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Pulsating turbulence in a marginally unstable stratified shear flow

Published online by Cambridge University Press:  01 June 2017

W. D. Smyth Open the ORCID record for W. D. Smyth [Opens in a new window] ,
H. T. Pham ,
J. N. Moum  and
S. Sarkar Open the ORCID record for S. Sarkar [Opens in a new window]
W. D. Smyth*
Affiliation:
College of Earth, Ocean and Atmospheric Sciences, Oregon State University, Corvallis, OR 97330, USA
H. T. Pham
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, San Diego, CA 92093, USA
J. N. Moum
Affiliation:
College of Earth, Ocean and Atmospheric Sciences, Oregon State University, Corvallis, OR 97330, USA
S. Sarkar
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, San Diego, CA 92093, USA
*
†Email address for correspondence: [email protected]
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Abstract

We describe a simple model for turbulence in a marginally unstable, forced, stratified shear flow. The model illustrates the essential physics of marginally unstable turbulence, in particular the tendency of the mean flow to fluctuate about the marginally unstable state. Fluctuations are modelled as an oscillatory interaction between the mean shear and the turbulence. The interaction is made quantitative using empirically established properties of stratified turbulence. The model also suggests a practical way to estimate both the mean kinetic energy of the turbulence and its viscous dissipation rate. Solutions compare favourably with observations of fluctuating ‘deep cycle’ turbulence in the equatorial oceans.

JFM classification

Geophysical and Geological Flows: Air/sea interactions Turbulent Flows: Shear layer turbulence Turbulent Flows: Stratified turbulence
Type
Papers
Information
Journal of Fluid Mechanics , Volume 822 , 10 July 2017 , pp. 327 - 341
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Copyright
© 2017 Cambridge University Press 

