Internal gravity waves in the energy and flux budget turbulence-closure theory for shear-free stably stratified flows.

We have advanced the energy and flux budget turbulence closure theory that takes into account a two-way coupling between internal gravity waves (IGWs) and the shear-free stably stratified turbulence. This theory is based on the budget equation for the total (kinetic plus potential) energy of IGWs, the budget equations for the kinetic and potential energies of fluid turbulence, and turbulent fluxes of potential temperature for waves and fluid flow. The waves emitted at a certain level propagate upward, and the losses of wave energy cause the production of turbulence energy. We demonstrate that due to the nonlinear effects more intensive waves produce more strong turbulence, and this, in turn, results in strong damping of IGWs. As a result, the penetration length of more intensive waves is shorter than that of less intensive IGWs. The anisotropy of the turbulence produced by less intensive IGWs is stronger than that caused by more intensive waves. The low-amplitude IGWs produce turbulence consisting up to 90% of turbulent potential energy. This resembles the properties of the observed high-altitude tropospheric strongly anisotropic (nearly two-dimensional) turbulence.

Regular and chaotic dynamics of a fountain in a stratified fluid.

In the present paper, we study by direct numerical simulation (DNS) and theoretical analysis, the dynamics of a fountain penetrating a pycnocline (a sharp density interface) in a density-stratified fluid. A circular, laminar jet flow of neutral buoyancy is considered, which propagates vertically upwards towards the pycnocline level, penetrates a distance into the layer of lighter fluid, and further stagnates and flows down under gravity around the up-flowing core thus creating a fountain. The DNS results show that if the Froude number (Fr) is small enough, the fountain top remains axisymmetric and steady. However, if Fr is increased, the fountain top becomes unsteady and oscillates in a circular flapping (CF) mode, whereby it retains its shape and moves periodically around the jet central axis. If Fr is increased further, the fountain top rises and collapses chaotically in a bobbing oscillation mode (or B-mode). The development of these two modes is accompanied by the generation of different patterns of internal waves (IW) in the pycnocline. The CF-mode generates spiral internal waves, whereas the B-mode generates IW packets with a complex spatial distribution. The dependence of the amplitude of the fountain-top oscillations on Fr is well described by a Landau-type two-mode-competition model.