Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-29T19:14:08.105Z Has data issue: false hasContentIssue false
  • English
  • Français

Effect of external turbulence on the evolution of a wake in stratified and unstratified environments

Published online by Cambridge University Press:  05 May 2015

Anikesh Pal  and
Sutanu Sarkar
Anikesh Pal
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 are performed to study the evolution of a towed stratified wake subject to external turbulence in the background. A field of isotropic turbulence is combined with an initial turbulent wake field and the combined wake is simulated in a temporally evolving framework similar to that of Rind & Castro (J. Fluid Mech., vol. 710, 2012a, p. 482). Simulations are performed for external turbulence whose initial level varies between zero and a moderate intensity of up to 7 % relative to the free stream and whose initial integral length scale is of the same order as that of the wake turbulence. A series of simulations are carried out at a Reynolds number of 10 000 and Froude number of 3. Background turbulence, especially at a level of 3 % or above, is found to have substantial quantitative effects in the stratified simulations. Turbulence inside the wake increases due to the entrainment of external turbulence, and the energy transfer through turbulent production from mean to fluctuating velocity also increases, leading to reduced mean velocity. The profiles of normalized mean and turbulence quantities in the stratified wake exhibit little change in the vertical direction but the horizontal spread increases in comparison to the case with undisturbed background. The spatial organization of the internal wave field is disrupted even at the 1 % level of external turbulence. However, key characteristics of stratified wakes such as the formation of coherent pancake vortices and the long lifetime of the mean wake are robust to the presence of fluctuations in the background. A corresponding series of simulations for the unstratified situation is carried out at the same Reynolds number of 10 000 and with similar levels of external turbulence. The change of mean and turbulence statistics is found to be weaker in the unstratified cases compared with the corresponding stratified cases and also weaker relative to that found by Rind & Castro (J. Fluid Mech., vol. 710, 2012a, p. 482) at a similar level of external turbulence relative to the free stream and similar integral length scale. Theoretical arguments and additional simulations are provided to show that the level of external turbulence relative to wake turbulence (dissimilar between the present investigation and Rind & Castro (J. Fluid Mech., vol. 710, 2012a, p. 482)) is a key governing parameter in both stratified and unstratified backgrounds.

