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Mixing in a stably stratified medium by horizontal shear near vertical walls

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Abstract

Stratified environmental flows near boundaries can have a horizontal mean shear component, orthogonal to the vertical mean density gradient. Vertical transport, against the stabilizing force of gravity, is possible in such situations if three-dimensional turbulence is sustained by the mean shear. A model problem, water with a constant mean density gradient flowing in a channel between parallel vertical walls, is examined here using the technique of large eddy simulation (LES). It is found that, although the mean shear is horizontal, the fluctuating velocity field has significant vertical shear and horizontal vorticity, thereby causing small-scale vertical mixing of the density field. The vertical stirring is especially effective near the boundaries where the mean shear is large and, consequently, the gradient Richardson number is small. The mean stratification is systematically increased between cases in our study and, as expected, the buoyancy flux correspondingly decreases. Even so, horizontal mean shear is found to be more effective than the well-studied case of mean vertical shear in inducing vertical buoyancy transport as indicated by generally larger values of vertical eddy diffusivity and mixing efficiency.

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References

  1. Arya, S.P.S.: Buoyancy effects in an horizontal flat-plane boundary layer. J. Fluid Mech. 68, 321 (1975)

    Google Scholar 

  2. Armenio, V., Piomelli, U.: A Lagrangian mixed subgrid-scale model in generalized coordinates. Flow Turbulence and Combustion 65, 51 (2000)

    Google Scholar 

  3. Armenio, V., Sarkar, S.: An investigation of stably-stratified turbulent channel flow using large eddy simulation. J. Fluid Mech. 459, 1 (2002)

    Google Scholar 

  4. Bardina, J., Ferziger, J.H., Reynolds, W.C.: Improved subgrid scale models for large eddy simulation. AIAA paper No. 80-1357 (1980)

  5. Diamessis, P.J., Nomura, K.K.: Interaction of vorticity, rate-of-strain, and scalar gradient in stratified homogeneous sheared turbulence. Phys. Fluids 12, 1166–1188 (2000)

    Google Scholar 

  6. Farmer, D.M., D’Asaro, E.A., Trevorrow, M.V., Dairiki, G.T.: Three-dimensional structure in a tidal convergence front. Continental Shelh Res. 15, 1649–1673 (1995)

    Google Scholar 

  7. Falcomer, L., Armenio, V.: Large-eddy simulation of secondary flow over longitudinally-ridged walls. J. Turbulence 3, 008 (2002)

    Google Scholar 

  8. Germano, M., Piomelli, U., Moin, P., Cabot, W.H.: A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A 3, 1760 (1991)

    Google Scholar 

  9. Gerz, T., Schumann, U., Elghobashi, S.E.: Direct numerical simulation of stratified homogeneous turbulent shear flows. J. Fluid Mech. 200, 563 (1989)

    Google Scholar 

  10. Holt, S.E., Koseff, J.R., Ferziger, J.H.: A numerical study of the evolution and structure of homogeneous stably stratified sheared turbulence. J. Fluid Mech. 237, 499 (1992)

    Google Scholar 

  11. Itsweire, E.C., Koseff, J.R., Briggs, D.A., Ferziger, J.H.: Turbulence in stratified shear flows: implications for interpreting shear-induced mixing in the ocean. J. Phys. Oceanogr. 23, 1508–1522 (1993)

    Google Scholar 

  12. Jacobitz, F.G., Sarkar, S., Van Atta, C.W.: Direct numerical simulations of the turbulence evolution in a uniformly sheared and stably stratified flow. J. Fluid Mech. 342, 231 (1997)

    Google Scholar 

  13. Jacobitz, F.G., Sarkar, S.: The effect of nonvertical shear on turbulence in a stably stratified medium. Phys. Fluids 10, 1158 (1999)

    Google Scholar 

  14. Jacobitz, F.G., Sarkar, S.: Turbulent Mixing in a Vertically Stably Stratified Fluid with Uniform Horizontal Shear. Flow, Turbulence and Combustion 63, 343–360 (2000)

    Google Scholar 

  15. Kaltenbach, H.-J., Gerz, T., Schumann, U.: Large-eddy simulation of homogeneous turbulence and diffusion in stably stratified shear flow. J. Fluid Mech. 280, 1 (1994)

    Google Scholar 

  16. Komori, S., Ueda, H., Ogino, F., Mizushina, T.: Turbulent structure in stably stratified open-channel flow. J. Fluid Mech. 130, 13 (1983)

    Google Scholar 

  17. Koop, G., Browand, F.K.: Instability and turbulence in stratified fluids with shear. J. Fluid Mech. 93, 135–159 (1979)

