Hostname: page-component-745bb68f8f-l4dxg Total loading time: 0 Render date: 2025-02-05T08:00:17.549Z Has data issue: false hasContentIssue false
  • English
  • Français

A comparative study of self-propelled and towed wakes in a stratified fluid

Published online by Cambridge University Press:  12 April 2010

KYLE A. BRUCKER  and
SUTANU SARKAR
KYLE A. BRUCKER
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, San Diego, CA 92093, USA
SUTANU SARKAR*
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, San Diego, CA 92093, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Direct numerical simulations (DNS) of axisymmetric wakes with canonical towed and self-propelled velocity profiles are performed at Re = 50 000 on a grid with approximately 2 billion grid points. The present study focuses on a comparison between towed and self-propelled wakes and on the elucidation of buoyancy effects. The development of the wake is characterized by the evolution of maxima, area integrals and spatial distributions of mean and turbulence statistics. Transport equations for mean and turbulent energies are utilized to help understand the observations. The mean velocity in the self-propelled wake decays more rapidly than the towed case due to higher shear and consequently a faster rate of energy transfer to turbulence. Buoyancy allows a wake to survive longer in a stratified fluid by reducing the 〈u1′u3′〉 correlation responsible for the mean-to-turbulence energy transfer in the vertical direction. This buoyancy effect is especially important in the self-propelled case because it allows regions of positive and negative momentum to become decoupled in the vertical direction and decay with different rates. The vertical wake thickness is found to be larger in self-propelled wakes. The role of internal waves in the energetics is determined and it is found that, later in the evolution, they can become a dominant term in the balance of turbulent kinetic energy. The non-equilibrium stage, known to exist for towed wakes, is also shown to exist for self-propelled wakes. Both the towed and self-propelled wakes, at Re = 50000, are found to exhibit a time span when, although the turbulence is strongly stratified as indicated by small Froude number, the turbulent dissipation rate decays according to inertial scaling.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 652 , 10 June 2010 , pp. 373 - 404
Copyright
Copyright © Cambridge University Press 2010

