An Improved Single Point Closure Model Based on Dissipation Anisotropy for Geophysical Turbulent Flows
This paper is a continuation of the work carried out by various turbulence modelers in Oceanography on the topic of oceanic turbulent mixing. It evaluates the evolution of ocean water temperature and salinity by the appropriate modeling of turbulent mixing utilizing proper prescription of eddy viscosity. Many modelers in past have suggested including terms like shear, buoyancy and vorticity to be the parameters that decide the slow pressure strain correlation. We add to it the fact that dissipation anisotropy also modifies the correlation through eddy viscosity parameterization. This recalibrates the established correlation constants slightly and gives improved results. This anisotropization of dissipation implies that the critical Richardson’s number increases much beyond unity (to 1.66) to accommodate enhanced mixing, as is seen in reality. The model is run for a couple of test cases in the General Ocean Turbulence Model (GOTM) and the results are presented here.
 Canuto et al, Vittorio M., et al. "Ocean turbulence. Part I: One-point closure model—Momentum and heat vertical diffusivities." Journal of Physical Oceanography 31.6 (2001): 1413-1426.
 Rodi, W. "Turbulence models and their application in hydraulics, Int." Association of Hydr. Res., Delft, The Netherlands (1980).
 Mellor, George L., and Tetsuji Yamada. "Development of a turbulence closure model for geophysical fluid problems." Reviews of Geophysics 20.4 (1982): 851-875.
 Fernando, Harindra JS. "Turbulent mixing in stratified fluids." Annual review of fluid mechanics 23.1 (1991): 455-493.
 Umlauf, Lars, and Hans Burchard. "Second-order turbulence closure models for geophysical boundary layers. A review of recent work." Continental Shelf Research 25.7 (2005): 795-827.
 Burchard Hans and Karsten Bolding. "Comparative analysis of four second-moment turbulence closure models for the oceanic mixed layer." Journal of Physical Oceanography 31.8 (2001): 1943-1968.
 Burchard, Hans, Ole Petersen, and Tom P. Rippeth. "Comparing the performance of the Mellor‐Yamada and the κ‐ε two‐equation turbulence models." Journal of Geophysical Research: Oceans 103.C5 (1998): 10543-10554.
 Launder, Brian Edward, and Dudley Brian Spalding. Mathematical models of turbulence. Academic press, 1972.
 Launder, B. E., G. Jr Reece, and W. Rodi. "Progress in the development of a Reynolds-stress turbulence closure." Journal of fluid mechanics 68.3 (1975): 537-566.
 Galperin, B., et al. "A quasi-equilibrium turbulent energy model for geophysical flows." Journal of the Atmospheric Sciences45.1 (1988): 55-62.
 Kantha, Lakshmi H., and Carol Anne Clayson. "An improved mixed layer model for geophysical applications." Journal of Geophysical Research: Oceans 99.C12 (1994): 25235-25266.
 Cheng, Y., V. M. Canuto et al, and A. M. Howard. "An improved model for the turbulent PBL." Journal of the Atmospheric sciences 59.9 (2002): 1550-1565.
 Speziale, Charles G., and Thomas B. Gatski. "Analysis and modeling of anisotropies in the dissipation rate of turbulence." Journal of Fluid Mechanics 344 (1997): 155-180.
 Hallbäck, Magnus, Johan Groth, and Arne V. Johansson. "An algebraic model for nonisotropic turbulent dissipation rate in Reynolds stress closures." Physics of Fluids A: Fluid Dynamics 2.10 (1990): 1859-1866.
 Oberlack, Martin. "Non-isotropic dissipation in non-homogeneous turbulence." Journal of Fluid Mechanics 350 (1997): 351-374.
 Warrior, Hari, et al. "An improved model for the return to isotropy of homogeneous turbulence." Journal of Fluids Engineering 136.3 (2014): 034501.
 Lumley, John L., and BejanKhajeh-Nouri. "Computational modeling of turbulent transport." Advances in Geophysics 18 (1975): 169-192.
 Pope, S. B. "A more general effective-viscosity hypothesis." Journal of Fluid Mechanics 72.2 (1975): 331-340.
 Lumley, John L. "Computational modeling of turbulent flows." Advances in applied mechanics 18 (1979): 123-176.
 Shih, Tsan-Hsing, and AamirShabbir. "Advances in modeling the pressure correlation terms in the second moment equations." Studies in Turbulence. Springer, New York, NY, 1992. 91-128.
 Panda, J. P., H. V. Warrior, S. Maity, A. Mitra, and K. Sasmal. "An improved model including length scale anisotropy for the pressure strain correlation of turbulence." Journal of Fluids Engineering 139, no. 4 (2017): 044503.
 Hanjalić, K., and B. E. Launder. "Contribution towards a Reynolds-stress closure for low-Reynolds-number turbulence." Journal of Fluid Mechanics 74.4 (1976): 593-610.
 Kebede, W., B. E. Launder, and B. A. Younis. "Large-amplitude periodic pipe flow-A second-moment closure study." 5th Symposium on Turbulent Shear Flows. 1985.
 Mansour, N. N., John Kim, and ParvizMoin. "Reynolds-stress and dissipation-rate budgets in a turbulent channel flow." Journal of Fluid Mechanics 194 (1988): 15-44.
 Durbin, P. A., and C. G. Speziale. "Local anisotropy in strained turbulence at high Reynolds numbers." Journal of Fluids Engineering 113.4 (1991): 707-709.
 Gilbert, N., and L. Kleiser. "Turbulence model testing with the aid of direct numerical simulation results." 8th Symposium on Turbulent Shear Flows, Volume 2. Vol. 2. 1991.
 Miles, John W. "On the stability of heterogeneous shear flows." Journal of Fluid Mechanics 10.4 (1961): 496-508.
 Howard, Louis N. "Note on a paper of John W. Miles." Journal of Fluid Mechanics 10.4 (1961): 509-512.
 Abarbanel, Henry DI, et al. "Richardson number criterion for the nonlinear stability of three-dimensional stratified flow." Physical Review Letters 52.26 (1984): 2352.
 MONIN, AS, and AM YAGLOW. "Statiscal Fluid Mechanics, Vols 1 &2., John Lumley." (1971).
 Martin, Paul J. "Simulation of the mixed layer at OWS November and Papa with several models." Journal of Geophysical Research: Oceans 90.C1 (1985): 903-916.
 Galperin, Boris, SemionSukoriansky, and Philip S. Anderson. "On the critical Richardson number in stably stratified turbulence." Atmospheric Science Letters 8.3 (2007): 65-69.
 Webster, C. A. G. "An experimental study of turbulence in a density-stratified shear flow." Journal of Fluid Mechanics 19.2 (1964): 221-245.
 Gerz, Thomas, Ulrich Schumann, and S. E. Elghobashi. "Direct numerical simulation of stratified homogeneous turbulent shear flows." Journal of Fluid Mechanics 200 (1989): 563-594
 Smyth, W. D., J. N. Moum, and D. R. Caldwell. "The efficiency of mixing in turbulent patches: Inferences from direct simulations and microstructure observations." Journal of Physical Oceanography 31.8 (2001): 1969-1992.
 Mashayek, A., C. P. Caulfield, and W. R. Peltier. "Time-dependent, non-monotonic mixing in stratified turbulent shear flows: implications for oceanographic estimates of buoyancy flux." Journal of Fluid Mechanics 736 (2013): 570-593.
 Burchard, Hans, Karsten Bolding, and Manuel R. Villarreal. GOTM, a general ocean turbulence model: theory, implementation and test cases. Space Applications Institute, 1999.