A Non-Linear Eddy Viscosity Model for Turbulent Natural Convection in Geophysical Flows
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 32794
A Non-Linear Eddy Viscosity Model for Turbulent Natural Convection in Geophysical Flows

Authors: J. P. Panda, K. Sasmal, H. V. Warrior


Eddy viscosity models in turbulence modeling can be mainly classified as linear and nonlinear models. Linear formulations are simple and require less computational resources but have the disadvantage that they cannot predict actual flow pattern in complex geophysical flows where streamline curvature and swirling motion are predominant. A constitutive equation of Reynolds stress anisotropy is adopted for the formulation of eddy viscosity including all the possible higher order terms quadratic in the mean velocity gradients, and a simplified model is developed for actual oceanic flows where only the vertical velocity gradients are important. The new model is incorporated into the one dimensional General Ocean Turbulence Model (GOTM). Two realistic oceanic test cases (OWS Papa and FLEX' 76) have been investigated. The new model predictions match well with the observational data and are better in comparison to the predictions of the two equation k-epsilon model. The proposed model can be easily incorporated in the three dimensional Princeton Ocean Model (POM) to simulate a wide range of oceanic processes. Practically, this model can be implemented in the coastal regions where trasverse shear induces higher vorticity, and for prediction of flow in estuaries and lakes, where depth is comparatively less. The model predictions of marine turbulence and other related data (e.g. Sea surface temperature, Surface heat flux and vertical temperature profile) can be utilized in short term ocean and climate forecasting and warning systems.

Keywords: Eddy viscosity, turbulence modeling, GOTM, CFD.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1315899

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 894


[1] Boussinesq, J., “The´orie de l’E´ coulementTourbillant,” Mem. Pre´sente´s par Divers Savants Acad. Sci. Inst. Fr. 1877; 23: pp. 46–50.
[2] Jones, W. P. and Launder, B. E., "The Prediction of Laminarization with a Two-equation Model of Turbulence", Int. J. Heat Mass Transfer 1972; 15: 301~314.
[3] Launder, B. E., and Spalding, D. B., “The Numerical Computation of Turbulent Flows,” Comput. Methods Appl. Mech. Eng. 1973; 3(2): pp. 269–289.
[4] Mellor, G. L., and Yamada, T., “Development of a Turbulence Closure Model for Geophysical Fluid Problems,” Rev. Geophys. Space Phys. 1982; 20(4): pp. 851–875.
[5] Wilcox, D. C., "Reassessment of the Scale-Determining Equation for Advanced Turbulence Models", AIAA J. 1988; 26-11: 1299~1310
[6] Kantha, L. H., and Clayson, C. A., “An Improved Mixed Layer Model for Geophysical Applications,” J. Geophys. Res.99- 1994; pp. 25235–25266.
[7] Burchard, H., Bolding, K., and Villarreal, M. R., “GOTM-A General Ocean Tubulence Model, Theory, Implementation and Test cases,” Technical Report EUR 18745- 1999; EN, European Commission, 3.
[8] Maity S., Warrior H., ''Reynolds Stress Anisotropy Based Turbulent Eddy Viscosity Model Applied to Numerical Ocean Models,'' ASME Journal of Fluids Engineering 2011; Vol. 133: 064501-1.
[9] Craft, T. J., Launder, B. E., and Suga, K., “Development and application of a cubic eddy viscosity model of turbulence,” Int. J. Heat FluidFlow 1996; 17: pp. 108–115.
[10] Sasmal K., Maity S., Warrior H., "On the application of a new formulation of nonlinear eddy viscosity based on anisotropy to numerical ocean models," Journal of Turbulence 2014; Vol. 15: No. 8, 516–539.
[11] Sasmal K., Maity S., Warrior H., " Modeling of turbulent dissipation and its validation in periodically stratified region in the Liverpool Bay and in the North Sea," Ocean Dynamics 2015, 65: 969–988.
[12] Craft, T. J., Launder, B. E., and Suga, K., “Prediction of Turbulent Transitional Phenomena with a Non-linear Eddy Viscosity Model,” Int. J. Heat Fluid Flow 1997, 18(1): pp. 15–28.
[13] Umlauf, S., Burchard, H., "Second-order turbulence closure models for geophysicalboundary layers. A review of recent work," Continental Shelf Research 2005; 25: pp. 795–827.
[14] Burchard, H., Bolding, K., "Comparative analysis of four second-moment turbulence closure models for the oceanic mixed layer". J. Phys. Oceanogr. 2001; 31: 1943–1968.
[15] Paulson, C. A., and J. J. Simpson, "Irradiance measurements in the upper ocean. J. Phys. Oceanogr. 1977; 7: 952–956.
[16] Jerlov, N.G., Marine Optics, Elsevier Oceanography Series 1968; 5.
[17] Kondo, J., "Air–sea bulk transfer coefficients in diabatic conditions". Bound.-Layer Meteor. 1975; 9: 91–112.
[18] Burchard, H., Bolding, K., Rippeth, T.P., Stips, A., Simpson, J.H., Sundermann, J., "Microstructure of turbulence in the Northern North Sea: a comparative studyof observations and model simulations", Journal of Sea Research 2002; 47: 223–238.
[19] Canuto VM, Howard A, Cheng Y, Dubovikov MS., "One-point closure model. Momentum and heat vertical diffusivities". J. Phys. Oceanogr. 2001; 31:1413–26.
[20] Speziale, C. G., Sarkar, S. and Gatski, T. B., "Modeling the pressure-strain correlation of turbulence: an invariant dynamical systems approach ". Journal of Fluid Mechanics 1991; 227: 245-272.
[21] Sarkar, S., and Speziale, C., “A Simple Non-Linear Model for Return to Isotropy in Turbulence” Phys. Fluids 1990; A 2: pp. 84–93.
[22] Warrior, H. V., Mathews, S., Maity, S., Sasmal, K., " An Improved Model for the Return to Isotropy of Homogeneous Turbulence", ASME Journal of Fluids Engineering 2014; Vol. 136: 034501-1.
[23] Breuer, S., Oberlack, M., Peters, N., "Non-Isotropic Length Scales During the Compression Stroke of a Motored Piston Engine", Flow, Turbulence and Combustion 2005; 74: pp 145–167.
[24] Panda J. P., Warrior, H. V., Maity, S., Mitra A., Sasmal, K., An improved model including length scale anisotropy for the pressure strain correlation of turbulence", ASME Journal of Fluids Engineering 2017; Vol. 139: 044503-1.
[25] Lumley, J. L., “Computational Modeling of Turbulent Flows,” Adv. Appl. Mech. 1978; 18: pp. 123–175.
[26] Patankar, S. V., Numerical Heat Transfer and Fluid Flow, McGraw-Hill, New York, 1980.