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Nonlinear waves in stably stratified dissipative media—solitary waves and turbulent bursts

Density stratification and wind shear provide background conditions conducive to wave propagation. Typical waves propagate by a coupling of the velocity field and the density field and are called internal gravity waves. When the shearing dominates the stratification (i.e. the global gradient Richardson Number Ri « 1) internal gravity waves are known to be strongly attenuated even at high Reynolds number. The type of waves that persist have different propagation dynamics. With small Richardson number, to a first approximation, the transport equations for thermal energy and momentum decouple. Thus, a large amplitude temperature wave has a small effect on the fluid velocity. From a dynamical systems viewpoint, dissipation attracts the velocity field toward a time asymptotic state driven by the passing temperature wave. However, transients are only weakly attracted when the forcing is strong and may oscillate if the dissipation is subcritical. The elements of nonlinearity, dissipation, and forcing are a prescription for the possibility of chaotic attractors.