The instability of internal gravity waves to localised disturbances

Physics

Scientific paper

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Amplitudes, Gravity Waves, Middle Atmosphere, Stability, Wave Interaction, Coefficients, Computerized Simulation, Eigenvalues, Eigenvectors, Shear Flow, Shear Layers

Scientific paper

The instability of an internal gravity wave due to nonlinear wave-wave interaction is studied theoretically and numerically. Three different aspects of this phenomenon are examined. 1. The influence of dissapation on both the resonant and the nonresonant interactions is analyzed using a normal mode expansion of the basic equations. In particular, the modifications induced in the interaction domain are calculated and as a result some modes are shown to be destabilized by dissapation. 2. The evolution of an initial unstable disturbance of finite vertical extent is described as the growth of two secondary wave packets travelling at the same group velocity. A quasilinear correction to the basic primary wave is calculated, corresponding to a localized amplitude decrease due to the disturbance growth. 3. Numerical experiments are carried out to study the effect of a basic shear on wave instability. It appears that the growing secondary waves can have a frequency larger than that of the primary wave, provided that the shear is sufficient. The instability of waves with large amplitude and long period, such as tides or planetary waves, could therefore be invoked as a possible mechanism for the generations of gravity waves with shorter period in the middle atmosphere.

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