Hostname: page-component-7c8c6479df-nwzlb Total loading time: 0 Render date: 2024-03-28T09:59:59.069Z Has data issue: false hasContentIssue false

Turbulent/non-turbulent interfaces in wakes in stably stratified fluids

Published online by Cambridge University Press:  16 May 2016

Tomoaki Watanabe*
Affiliation:
Department of Mechanical Engineering, University of Washington, Seattle, WA 98195, USA Department of Aerospace Engineering, Nagoya University, Nagoya 464-8603, Japan
James J. Riley
Affiliation:
Department of Mechanical Engineering, University of Washington, Seattle, WA 98195, USA
Stephen M. de Bruyn Kops
Affiliation:
Department of Mechanical and Industrial Engineering, University of Massachusetts Amherst, Amherst, MA 01003-9284, USA
Peter J. Diamessis
Affiliation:
School of Civil and Environmental Engineering, Cornell University, Ithaca, NY 14853, USA
Qi Zhou
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, UK
*
Email address for correspondence: tomoakiw@uw.edu

Abstract

We report on a study, employing direct numerical simulations, of the turbulent/non-turbulent interface of a wake in a stably stratified fluid. It is found that thresholds for both enstrophy and potential enstrophy are needed to identify the interface. Using conditional averaging relative to the location of the interface, various quantities of interest are examined. The thickness of the interface is found to scale with the Kolmogorov scale. From an examination of the Ozmidov and Kolmogorov length scales as well as the buoyancy Reynolds number, it is found that the buoyancy Reynolds number decreases and becomes of order 1 near the interface, indicating the suppression of the turbulence there by the stable stratification. Finally the overall rate of loss of energy due to internal wave radiation is found to be comparable to the overall rate of loss due to turbulent kinetic energy dissipation.

