Hostname: page-component-8448b6f56d-c4f8m Total loading time: 0 Render date: 2024-04-23T23:34:28.879Z Has data issue: false hasContentIssue false
  • English
  • Français

A turbulent patch arising from a breaking internal wave

Published online by Cambridge University Press:  07 April 2011

SERGEY N. YAKOVENKO ,
T. GLYN THOMAS  and
IAN P. CASTRO
SERGEY N. YAKOVENKO
Affiliation:
Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences, Novosibirsk 630090, Russia School of Engineering Sciences, University of Southampton, Highfield, Southampton SO17 1BJ, UK
T. GLYN THOMAS
Affiliation:
School of Engineering Sciences, University of Southampton, Highfield, Southampton SO17 1BJ, UK
IAN P. CASTRO*
Affiliation:
School of Engineering Sciences, University of Southampton, Highfield, Southampton SO17 1BJ, UK
*
†Email address for correspondence: i.castro@soton.ac.uk
Get access Rights & Permissions [Opens in a new window]

Abstract

Results of direct numerical simulations of the development of a breaking internal gravity wave are presented. The wave was forced by the imposition of an appropriate bottom boundary shape (a two-dimensional cosine hill) within a density-stratified domain having a uniform upstream velocity and density gradient. The focus is on turbulence generation and maintenance within the turbulent patch generated by the wave breaking. Pathlines, density contours, temporal and spatial spectra, and second moments of the velocity and density fluctuations and turbulent kinetic energy balance terms obtained from the data averaged over the span in the mixed zone are all used in the analysis of the flow. Typical Reynolds numbers, based on the vertical scale of the breaking region and the upstream velocity, were around 6000 and the fully resolved computations yielded sufficient resolution to capture the fine-scale transition processes as well as the subsequent fully developed turbulence. It is shown that globally, within the turbulent patch, there is an approximate balance in the production, dissipation and transport processes for turbulent kinetic energy, so that the patch remains quasi-steady over a significant time. Although it is far from being axially homogeneous, with turbulence generation occurring largely near the upstream bottom part of the patch where the mean velocity shear is particularly large, it has features not dissimilar to those of a classical turbulent wake.

JFM classification

Geophysical and Geological Flows: Atmospheric flows Geophysical and Geological Flows: Internal waves Turbulent Flows: Turbulence simulation
Type
Papers
Information
Journal of Fluid Mechanics , Volume 677 , 25 June 2011 , pp. 103 - 133
Copyright
Copyright © Cambridge University Press 2011