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References

Alford, M. H. & Whitmont, M. 2007 Seasonal and spatial variability of near-inertial kinetic energy from historical moored velocity records. J. Phys. Oceanogr. 37, 2022–2037.CrossRefGoogle Scholar
Canuto, V. M., Howard, A. M., Cheng, Y., Muller, C. J., Leboissetier, A. & Jayne, S. R. 2010 Ocean turbulence, III: New GISS vertical mixing scheme. Ocean Model. 34, 70–91.Google Scholar
Crawford, W. R. 1982 Pacific equatorial turbulence. J. Phys. Oceanogr. 12, 1137–1149.2.0.CO;2>CrossRefGoogle Scholar
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 318, 140–144.CrossRefGoogle Scholar
Itsweire, E. C., Koseff, J. R., Briggs, D. A. & Ferziger, J. H. 1993 Turbulence in stratified shear flows: implications for interpreting shear-induced mixing in the ocean. J. Phys. Oceanogr. 23, 1508–1522.Google Scholar
Ivey, G. N., Winters, K. B. & Koseff, J. R. 2008 Density stratification, turbulence, but how much mixing? Annu. Rev. Fluid Mech. 40, 169–184.Google Scholar
Jacobitz, F. G., Sarkar, S. & Van Atta, C. W. 1997 Direct numerical simulations of the turbulence evolution in a uniformly sheared and stratified flow. J. Fluid Mech. 342, 231–261.CrossRefGoogle Scholar
Luznik, L., Zhu, W., Gurka, R., Katz, J., Nimmo Smith, W. A. M. & Osborn, T. R. 2007 Distribution of energy spectra, Reynolds stresses, turbulence production, and dissipation in a tidally driven bottom boundary layer. J. Phys. Oceanogr. 37 (6), 1527–1550.Google Scholar
Mater, B. D. & Venayagamoorthy, S. K. 2014 A unifying framework for parameterizing stably stratified shear-flow turbulence. Phys. Fluids 26 (3), 036601.Google Scholar
McPhaden, M. J. 1995 The tropical atmosphere ocean array is completed. Am. Met. Soc. Bull. 76, 739–741.Google Scholar
Moum, J. N. 1996a Efficiency of mixing in the main thermocline. J. Geophys. Res. 101 (C5), 12057–12069.Google Scholar
Moum, J. N. 1996b Energy-containing scales of turbulence in the ocean thermocline. J. Geophys. Res. 101 (C6), 14095–14109.CrossRefGoogle Scholar
Moum, J. N. & Caldwell, D. R. 1985 Local influences on shear flow turbulence in the equatorial ocean. Science 230, 315–316.Google Scholar
Moum, J. N., Gregg, M. C., Lien, R.-C. & Carr, M. E. 1995 Comparison of turbulence kinetic energy dissipation rate estimates from two ocean microstructure profilers. J. Atmos. Ocean. Technol. 12 (2), 346–366.Google Scholar
Moum, J. N., Hebert, D., Paulson, C. A. & Caldwell, D. R. 1992 Turbulence and internal waves at the equator. Part I: Statistics from towed thermistor chains and a microstructure profiler. J. Phys. Oceanogr. 22, 1330–1345.Google Scholar
Moum, J. N., Lien, R.-C., Perlin, A., Nash, J. D., Gregg, M. C. & Wiles, P. J. 2009 Sea surface cooling at the equator by subsurface mixing in tropical instability waves. Nat. Geosci. 2, 761–765.Google Scholar
Osborn, T. R. 1980 Estimates of the local rate of vertical diffusion from dissipation measurements. J. Phys. Oceanogr. 10, 83–89.Google Scholar
Peters, H., Gregg, M. C. & Sanford, T. B. 1995 On the parameterization of equatorial turbulence: effect of finescale variations below the range of the diurnal cycle. J. Geophys. Res. 100, 18333–18348.CrossRefGoogle Scholar
Pham, H. T., Sarkar, S. & Winters, K. 2013 Large-eddy simulation of deep-cycle turbulence in an upper-equatorial undercurrent model. J. Phys. Oceanogr. 43 (11), 2490–2502.Google Scholar
Pollard, R. T. & Millard, R. C. 1970 Comparison between observed and simulated wind-generated inertial oscillations. In Deep Sea Research and Oceanographic Abstracts, vol. 17, pp. 813–816, IN5, 817–821. Elsevier.Google Scholar
Pollard, R. T., Rhines, P. B. & Thompson, R. O. R. Y. 1972 The deepening of the wind-mixed layer. Geophys. Fluid Dyn. 4 (1), 381–404.Google Scholar
Saddoughi, S. G. 1997 Local isotropy in complex turbulent boundary layers at high Reynolds number. J. Fluid Mech. 348, 201–245.Google Scholar
Saddoughi, S. G. & Veeravalli, S. V. 1994 Local isotropy in turbulent boundary layers at high Reynolds number. J. Fluid Mech. 268, 333–372.CrossRefGoogle Scholar
Schudlich, R. & Price, J. 1992 Diurnal cycles of current, temperature, and turbulent dissipation in a model of the equatorial upper ocean. J. Geophys. Res. 97, 5409–5422.CrossRefGoogle Scholar
Smyth, W. D. & Moum, J. N. 2000 Anisotropy of turbulence in stably stratified mixing layers. Phys. Fluids 12, 1343–1362.Google Scholar
Smyth, W. D. & Moum, J. N. 2013 Seasonal cycles of marginal instability and deep cycle turbulence in the eastern equatorial Pacific ocean. Geophys. Res. Lett. 40, 6181–6185.Google Scholar
Smyth, W. D., Moum, J. N., Li, L. & Thorpe, S. A. 2013 Diurnal shear instability, the descent of the surface shear layer, and the deep cycle of equatorial turbulence. J. Phys. Oceanogr. 43, 2432–2455.Google Scholar
Sun, C., Smyth, W. D. & Moum, J. N. 1998 Dynamic instability of stratified shear flow in the upper equatorial Pacific. J. Geophys. Res. 103, 10323–10337.CrossRefGoogle Scholar
Thorpe, S. A. & Liu, Z. 2009 Marginal instability? J. Phys. Oceanogr. 39, 2373–2381.Google Scholar
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow. Cambridge University Press.Google Scholar
Zervakis, V. & Levine, M. D. 1995 Near-inertial energy propagation from the mixed layer: theoretical considerations. J. Phys. Oceanogr. 25 (11), 2872–2889.Google Scholar