Work is worthy of particular regret, as it represents lecture notes and is designed for students. For example, we give several studies, published after 2012, and, as before, consider liquids as incompressible and their motion as potential. This is evidenced by the fact that they are scarcely cited. Although those papers received highly favorable reviews, they were neglected by the scientific community. The subsequent papers based on the critical analysis of the works of other authors persuasively proved existence of the aforementioned contradictions, suggesting the ways of overcoming them. Apparently, he opted for the Helmholtz theorem, according to which circulation of speed vector in gravity field is preserved (§1.2).ĭiscussion of this problem with particular intensity started from 2012, after publication of work. Notwithstanding this, the author himself contradicts this theorem when solving the linear problem of capillary-gravity waves, where motions of liquids are potential (§62). įallacy of the second assumption is proved by the Thompson theorem (1869), according to which liquid motion in the gravity field of the Earth cannot be potential, since it represents a nonisentropic medium (§9). Disregard of this summand leads to existence of internal gravity wave (§13) whose nature is unclear. When the first summand equals zero, which is the condition for incompressibility of the medium, the second summand remains, equaling isobaric change of its density. The generalized mass conservation equation is obtained in work, in the right part of which an additional summand is entered determining the change of density of constant mass, under isobaric change of its volume as a result of temperature variations conditioned by entropy oscillations in inhomogeneous (nonisentropic) medium. It appeared that the equation in its current form is fair only for homogeneous medium and as any medium in gravity field is more or less inhomogeneous, it needs to be generalized. These results led to necessity of changing the mass conservation equation. Strongly inhomogeneous medium, which is largely influenced by external force filed, is always incompressible and sound speed in it is isobaric.
Speed of sound at altitude free#
Homogeneous medium, which is free from the influence of external force field, is always compressible and sound speed in it is adiabatic. Upon correct determination of sound speed, according to which its true (real) value in the medium is determined by combination of adiabatic and isobaric sound speeds, it became evident that compressibility and incompressibility have thermodynamic rather than mechanic meaning and they are directly related to homogeneity or inhomogeneity of the medium. Irrelevance of condition of incompressibility to liquids was shown in work.
If the medium is incompressible within the above sense, then any perturbation will be propagated with infinite velocity and thus, generation of wave is impossible. The first assumption apparently contradicts the concept of mechanical wave in medium itself, since it is known that a wave is propagated only when, under disturbance of density of medium in any point, the elastic forces originate, spreading these perturbations to other points. The vast majority of these works rely on two assumptions: (a) liquids are incompressible (i.e., their densities are constant) and (b) liquid motions are potential, that is, noncircuital. A great number of scientific publications have been dedicated to the study of this problem, which stemmed from the second half of the 18th century. Such waves arise in consequence of disturbance of these surfaces and depending on the volume of disturbance, they may be either linear (when disturbances of parameters of liquids are much less than their equilibrium value) or nonlinear (when disturbances of parameters of liquids are bigger or of the order of their equilibrium value).
Surface gravity waves are generated and propagated on the interface of two liquids therefore, while studying them, the methods of theory of hydrodynamic tangential gap are applied. The paper considers the applied problems of hydrodynamics and based on the new results, published by the author in recent years, shows that main assumptions used in the course of their solution, namely, incompressibility of liquids and potentiality of their movement, are not applicable to liquids in the gravitational field of the Earth.
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