Diiusion in Turbulence

Diiusion and Weak Turbulence in Capillary Waves and in the Complex Ginzburg-landau Equation

Nonlinear Diiusion Control of Spatiotemporal Chaos in the Complex Ginzburg Landau Equation Typeset Using Revt E X

The role of nonlinear diiusion terms in the stability of periodic solutions in the regime of spatio temporal chaos is studied. The stabilization of unstable plane waves in the Complex Ginzburg Landau equation in weakly chaotic regimes such as phase turbulence and spatiotemporal intermittency or in strong chaotic ones like defect turbulence is demonstrated.

Monotone Difference Approximations Of BV Solutions To Degenerate Convection-Diffusion Equations

We consider consistent, conservative-form, monotone nite diierence schemes for nonlinear convection-diiusion equations in one space dimension. Since we allow the diiusion term to be strongly degenerate, solutions can be discontinuous and are in general not uniquely determined by their data. Here we choose to work with weak solutions that belong to the BV (in space and time) class and, in additi...

Viscous splitting approximation of mixed hyperbolic-parabolic convection-diffusion equations

We rst analyse a semi-discrete operator splitting method for nonlinear, possibly strongly degenerate, convection-diiusion equations. Due to strong degeneracy, solutions can be discontinuous and are in general not uniquely determined by their data. Hence weak solutions satisfying an entropy condition are sought. We then propose and analyse a fully discrete splitting method which employs a front ...

A Nonlocal Parabolic Equation Arising in a Turbulence Model

We consider a class of parabolic partial diierential equations with nonlocal diiusion coeecient. The study is motivated by a model of turbulent viscosity for a developed ow in a duct between parallel walls. Under rather more general conditions, we use a rescaling in t to prove existence and well-posedness for weak solutions. Sharp comparison estimates enable us to bound from below the spatial d...