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

REFERENCES

Afanasyev, Y. D. & Peltier, W. R. 1998 The three-dimensionalisation of stratified flow over two-dimensional topography. J. Atmos. Sci. 55, 19–39.2.0.CO;2>CrossRefGoogle Scholar
Baines, P. G. 1995 Topographic Effects in Stratified Flows. CUP.CrossRefGoogle Scholar
Barri, M., Khoury, G. K. El, Andersson, H. I. & Petterson, B. 2010 DNS of backward-facing step flow with fully turbulent inflow. Intl J. Numer. Meth. Fluids 64, 777–792.CrossRefGoogle Scholar
Bodony, D. J. 2006 Analysis of sponge zones for computational fluid mechanics. J. Comput. Phys. 212, 681–702.CrossRefGoogle Scholar
Castro, I. P. & Snyder, W. H. 1993 Experiments on wave breaking in stratified flow over obstacles. J. Fluid Mech. 255, 195–211.CrossRefGoogle Scholar
Castro, I. P., Snyder, W. H. & Baines, P. G. 1990 Obstacle drag in stratified flow. Proc. R. Soc. Lond. A 429, 119–140.Google Scholar
Castro, I. P., Snyder, W. H. & Marsh, G. L. 1983 Stratified flow over three-dimensional ridges. J. Fluid Mech. 135, 261–282.CrossRefGoogle Scholar
Clark, T. L., Hall, W. D., Kerr, R. M. & Middleton, D. 2000 Origins of aircraft-damaging clear-air turbulence during the 9 December 1992 Colorado downslope windstorm: numerical simulations and comparison with observations. J. Atmos. Sci. 57, 1105–1131.2.0.CO;2>CrossRefGoogle Scholar
Clarke, T. L. & Peltier, W. R. 1977 On the evolution and stability of finite-amplitude mountain waves. J. Atmos. Sci. 34, 1715–1730.2.0.CO;2>CrossRefGoogle Scholar
Dornbrack, A. 1998 Turbulent mixing by breaking gravity waves. J. Fluid Mech. 375, 113–141.CrossRefGoogle Scholar
Doyle, J. D. & Durran, D. R. 2007 Rotor and subrotor dynamics in the lee of three-dimensional terrain. J. Atmos. Sci. 64, 4202–4221.CrossRefGoogle Scholar
Doyle, J. D., Shapiro, M. A., Jiang, Q. & Bartels, D. I. 2005 Large-amplitude mountain wave breaking over Greenland. J. Atmos. Sci. 62, 3106–3126.CrossRefGoogle Scholar
Eiff, O. F. & Bonneton, P. 2000 Lee-wave breaking over obstacles in stratified flow. Phys. Fluids 12, 1073–1086.CrossRefGoogle Scholar
Eiff, O., Huteau, F. & Tolu, J. 2005 High-Reynolds-number orographic wave-breaking experiments. Dyn. Atmos. Oceans 40, 71–89.CrossRefGoogle Scholar
Gheusi, F., Stein, J. & Eiff, O. F. 2000 A numerical study of three-dimensional orographic gravity-wave breaking observed in a hydraulic tank. J. Fluid Mech. 410, 67–99.CrossRefGoogle Scholar
Grubisic, V. & Lewis, J. M. 2004 Sierra wave project revisited: 50 years later. Bull. Am. Meteorol. Soc. 85, 1127–1142.CrossRefGoogle Scholar
Ivey, G. N. & Imberger, J. 1991 On the nature of turbulence in a stratified fluid. Part I. The energetics of mixing. J. Phys. Oceanogr. 21, 650–658.2.0.CO;2>CrossRefGoogle Scholar
Kim, J., Moin, P. & Moser, R. 1987 Turbulence statistics in fully developed turbulent channel flow at low Reynolds number. J. Fluid Mech. 177, 133–166.CrossRefGoogle Scholar
Klemp, J. B. & Lilly, D. K. 1977 Numerical simulation of hydrostatic mountain waves. J. Atmos. Sci. 35, 78–107.2.0.CO;2>CrossRefGoogle Scholar
Lilley, D. K. & Klemp, J. B. 1979 The effects of terrain shape on nonlinear hydrostatic mountain waves. J. Fluid Mech. 95, 241–261.CrossRefGoogle Scholar
Lilly, D. K. & Kennedy, P. J. 1973 Observations of a stationary mountain wave and its associated momentum flux and energy dissipation. J. Atmos. Sci. 30, 1135–1152.2.0.CO;2>CrossRefGoogle Scholar
Long, R. R. 1955 Some aspects of flow of stratified fluids. III. continuous density gradients. Tellus 7, 341–357.Google Scholar