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

Basak, S. 2005 Dynamics of stratified shear layers with horizontal shear. PhD thesis, University of California, San Diego, CA.CrossRefGoogle Scholar
Basak, S. & Sarkar, S. 2006 Dynamics of a stratified shear layer with horizontal shear. J. Fluid Mech. 568, 19–54.CrossRefGoogle Scholar
Bevilaqua, P. M. & Lykoudis, P. S. 1978 Turbulence memory in self-preserving wakes. J. Fluid Mech. 89 (3), 589–606.CrossRefGoogle Scholar
Bonnier, M., Bonneton, P. & Eiff, O. 1998 Far-wake of a sphere in a stably stratified fluid: characterization of the vortex structures. Appl. Sci. Res. 59, 269–281.CrossRefGoogle Scholar
Bonnier, M. & Eiff, O. 2002 Experimental investigation of the collapse of a turbulent wake in a stably stratified fluid. Phys. Fluids 14 (2), 791–801.CrossRefGoogle Scholar
Brethouwer, G., Billant, P., Lindborg, E. & Chomaz, J.-M. 2007 Scaling analysis and simulation of strongly stratified turbulent flow. J. Fluid Mech. 585, 343–368.CrossRefGoogle Scholar
Brucker, K. A. & Sarkar, S. 2007 Evolution of an initially turbulent stratified shear flow. Phys. Fluids 19 (10), 105105.CrossRefGoogle Scholar
Chomaz, J.-M., Bonneton, P. & Hopfinger, E. J. 1993 The structure of the near wake of a sphere moving horizontally in a stratified fluid. J. Fluid Mech. 254, 1–21.CrossRefGoogle 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 (1), 298–322.CrossRefGoogle Scholar
Diamessis, P. J. & Spedding, G. R. 2006 Scaling and structure of turbulent wakes at high Reynolds number. Proceedings of the Sixth International Symposium on Stratified Flows, 11–14 December, 2006, Perth, Australia.Google Scholar
Dommermuth, D., Rottman, J. W., Innis, G. E. & Novikov, E. A. 2002 Numerical simulation of the wake of a towed sphere in a weakly stratified fluid. J. Fluid Mech. 473, 83–101.CrossRefGoogle Scholar
Faure, T. & Robert, G. 1996 Turbulent kinetic energy balance in the wake of a self-propelled body. Exp. Fluids 21 (4), 268–274.CrossRefGoogle Scholar
Finson, M. L. 1975 Similarity behaviour of momentumless turbulent wakes. J. Fluid Mech. 71 (3), 465–479.CrossRefGoogle Scholar
Ghosal, S. & Rogers, M. M. 1997 A numerical study of self-similarity in a turbulent plane wake using large-eddy simulation. Phys. Fluids 9 (6), 1729–1739.CrossRefGoogle Scholar
Gourlay, M. J., Arendt, S. C., Fritts, D. C. & Werne, J. 2001 Numerical modelling of initially turbulent wakes with net momentum. Phys. Fluids 13 (12), 3783–3802.CrossRefGoogle Scholar
Gran, R. L. 1973 An Experiment on the wake of a propeller driven body. Tech. Rep. Rept. 20086-6006-RU-00. TRW Systems, Redondo Beach, CA.CrossRefGoogle Scholar
Higuchi, H. & Kubota, T. 1990 Axisymmetric wakes behind a slender body including zero-momentum configurations. Phys. Fluids A 2 (9), 1615–1623.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 (7), 1508–1522.2.0.CO;2>CrossRefGoogle Scholar
Lin, Q., Boyer, D. L. & Fernando, H. J. S. 1992 Turbulent wakes of linearly stratified flow past a sphere. Phys. Fluids A 4 (8), 1687–1696.CrossRefGoogle Scholar
Lin, J.-T. & Pao, Y.-H. 1974 The turbulent wake of a propeller-driven slender body in a stratified fluid. Tech. Rep. 14. Flow Research Inc.Google Scholar
Lin, J.-T. & Pao, Y.-H. 1979 Wakes in stratified fluids. Annu. Rev. Fluid Mech. 11, 317–338.CrossRefGoogle Scholar
Lofquist, K. E. B. & Purtell, P. 1984 Drag on a sphere moving horizontally through a stratified liquid. J. Fluid Mech. 148, 271–284.CrossRefGoogle Scholar
Meunier, P. & Spedding, G. R. 2006 Stratified propelled wakes. J. Fluid Mech. 552, 229–256.CrossRefGoogle Scholar
Moser, R. D., Rogers, M. M. & Ewing, D. W. 1998 Self-similarity of time-evolving plane wakes. J. Fluid Mech. 367, 255–289.CrossRefGoogle Scholar
Naudascher, E. 1965 Flow in the wake of self-propelled bodies and related sources of turbulence. J. Fluid Mech. 22 (4), 625–656.CrossRefGoogle Scholar
Pham, H., Sarkar, S. & Brucker, K. A. 2009 Dynamics of a stratified shear layer above a region of deep stratification. J. Fluid Mech. 630, 191–223.CrossRefGoogle Scholar
Riley, J. J. & de Bruyn Kops, S. M. 2003 Dynamics of turbulence strongly influenced by buoyancy. Phys. Fluids 15 (7), 2047–2059.CrossRefGoogle Scholar
Rogallo, R. S. 1981 Numerical experiments in homogeneous turbulence. Tech. Rep. TM-81315. NASA, Ames Research Center.Google Scholar
Rogers, M. M. & Moser, R. D. 1994 Direct simulation of a self-similar turbulent mixing layer. Phys. Fluids 6 (2), 903–923.CrossRefGoogle Scholar
Rottman, J. W., Dommermuth, D. G., Innis, G. E., O'Shea, T. T. & Novikov, E. 2003 Numerical simulation of wakes in a weakly stratified fluid. Proceedings of the 24th Symposium on Naval Hydrodynamics, 8–13 July, 2002, Fukuoka, Japan, pp. 517–533.Google Scholar
Sirviente, A. I. & Patel, V. C. 2000 Wake of a self-propelled body. Part 1. Momentumless wake. AIAA J. 38 (4), 613–619.CrossRefGoogle Scholar
Spedding, G. R. 1997 The evolution of initially-turbulent bluff body wakes of at high internal froude number. J. Fluid Mech. 337, 283–301.CrossRefGoogle Scholar
Spedding, G. R. 2001 Anisotropy in turbulence profiles of stratified wakes. Phys. Fluids 13 (8), 2361–2372.CrossRefGoogle Scholar
Spedding, G. R. 2002 Vertical structure in stratified wakes with high initial froude number. J. Fluid Mech. 454, 71–112.CrossRefGoogle Scholar
Spedding, G. R., Browand, F. K. & Fincham, A. M. 1996 The long-time evolution of the initially turbulent wake of a sphere in a stable stratification. Dyn. Atmos. Oceans 23 (1–4), 171–182.CrossRefGoogle Scholar
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. The MIT Press.CrossRefGoogle Scholar
Uberoi, M. S. & Freymuth, P. 1970 Turbulent energy balance and spectra of the axisymmetric wake. Phys. Fluids 13 (9), 2205–2210.CrossRefGoogle Scholar
Voropayev, S. I. & Fernando, H. J. S. 2009 Wakes of maneuvering body in stratified fluid. In Proceedings of the European Consortium for Mathematics in Industry (ECMI) 2008 Conference, 30 June–4 July, 2008, London.Google Scholar
Voropayev, S. I., McEachern, G. B., Fernando, H. J. S. & Boyer, D. L. 1999 Large vortex structures behind a manuvering body in stratified fluids. Phys. Fluids 11 (6), 1682–1684.CrossRefGoogle Scholar
Williamson, J. H. 1980 Low-storage Runge–Kutta schemes. J. Comput. Phys. 35, 48–56.CrossRefGoogle Scholar