We have shown in the previous lectures that the −vU ′ term in the u equation, that is ∂tu = −vU ′ + · · · , is the key term leading to momentum transport −uv ∼ vvU ′t and perturbation energy production −uv U ′ ∼ vv(U ′)2t > 0. This term is the redistribution of streamwise velocity that releases energy from the background shear to enable bifurcation to turbulent flow. However, in shear flows we ...

A two-dimensional double Multiple-Relaxation-Time thermal lattice Boltzmann method is used to simulate natural convection flows in differentially heated cavities. The buoyancy effects are considered under the Boussinesq assumption. Flow and temperature fields are respectively solved with nine and five discrete velocities models. Boundary conditions are implemented with the classical bounce-back...

Convective motions in a fluid layer are affected by its orientation with respect to the gravitational field. We investigate the long-term stability of a thermally stressed layer of a binary liquid mixture and show that pattern formation is strongly affected by marginal inclinations as small as a few milliradians. At small Rayleigh numbers, the mass transfer is dominated by the induced large sca...

Within basins that exhibit open-ocean convection, convectively mixed fluid is often observed in regions of upward-doming isopycnal surfaces, preconditioned by either cyclonic circulation and/or bottom topography. Here, an equilibrium statistical theory for open-ocean convection, developed in the context of two-layer heton models, is adapted to study the outcome of basinwide cooling events over ...

Outflows and convective motions in accretion flows have been intensively discussed recently in the context of advection-dominated accretion flow (ADAF) based on two-dimensional (2D) and three-dimensional (3D) hydrodynamical simulations. We, however, point that without proper treatments of the disk magnetic fields, a major source of viscosity, one can never derive general, firm conclusions conce...

We consider the effects of a shear on velocity fluctuations in a flow. The shear gives rise to a transient amplification that not only influences the amplitude of perturbations but also their time correlations. We show that, in the presence of white noise, time correlations of transversal velocity components are exponential and that correlations of the longitudinal components are exponential wi...

The general aspects of zonal flow physics, their formation, damping and interplay with quasi two dimensional turbulence are explained in the context of magnetized plasmas and quasi-geostrophic fluids with an emphasis on formation and selection of spatial patterns. General features of zonal flows as they appear in planetary atmospheres, rotating convection experiments and fusion plasmas are revi...