Lumley, J. 1964 The spectrum of nearly inertial turbulence in a stably stratified fluid. J. Atmos. Sci. 21, 99–102.2.0.CO;2>CrossRefGoogle Scholar
Nastrom, G. D. & Gage, K. S. 1985 A climatology of atmospheric wavenumber spectra of wind and temperature observed by commercial aircraft. J. Atmos. Sci. 42, 950–960.2.0.CO;2>CrossRefGoogle Scholar
Paisley, M. F. & Castro, I. P. 1995 Numerical experiments of stratified flow over three-dimensional obstacles. In Numerical Methods for Fluid Dynamics V (ed. Morton, K. W. & Baines, M. J.), pp. 523–531. Oxford University Press.Google Scholar
Paisley, M. F. & Castro, I. P. 1996 A numerical study of wave-breaking in stratified flow over obstacles. Dyn. Atmos. Oceans 23, 309–319.CrossRefGoogle Scholar
Pham, H. T. & Sarkar, S. 2010 Internal waves and turbulence in a stable stratified jet. J. Fluid Mech. 648, 297–324.CrossRefGoogle Scholar
Pham, H. T., Sarkar, S. & Brucker, K. A. 2009 Dynamics of a stratified shear layer above a region of uniform stratification. J. Fluid Mech. 630, 191–223.CrossRefGoogle Scholar
Pope, S. B. 2000 Turbulent Flows. CUP.CrossRefGoogle Scholar
Richard, E., Mascart, P. & Nickerson, E. 1989 On the role of surface friction in downslope windstorms. J. Appl. Meteorol. 28, 241–251.2.0.CO;2>CrossRefGoogle Scholar
Rottman, J. W., Broutman, D. & Grimshaw, R. 1996 Numerical simulations of uniformly stratified flow over topography. J. Fluid Mech. 306, 1–30.CrossRefGoogle Scholar
Scinocca, J. & Peltier, W. R. 1993 The instability of Long's stationary solution and the evolution toward severe downslope windstorm flow. Part I. Nested grid numerical simulation. J. Atmos. Sci. 50, 2245–2263.2.0.CO;2>CrossRefGoogle Scholar
Smith, R. B. 1985 On severe downslope winds. J. Atmos. Sci. 42, 2597–2603.2.0.CO;2>CrossRefGoogle Scholar
Smyth, W. D., Hebert, D. & Moum, J. N. 1996 Local ocean response to a multiphase westerly wind burst. Part 2. Thermal and fresh water responses. J. Geophys. Res. 101 (C10), 22513–22533.CrossRefGoogle 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, 1969–1992.2.0.CO;2>CrossRefGoogle Scholar
Sreenivasan, K. R. 1995 On the universality of the Kolmogorov constant. Phys. Fluids 7, 2778–2784.CrossRefGoogle Scholar
Sreenivasan, K. R. 1996 The passive scalar spectrum and the Obukhov–Corrsin constant. Phys. Fluids 8, 189–196.CrossRefGoogle Scholar
Sveen, J. K., Guo, Y., Davies, P. A. & Grue, J. 2002 On the breaking of internal solitary waves at a ridge. J. Fluid Mech. 469, 161–188.CrossRefGoogle Scholar
Thomas, T. G. & Williams, J. J. R. 1997 Development of a parallel code to simulate skewed flow over a bluff body. J. Wind Engng Ind. Aerodyn. 67–68, 155–167.CrossRefGoogle Scholar
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow, 2nd edn. CUP.Google Scholar
Voropayev, S. I., Afanasyev, Y. D. & vanHeijst, G. J. F. Heijst, G. J. F. 1993 Experiments on the evolution of gravitational instability of an overturned, initially stably stratified fluid. Phys. Fluids A 5, 2461–2466.CrossRefGoogle Scholar
Warhaft, Z. 2000 Passive scalars in turbulent flows. Annu. Rev. Fluid Mech. 32, 203–240.CrossRefGoogle Scholar
Yakovenko, S. N., Thomas, T. G. & Castro, I. P. 2009 DNS of turbulence in breaking waves. Parts I–IV. Internal reports, AFM08.3, 8.4, 9.1 and 9.3. University of Southampton.Google Scholar
Ying, Q. & Baopu, F. 1993 Turbulence in broken lee waves. Acta Mechanica Sin. 9, 210–222.CrossRefGoogle Scholar
Zhou, Y. & Antonia, R. A. 1995 Memory effects in a turbulent plane wake. Exp. Fluids 19, 112–120.CrossRefGoogle Scholar