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Mixing events in a stratified jet subject to surface wind and buoyancy forcing

Published online by Cambridge University Press:  19 September 2011

Hieu T. Pham  and
Sutanu Sarkar
Hieu T. Pham
Affiliation:
Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, CA 92093, USA
Sutanu Sarkar*
Affiliation:
Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, CA 92093, USA
*
†Email address for correspondence: [email protected]
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Abstract

The fine-scale response of a subsurface stable stratified jet subject to the forcing of surface wind stress and surface cooling is investigated using direct numerical simulation. The initial velocity profile consists of a symmetric jet located below a surface layer driven by a constant wind stress. The initial density profile is well-mixed in the surface layer and linearly stratified in both upper and lower flanks of the jet. The minimum value of the gradient Richardson number in the upper flank of the jet exceeds the critical value of 0.25 for linear shear instability. Broadband finite-amplitude fluctuations are introduced to the surface layer to initiate the simulation. Turbulence is generated in the surface layer and deepens into the jet upper flank. Internal waves generated by the turbulent surface layer are observed to propagate downward across the jet. The momentum flux carried by the waves is significantly smaller than the Reynolds shear stress extracted from the background velocity. The wave energy flux is also smaller than the turbulence production by mean shear. Ejections of fluid parcels by horseshoe-like vortices cause intermittent patches of intense dissipation inside the jet upper flank where the background gradient Richardson number is larger than 0.25. Drag due to the wind stress is smaller than the drag caused by turbulent stress in the flow. Analysis of the mean and turbulent kinetic energy budgets suggests that the energy input by surface forcing is considerably smaller than the energy extracted from the initially imposed background shear in the surface layer.

JFM classification

Geophysical and Geological Flows: Ocean processes Turbulent Flows: Stratified turbulence
Type
Papers
Information
Journal of Fluid Mechanics , Volume 685 , 25 October 2011 , pp. 54 - 82
Copyright
Copyright © Cambridge University Press 2011

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References

1. Basak, S. & Sarkar, S. 2006 Dynamics of a stratified shear layer with horizontal shear. J. Fluid Mech. 568, 19–54.CrossRefGoogle Scholar
2. Brown, G. L. & Sutherland, B. R. 2007 Internal wave tunnelling through non-uniformly stratified shear flow. Atmos.-Ocean 45, 47–56.CrossRefGoogle Scholar
3. Brucker, K. & Sarkar, S. 2007 Evolution of an initially turbulent stratified shear layer. Phys. Fluids 19, 101105.CrossRefGoogle Scholar
4. Galperin, B. & Sukoriansky, S. 2010 Geophysical flows with anisotropic turbulence and dispersive waves: flows with stable stratification. Ocean Dyn. 60, 1319–1337.CrossRefGoogle Scholar
5. Gayen, B., Sarkar, S. & Taylor, J. R. 2010 Large eddy simulation of a stratified boundary layer under an oscillatory current. J. Fluid Mech. 643, 233–266.CrossRefGoogle Scholar
6. Gregg, M. C., Peters, H., Wesson, J. C., Oakey, N. S. & Shay, T. J. 1985 Intensive measurements of turbulence and shear in the equatorial undercurrent. Nature 314 (14), 140–144.CrossRefGoogle Scholar
7. Hebert, D., Moum, J., Paulson, C. & Caldwell, D. 1992 Turbulence and internal waves at the equator. Part ii: details of a single event. J. Phys. Oceanogr. 22, 1346–1356.2.0.CO;2>CrossRefGoogle Scholar
8. Lien, R.-C., McPhaden, M. & Gregg, M. 1996 High-frequency internal waves at 0∘, 140∘ w and their possible relationship to deep-cycle turbulence. J. Phys. Oceanogr. 26, 581–600.2.0.CO;2>CrossRefGoogle Scholar
9. Mahalov, A., Moustaoui, M., Nicolaenko, B. & Tse, K. L. 2007 Computational studies of inertia-gravity waves radiated from upper tropospheric jets. Theor. Comput. Fluid Dyn. 21, 399–422.CrossRefGoogle Scholar
10. Moum, J., Hebert, D., Paulson, C. & Caldwell, D. 1992 Turbulence and internal waves at the equator. Part i: statistics from towed thermistors and a microstructure profiler. J. Phys. Oceanogr. 22, 1330–1345.2.0.CO;2>CrossRefGoogle Scholar
11. Pham, H. T. & Sarkar, S. 2010a Internal waves and turbulence in a stable stratified jet. J. Fluid Mech. 648, 297–324.CrossRefGoogle Scholar
12. Pham, H. T. & Sarkar, S. 2010b Transport and mixing of density in a continuously stratified shear layer. J. Turbul. 24 (11), 1–23.Google Scholar
13. 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
14. Philander, S. 1980 The equatorial undercurrent revisited. Annu. Rev. Earth Planet. Sci. 8, 191–204.CrossRefGoogle Scholar
15. Shih, L. H., Koseff, J. R., Ivey, G. N. & Ferziger, J. H. 2005 Parameterization of turbulent fluxes and scales using homogeneous sheared stably stratified turbulence simulations. J. Fluid Mech. 525, 193–214.CrossRefGoogle Scholar
16. Skyllingstad, E. & Denbo, D. 1994 The role of internal gravity waves in the equatorial current system. J. Phys. Oceanogr. 24, 2093–2110.2.0.CO;2>CrossRefGoogle Scholar
17. Smyth, W. & Moum, J. 2002 Shear instability and gravity wave saturation in an asymmetrically stratified jet. Dyn. Atmos. Oceans 35, 265–294.CrossRefGoogle Scholar
18. Smyth, W. D., Moum, J. N. & Nash, J. D. 2011 Narrowband oscillations in the upper equatorial ocean. Part II: properties of shear instabilities. J. Phys. Oceanogr. 41, 412–428.CrossRefGoogle Scholar
19. Sun, C., Smyth, W. & Moum, J. 1998 Dynamic instability of stratified shear flow in the upper equatorial pacfic. J. Geophys. Res. 103, 10323–10337.CrossRefGoogle Scholar
20. Sutherland, B. R. 2006 Rayleigh wave-internal wave coupling and internal wave generation above a model jet stream. J. Atmos. Sci. 63, 1042–1055.CrossRefGoogle Scholar
21. Sutherland, B. & Linden, P. 1998 Internal wave excitation from stratified flow over thin barrier. J. Fluid Mech. 377, 223–252.CrossRefGoogle Scholar
22. Taylor, J. R. & Sarkar, S. 2008 Stratification effects in a bottom Ekman layer. J. Phys. Oceanogr. 38, 2535–2555.CrossRefGoogle Scholar
23. Tsai, W., Chen, S. & Moeng, C. 2005 A numerical study on the evolution and structure of a stress-driven free-surface turbulent shear flow. J. Fluid Mech. 545, 163–192.Google Scholar
24. Tse, K. L., Mahalov, A., Nicolaenko, B. & Fernando, H. J. S. 2003 Quasi-equilibrium dynamics of shear-stratified turbulence in a model tropospheric jet. J. Fluid Mech. 496, 73–103.CrossRefGoogle Scholar
25. Wang, D., McWiliams, J. & Large, W. 1998 Large-Eddy simulation of the diurnal cycle of deep equatorial turbulence. J. Phys. Oceanogr. 28, 129–148.2.0.CO;2>CrossRefGoogle Scholar
26. Wang, D. & Muller, P. 2002 Effects of equatorial undercurrent shear on upper-ocean mixing and internal waves. J. Phys. Oceanogr. 32, 1041–1057.2.0.CO;2>CrossRefGoogle Scholar