Abstract
Based on a brief historical excursion, a list of principles is formulated which substantiates the choice of axioms and methods for studying nature. The axiomatics of fluid flows are based on conservation laws in the frames of engineering mathematics and technical physics. In the theory of fluid flows within the continuous medium model, a key role for the total energy is distinguished. To describe a fluid flow, a system of fundamental equations is chosen, supplemented by the equations of the state for the Gibbs potential and the medium density. The system is supplemented by the physically based initial and boundary conditions and analyzed, taking into account the compatibility condition. The complete solutions constructed describe both the structure and dynamics of non-stationary flows. The classification of structural components, including waves, ligaments, and vortices, is given on the basis of the complete solutions of the linearized system. The results of compatible theoretical and experimental studies are compared for the cases of potential and actual homogeneous and stratified fluid flow past an arbitrarily oriented plate. The importance of studying the transfer and transformation processes of energy components is illustrated by the description of the fine structures of flows formed by a free-falling drop coalescing with a target fluid at rest.
Highlights
By recognizing mathematics as “the language in which the book of the Universe is written. . . ” in the polemical treatise “Assaying Master”, G
The general basis for the construction of the theory and methods of experimental studies of a fluid and gas flow in engineering mechanics is the laws of physical quantity conservation within the continuous medium model, which admits infinitesimal representations of physical quantities
The description of substance flows in liquid, gaseous, and plasma states is based on the concept of a “continuous medium”, which allows the use of continuous functions over the entire range of scales
Summary
By recognizing mathematics as “the language in which the book of the Universe is written. . . ” in the polemical treatise “Assaying Master”, G. The basis of mechanics is formed by the axiomatically defined mathematical and physical concepts of number, set, space and time, motion, matter (constituents of fluid or gas and their properties), and flow;. The general basis for the construction of the theory and methods of experimental studies of a fluid and gas flow in engineering mechanics is the laws of physical quantity conservation within the continuous medium model, which admits infinitesimal representations of physical quantities. The conservation laws have generalized the historical experience of describing phenomena, reflecting the fundamental properties of the existence and immutability of matter (its possible transformations, such as radioactive transformations in nuclear physics, will not be considered here), as well as the parameters of its motion They are based on the concept of homogeneity of space and time and the isotropy of space. The rules for choosing the quantities and methods for comparing their values in relation to the description of a fluid or gas flow will be considered below
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