We study the homogenization of Lagrangian functionals of Hamilton-Jacobi equations (HJ) with quadratic nonlinearity and unbounded stationary ergodic random potential in R, d≥1. We show that homogenization holds if and only if the potential is bounded from above. When the potential is unbounded from above, homogenization breaks down, due to the almost sure growth of the running maxima of the ran...

A family of moment-conserving advection schemes in 1-D was introduced by van Leer in the mid 1970s. Of these, MUSCL advection is the best known. That advection scheme represents the advected function, which we will call a , by a linear function within each grid cell. The linear function is determined by the values of the first two moments of this density distribution within the cell, namely the...

The instability of the Kármán vortex street is revisited under a spatio-temporal perspective that allows the taking into account of the advection of the vortices by the external flow. We analyse a simplified point vortex model and show through numerical simulations of its linear impulse response that the system becomes convectively unstable above a certain critical advection velocity. This crit...

In the absence of diapycnal mixing processes, fluid parcels move in directions along which they do not encounter buoyant forces. These directions define the local neutral tangent plane. Because of the nonlinear nature of the equation of state of seawater, these neutral tangent planes cannot be connected globally to form a welldefined surface in three-dimensional space; that is, continuous ‘‘neu...

We present a theoretical study of nonlinear pattern selection mechanisms in a model of bounded reaction-diffusion-advection system. The model describes the activator-inhibitor type dynamics of a membrane reactor characterized by a differential advection and a single diffusion; the latter excludes any finite wave number instability in the absence of advection. The focus is on three types of diff...