Fluid Mechanics: Consistent Analytical, Numerical and Laboratory Models of Stratified Flows

The results of the consistent analytical, numerical and laboratory modeling of dynamics and internal structure of flows are presented. A fundamental set of equations of the inhomogeneous fluids mechanics is mathematical basis. This set includes the differential equations of continuity, momentum balance, energy, diffusion components and closing equation of state. This simultaneous equations is analyzed under accounting of compatibility and observability conditions of incoming physical quantities. Symmetries of the fundamental set correspond to the basic principles of physics in contrast to many reduced and constitutive models. A complete mathematical classification for the components of periodic large- and small-scales flows is given. As an example, the full solution of definition problem for two-dimensional flows induced by diffusion on the topography and the linearized theory of periodic internal waves are considered. We discuss the physical and mathematical content of the concepts of "mechanical motion" and the "fluid flow", following requirements for measurement technique and methodology in order to ensure the fulfillment of the condition for the experiment efficiency.

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