JFM classification

Turbulent Flows: Stratified turbulence Turbulent Flows: Turbulent Flows Wakes/Jets: Wakes/Jets
Type
Papers
Information
Journal of Fluid Mechanics , Volume 772 , 10 June 2015 , pp. 361 - 385
Check for updates
Copyright
© 2015 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, 104–139.Google Scholar
Amoura, Z., Roig, V., Risso, F. & Billet, A.-M. 2010 Attenuation of the wake of a sphere in an intense incident turbulence with large length scales. Phys. Fluids 22, 055105.Google Scholar
Bagchi, P. & Balachandar, S. 2004 Response of the wake of an isolated particle to an isotropic turbulent flow. J. Fluid Mech. 518 (1), 95–123.Google Scholar
Bazilevs, Y., Yan, J., deStadler, M. & Sarkar, S. 2014 Computation of the flow over a sphere at $\mathit{Re}=3700$ : a comparison of uniform and turbulent inflow conditions. Trans. ASME J. Appl. Mech. 81, 121003.Google Scholar
Bevilaqua, P. M. & Lykoudis, P. S. 1978 Turbulence memory in self-preserving wakes. J. Fluid Mech. 89 (3), 589–606.Google Scholar
Bonneton, P., Chomaz, J. M., Hopfinger, E. & Perrier, M. 1996 The structure of the turbulent wake and the random internal wave field generated by a moving sphere in a stratified fluid. Dyn. Atmos. Oceans 23 (1), 299–308.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, 23–40.Google Scholar
Bonnier, M. & Eiff, O. 2002 Experimental investigation of the collapse of a turbulent wake in a stably stratified fluid. Phys. Fluids 14, 791–801.CrossRefGoogle Scholar
Brucker, K. A. & Sarkar, S. 2007 Evolution of an initially turbulent stratified shear layer. Phys. Fluids 19, 105105.CrossRefGoogle Scholar
Brucker, K. A. & Sarkar, S. 2010 A comparative study of self-propelled and towed wakes in a stratified fluid. J. Fluid Mech. 652, 373–404.CrossRefGoogle Scholar
Chomaz, J. M., Bonneton, P. & Hopfinger, E. J. 1993a The structure of the near wake of a sphere moving horizontally in a stratified fluid. J. Fluid Mech. 254 (1), 1–21.Google Scholar
Diamessis, P. J., Spedding, G. R. & Domaradzki, J. A. 2011 Similarity scaling and vorticity structure in high Reynolds number stably stratified turbulent wakes. J. Fluid Mech. 671, 52–95.Google Scholar
Dommermuth, D. G., 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
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.Google Scholar
Gilreath, H. E. & Brandt, A. 1985 Experiments on the generation of internal waves in a stratified fluid. AIAA J. 23 (5), 693–700.CrossRefGoogle Scholar
Gourlay, M. J., Arendth, S. C., Fritts, D. C. & Werne, J. 2001 Numerical modeling of initially turbulent wakes with net momentum. Phys. Fluids A 13, 3783–3802.Google Scholar
Legendre, D., Merle, A. & Magnaudet, J. 2006 Wake of a spherical bubble or a solid sphere set fixed in a turbulent environment. Phys. Fluids 18, 048102.Google Scholar
Lin, J. T. & Pao, Y. H. 1979 Wakes in stratified fluids. Annu. Rev. Fluid Mech. 11, 317–338.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.Google Scholar
Pal, A., de Stadler, M. B. & Sarkar, S. 2013 The spatial evolution of fluctuations in a self-propelled wake compared to a patch of turbulence. Phys. Fluids 25, 095106.CrossRefGoogle Scholar
Redford, J. A., Castro, I. P. & Coleman, G. N. 2012 On the universality of turbulent axisymmetric wakes. J. Fluid Mech. 710, 419–452.Google Scholar
Redford, J. A. & Coleman, G. N.2007 Numerical study of turbulent wakes in background turbulence. In 5th International Symposium on Turbulence and Shear Flow Phenomena (TSFP-5 Conference), Munich, Germany, pp. 561–566.Google Scholar
Rind, E. & Castro, I. P. 2012a Direct numerical simulation of axisymmetric wakes embedded in turbulence. J. Fluid Mech. 710, 482–504.Google Scholar
Rind, E. & Castro, I. P. 2012b On the effects of free-stream turbulence on axisymmetric disc wakes. Exp. Fluids 53 (2), 301–318.Google Scholar
Rodriguez, I., Borelli, Y., Lehmkuhl, O., Perez Segarra, C. D. & Assensi, O. 2011 Direct numerical simulation of the flow over a sphere at $\mathit{Re}=3700$ . J. Fluid Mech. 679, 263–287.Google Scholar
Spedding, G. R., Browand, F. K. & Fincham, A. M. 1996a The long-time evolution of the initially turbulent wake of a sphere in a stable stratification. Dyn. Atmos. Oceans 23 (1–4), 171–182.Google Scholar
de Stadler, M. B. & Sarkar, S. 2012 Simulation of a propelled wake with moderate excess momentum in a stratified fluid. J. Fluid Mech. 692, 28–52.Google Scholar
Uberoi, M. S. & Freymuth, P. 1970 Turbulent energy balance and spectra of axisymmetric wake. Phys. Fluids 13 (9), 2205–2210.CrossRefGoogle Scholar
Wu, J.-S. & Faeth, G. M. 1994 Sphere wakes at moderate Reynolds numbers in a turbulent environment. AIAA J. 32 (3), 535–541.CrossRefGoogle Scholar
Wu, J.-S. & Faeth, G. M. 1995 Effect of ambient turbulence intensity on sphere wakes at intermediate Reynolds number. AIAA J. 33 (1), 171–173.CrossRefGoogle Scholar