A simple finite-dimensional mechanism is described that appears to be responsible for the presence of bursts near onset of primary instability in a number of fluid systems. The manifestation of the mechanism differs dramatically from system to system, but the mechanism is common to all of them. The geometrical ideas behind the mechanism are discussed, and the results applied to three systems, (...

We design several implicit asymptotic-preserving schemes for the linear semiconductor Boltzmann equation with a diffusive scaling, which lead asymptotically to the implicit discretizations of the drift-diffusion equation. The constructions are based on a stiff relaxation step and a stiff convection step obtained by splitting the system equal to the model equation. The one space dimensional sche...

-The ratio of the fluxes of heat and salt across a diffusive interface is investigated on the premise that there are two contributions to the flux of each component. These contributions arise from the two transport mechanisms which can operate at a diffusive interface, viz. double-diffusive convection and turbulent entrainment. Estimates of the fluxes are provided for each process, and their co...

The diffusive (or semiconvection) regime of double-diffusive convection (DDC) is widespread in the polar oceans, generating ‘‘staircases’’ consisting of high-gradient interfaces of temperature and salinity separated by convectively mixed layers. Using two-dimensional direct numerical simulations, support is provided for a previous theory that rotation can influence DDC heat fluxes when the thic...

Based on radiation hydrodynamics modeling of stellar convection zones, a diffusion scheme has been devised describing the downward penetration of convective motions beyond the Schwarzschild boundary (overshoot) into the radiative interior. This scheme of exponential diffusive overshoot has already been successfully applied to AGB stars. Here we present an application to the Sun in order to dete...