Coupling the Stokes and Navier-Stokes equations with two scalar nonlinear parabolic equations
Coupling the Stokes and Navier–Stokes equations with two scalar nonlinear parabolic equations
This work deals with a system of nonlinear parabolic equations arising in turbulence modelling. The unknowns are the components of the velocity field coupled with two scalar quantities and . The system presents nonlinear turbulent viscosity and nonlinear source terms of the form and lying in . Some existence results are shown in this paper, including -estimates and positivity for both and .
Numerical modelling of algebraic closure models of oceanic turbulent mixing layers
We introduce in this paper some elements for the mathematical and numerical analysis of algebraic turbulence models for oceanic surface mixing layers. In these models the turbulent diffusions are parameterized by means of the gradient Richardson number, that measures the balance between stabilizing buoyancy forces and destabilizing shearing forces. We analyze the existence and linear exponential asymptotic stability of continuous and discrete equilibria states. We also analyze the well-posedness...
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