Google Scholar