Type
Rapids
Copyright
© 2016 Cambridge University Press 

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

Abdilghanie, A. M. & Diamessis, P. J. 2013 The internal gravity wave field emitted by a stably stratified turbulent wake. J. Fluid Mech. 720, 104139.Google Scholar
Attili, A., Cristancho, J. C. & Bisetti, F. 2014 Statistics of the turbulent/non-turbulent interface in a spatially developing mixing layer. J. Turbul. 15 (9), 555568.Google Scholar
Bisset, D. K., Hunt, J. C. R. & Rogers, M. M. 2002 The turbulent/non-turbulent interface bounding a far wake. J. Fluid Mech. 451, 383410.Google Scholar
Bonneton, P., Chomaz, J. M. & Hopfinger, E. J. 1993 Internal waves produced by the turbulent wake of a sphere moving horizontally in a stratified fluid. J. Fluid Mech. 254, 2340.CrossRefGoogle Scholar
de Bruyn Kops, S. M. 2015 Classical turbulence scaling and intermittency in stably stratified Boussinesq turbulence. J. Fluid Mech. 775, 436463.Google Scholar
Corrsin, S. & Kistler, A. L. 1955 Free-stream boundaries of turbulent flows. NACA Tech. Rep. 1224, 10331064.Google Scholar
Diamessis, P. J., Domaradzki, J. A. & Hesthaven, J. S. 2005 A spectral multidomain penalty method model for the simulation of high Reynolds number localized incompressible stratified turbulence. J. Comput. Phys. 202, 298322.Google Scholar
Diamessis, P. J., Spedding, G. R. & Domaradzki, J. A. 2011 Scaling and structure of stably stratified wakes at high Reynolds number. J. Fluid Mech. 671, 5295.Google Scholar
Gibson, G. H. 1980 Fossil temperature, salinity, and vorticity in turbulence in the ocean. Marine Turbul. 221256.Google Scholar
Gilreath, H. E. & Brandtl, A. 1985 Experiments on the generation of internal waves in a stratified fluid. AIAA J. 23 (5), 693700.CrossRefGoogle Scholar
Hebert, D. A. & de Bruyn Kops, S. M. 2006 Predicting turbulence in flows with strong stable stratification. Phys. Fluids 18 (6), 110.Google Scholar
Holzner, M. & Lüthi, B. 2011 Laminar superlayer at the turbulence boundary. Phys. Rev. Lett. 106 (13), 134503.Google 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, 15081522.Google 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, 650658.2.0.CO;2>CrossRefGoogle Scholar
Lalescu, C. C., Meneveau, C. & Eyink, G. L. 2013 Synchronization of chaos in fully developed turbulence. Phys. Rev. Lett. 110, 084102.Google Scholar
Maffioli, A., Davidson, P. A., Dalziel, S. B. & Swaminathan, N. 2014 The evolution of a stratified turbulent cloud. J. Fluid Mech. 739, 229253.Google Scholar
Meunier, P., Diamessis, P. J. & Spedding, G. R. 2006 Self-preservation in stratified momentum wakes. Phys. Fluids 18, 106601.Google Scholar
Moum, J. N., Paulson, C. A. & Caldwell, D. R. 1992 Turbulence and internal waves at the equator. Part I: statistics from towed thermistors and a microstructure profiler. J. Phys. Oceanogr. 22, 13301345.Google Scholar
Munroe, J. R. & Sutherland, B. R. 2014 Internal wave energy radiated from a turbulent mixed layer. Phys. Fluids 26, 096604.Google Scholar
Muschinski, A., Chilson, P. B., Palmer, R. D., Hooper, D. A., Schmidt, G. & Steinhagen, H. 2001 Boundary-layer convection and diurnal variation of vertical-velocity characteristics in the free atmosphere. Q. J. R. Meteorol. Soc. 127, 423443.Google Scholar
Riley, J. J. & Lelong, M. P. 2000 Fluid motions in the presence of strong stable stratification. Annu. Rev. Fluid Mech. 32, 613657.CrossRefGoogle Scholar
Riley, J. J. & Lindborg, E. 2013 Recent progress in stratified turbulence. In Ten Chapters in Turbulence (ed. Davidson, P. A., Kaneda, Y. & Sreenivasan, K. R.), pp. 269317. Cambridge University Press.Google Scholar
Rohr, J. J., Itsweire, E. C., Helland, K. N. & Van Atta, C. W. 1988 Growth and decay of turbulence in a stably stratified shear flow. J. Fluid Mech. 195, 77111.Google Scholar
da Silva, C. B., Hunt, J. C. R., Eames, I. & Westerweel, J. 2014 Interfacial layers between regions of different turbulence intensity. Annu. Rev. Fluid Mech. 46, 567590.Google Scholar
Spedding, G. R. 1997 The evolution of initially turbulent bluff-body wakes at high internal Froude number. J. Fluid Mech. 337, 283301.Google Scholar
Spedding, G. R. 2002 Vertical structure in stratified wakes with high initial Froude number. J. Fluid Mech. 454, 71112.Google Scholar
Taveira, R. R., Diogo, J. S., Lopes, D. C. & da Silva, C. B. 2013 Lagrangian statistics across the turbulent–nonturbulent interface in a turbulent plane jet. Phys. Rev. E 88 (4), 043001.Google Scholar
Taveira, R. R. & da Silva, C. B. 2014 Characteristics of the viscous superlayer in shear free turbulence and in planar turbulent jets. Phys. Fluids 26 (2), 021702.Google Scholar
Taylor, J. R. & Sarkar, S. 2007 Internal gravity waves generated by a turbulent bottom Eckman layer. J. Fluid Mech. 590, 331354.CrossRefGoogle Scholar
Thorpe, S. A. 2005 The Turbulent Ocean. Cambridge University Press.Google Scholar
Watanabe, T., Sakai, Y., Nagata, K., Ito, Y. & Hayase, T. 2014 Vortex stretching and compression near the turbulent/nonturbulent interface in a planar jet. J. Fluid Mech. 758, 754785.Google Scholar
Watanabe, T., Sakai, Y., Nagata, K., Ito, Y. & Hayase, T. 2015 Turbulent mixing of passive scalar near turbulent and non-turbulent interface in mixing layers. Phys. Fluids 27 (8), 085109.Google Scholar
Watanabe, T., da Silva, C. B., Yasuhiko, S., Nagata, K. & Hayase, T. 2016 Lagrangian properties of the entrainment across turbulent/non-turbulent interface layers. Phys. Fluids 27, 031701.Google Scholar
Westerweel, J., Fukushima, C., Pedersen, J. M. & Hunt, J. C. R. 2009 Momentum and scalar transport at the turbulent/non-turbulent interface of a jet. J. Fluid Mech. 631, 199230.Google Scholar
Westerweel, J., Hofmann, T., Fukushima, C. & Hunt, J. C. R. 2002 The turbulent/non-turbulent interface at the outer boundary of a self-similar turbulent jet. Exp. Fluids 33 (6), 873878.CrossRefGoogle Scholar
Wijesekera, H. W. & Dillon, T. M. 1991 Internal waves and mixing in the upper equatorial Pacific ocean. J. Geophys. Res. 96 (C4), 71157125.Google Scholar
Wolf, M., Holzner, M., Lüthi, B., Krug, D., Kinzelbach, W. & Tsinober, A. 2013 Effects of mean shear on the local turbulent entrainment process. J. Fluid Mech. 731, 95116.Google Scholar
Zhou, Q.2015 Far-field evolution of turbulence-emitted internal waves and Reynolds number effects on a localized stratified turbulent flow, PhD thesis, Cornell University.Google Scholar