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WEAKLY-NONLINEAR INSTABILITY DEVELOPMENT IN A SHARPLY STRATIFIED SHEAR FLOW WITH AN INFLECTION-FREE VELOCITY PROFILE

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Within the framework of weakly nonlinear approach, we study the development of an ensemble of unstable waves with so close phase velocities that the waves share a common critical layer. It is shown that their amplitudes increase, as a rule, explosively. During the initial stage the three-wave interaction is dominant and the low-frequency part of the spectrum grows faster. Later, when the higher-order interactions come into play, the growth of the high-frequency part of the spectrum is accelerating in such a way that to the end of the weakly nonlinear stage all the waves come with the amplitudes of order unity.

Author(s):

Semyon Churilov    
Institute of Solar-Terrestrial Physics of Siberian Branch of Russian Academy of Sciences
Russian Federation