Basic properties of free stratified flows
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Results of analytical studies of the governing equations of stratified rotating fluids based on the unification of theories of continuous and discrete groups, perturbations and modern numerical visualizations are described. Symmetries of basic systems and their simplified versions, different approximations and constitutive turbulent models are compared. A new method to calculate discrete groups analytically, which does not need a preliminary search for continuous groups, is developed. As an example of the practical use of the developed algorithm, a complete classification of cellular and roll structures of Bénard convection is presented. A complete classification of 3D periodic motions in compressible viscous stratified and rotating fluids, including regular (wave) and singular elements, is performed by perturbation methods. In all cases, in a viscous fluid, besides waves there are two different periodic boundary layers. In a homogeneous fluid the split boundary layers are merged, thus forming a joint doubly-degenerate structure. Stratification and rotation reduce the degeneration of the 3D periodic boundary layers. Calculations of a 3D periodic wave beam emitted by an oscillating part of a sloping plane are visualized by a computer-graphics method. The existence of thin extended components on the edges of the 3D wave cone is demonstrated.
Keywordsboundary layers complete equations continuous and discrete groups exact solutions internal waves
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