Analysis of Fundamentals of Calculation and Measuring Techniques in Fluid Dynamics

Abstract

The logics of contemporary scientific researches includes the requirement of formulation for distinctive determining the branch of science, the physical medium, and methods for solving problems. Flows are studied in two scientific disciplines, vis., engineering mathematics and technical physics. A flowing medium is characterized by equations of state for the Gibbs potential, density, and velocity of sound, as well as kinetic and other physical coefficients. Fluid flows are treated as transport of momentum, energy, and mass, which causes self-consistent changes in other physical quantities. Flows are described by the unified system of fundamental equations for all media (differential form of conservation laws). Calculations are performed in the algebra of complex numbers, where frequency is assumed to be real-valued, while wavenumber is complex-valued. Natural stratifications of the atmosphere and ocean are characterized by the buoyancy parameters. The classification of flow components is based on complete solutions to linearized and weakly nonlinear forms of fundamental equations, which are obtained by the methods of the singular perturbation theory. Regular components of solutions describe flows and waves on the surface of in the bulk of a fluid, while singular solutions describe the fine structure of the medium. In experiments performed on the stands of the Unique Hydrophysical Complex of the Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, upstream perturbations, internal wave fields, wakes with submerged and suspended vortices structured by interfaces and fibers during the motion of a plate, cylinder, and sphere in stratified and homogeneous fluids are singled out. Numerical calculations of a flow past a plate in a wide range of Reynolds numbers, including creeping flows with Re ~ 1 and nonstationary vortex regimes with Re ~ 100 000, are in qualitative agreement with the observations of schlieren patterns of flows in a stratified aqueous medium in the laboratory basin and in wind tunnels. The conditions for the extension of results to flows in natural conditions and problems in metrology in flight regimes are considered shortly.