Nonlinear unsteady motions in dispersive planetary atmospheres

Astronomy and Astrophysics – Astronomy

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Atmospheric Circulation, Gravitational Waves, Planetary Atmospheres, Discontinuity, Korteweg-Devries Equation, Nonlinear Systems, Unsteady State

Scientific paper

Unsteady gravitational waves are investigated with allowance for nonlinear and dispersive effects. As an example, the problem of initial discontinuity evolution is analyzed using the Kortweg-de Vries equation. In the case of rarefaction waves, the solution obtained in the context of dissipative hydrodynamics is similar to the corresponding solution in convectional hydrodynamics. However, in the case of compression waves, an essentially new phenomenon is observed. Instead of a shock wave moving at constant velocity, an oscillatory region arises which is spread in a self-similar way, i.e., the front of a nondissipative shock wave rapidly spreads due to the generation of oscillations.

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