    Google Scholar 

  18. Lu, Y., Lueck, R.G., Huang, D.: Turbulence characteristics in a tidal channel J. Phys. Oceanogr. 30, 855–867 (2000)

    Google Scholar 

  19. Lueck, R.G., Mudge, T.D.: Topographically induced mixing around a shallow seamount. Science 276, 1831–1833 (1997)

    Google Scholar 

  20. Mason, P.J., Derbyshire, S.H.: Large eddy simulation of the stably-stratified atmospheric boundary layer. Boundary-Layer Meteorology 53, 117–162 (1990)

    Google Scholar 

  21. Matsubara, K., Kobayashi, M., Maekawa, H.: Direct numerical simulation of a turbulent channel flow with a linear spanwise mean temperature gradient. Int. J. Heat Transfer 41, 3627 (1998)

    Google Scholar 

  22. Miles, J.W.: On the stability of heterogeneous shear flows. J. Fluid Mech. 10, 496 (1961)

    Google Scholar 

  23. Moser, R.D., Kim, J., Mansour, N.M.: Direct numerical simulation of turbulent channel flow up to Reτ=590. Phys. Fluids 11, 943 (1999)

    Google Scholar 

  24. Osborn, T.R.: Estimates of the local rate of vertical diffusion from dissipation measurements. J. Phys. Oceanogr. 10, 83–89 (1980)

    Google Scholar 

  25. Piat, J.-F., Hopfinger, E.J.: A boundary layer topped by a density interface. J. Fluid Mech. 113, 411 (1981)

    Google Scholar 

  26. Piccirillo, P.S., Van Atta, C.W.: The evolution of a uniformly sheared thermally stratified turbulent flow. J. Fluid Mech. 334, 61 (1995)

    Google Scholar 

  27. Rohr, J.J., Itsweire, E.C., Helland, K.N., Van Atta, C.N.: Growth and decay of turbulence in a stably stratified shear flow. J. Fluid Mech. 195, 77 (1988)

    Google Scholar 

  28. Sarkar, S.: Turbulence anisotropy in stratified uniform shear flow. Fifth Intl. Symposium on Stratified Flows, Vancouver, G.A. Lawrence, R. Pieters, N. Yonemitsu (eds.), 1245–1250 (2000)

  29. Schumann, U., Gerz, T.: Turbulent mixing in stably stratified shear flows. J. Appl. Meteor. 34, 33 (1995)

    Google Scholar 

  30. Smagorinsky, J.: General circulation experiments with the primitive equations. I The basic experiment. Monthly Weather Review 91, 99 (1963)

    Google Scholar 

  31. Smyth, W.D., Moum, J.N.: Length scales of turbulence in stably stratified mixing layers. Phys. Fluids 12, 1327–1342 (2000)

    Google Scholar 

  32. Stacey, M.T., Monismith, S.G., Burau, J.R.: Observations of turbulence in a partially stratified estuary. J. Phys. Oceanogr. 29, 1950–1970 (1999)

    Google Scholar 

  33. Staquet, C.: Two-dimensional secondary instabilities in a strongly stratified shear layer. J. Fluid Mech. 296, 73–126 (1995)

    Google Scholar 

  34. Strang, E.J., Fernando, H.J.S.: Entrainment and mixing in stratified shear flows. J. Fluid Mech. 428, 349–386 (2001)

    Google Scholar 

  35. Thorpe, S.A.: Experiments on instability and turbulence in a stratified shear flow. J. Fluid Mech. 61, 731–752 (1973)

    Google Scholar 

  36. Turner, J.S.: Buoyancy effects in fluids. Cambridge University Press, 368 pp. /1973)

  37. Zang, Y., Street, R.L., Koseff, J.: A non-staggered grid, fractional step method for the time-dependent incompressible Navier–Stokes equation in curvilinear coordinates. J. Comput. Phys. 114, 18 (1994)

    Google Scholar 

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Authors and Affiliations

  1. Dipartimento di Ingegneria Civile, Università degli Studi di Trieste, Trieste, Piazzale Europa 1, 34127, Italy

    Vincenzo Armenio

  2. Department of Mechanical and Aerospace Engineering, University of California San Diego, 9500 Gilman drive, La Jolla, USA

    Sutanu Sarkar

Authors
  1. Vincenzo Armenio
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  2. Sutanu Sarkar
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Correspondence to Sutanu Sarkar.

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Y. Zhou

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Armenio, V., Sarkar, S. Mixing in a stably stratified medium by horizontal shear near vertical walls. Theoret Comput Fluid Dynamics 17, 331–349 (2004). https://doi.org/10.1007/s00162-004-0121-9

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  • DOI: https://doi.org/10.1007/s00162-004-0121-9

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