Nonlinear stability results for plane Couette and Poiseuille flows.

We prove that the plane Couette and Poiseuille flows are nonlinearly stable if the Reynolds number is less than Re_{Orr}(2π/(λsinθ))/sinθ when a perturbation is a tilted perturbation in the direction x^{'} which forms an angle θ∈(0,π/2] with the direction i of the basic motion and does not depend on x^{'}. Re_{Orr} is the critical Orr-Reynolds number for spanwise perturbations which is computed for wave number 2π/(λsinθ), with λ being any positive wavelength. By taking the minimum with respect to λ, we obtain the critical energy Reynolds number for a fixed inclination angle and any wavelength: for plane Couette flow, it is Re_{Orr}=44.

Inclined convection in a porous Brinkman layer: linear instability and nonlinear stability.

In this article, we deal with thermal convection in an inclined porous layer modelled by the . Inertial effects are taken into account, and the physically significant rigid boundary conditions are imposed. This model is an extension of the work by Rees & Bassom (Rees & Bassom 2000 , 103-118 (doi:10.

Bidispersive-inclined convection.

A model is presented for thermal convection in an inclined layer of porous material when the medium has a bidispersive structure. Thus, there are the usual macropores which are full of a fluid, but there are also a system of micropores full of the same fluid. The model we employ is a modification of the one proposed by Nield & Kuznetsov (2006 , 3068-3074.