Physical Oceanography, Vol.
5, January, 2011 (Ukrainian Original No. 5, September–October, 2010)
THERMOHYDRODYNAMICS OF THE OCEAN
HIERARCHY OF THE MODELS OF CLASSICAL MECHANICS OF
Yu. D. Chashechkin
The methods of perturbation theory and integral representations are used to analyze the general proper-
ties of a system of equations of the mechanics of inhomogeneous fluids including the equations of mo-
mentum, mass, and temperature transfer. We also consider various submodels of this system, including
the reduced systems in which some kinetic coefficients are equal to zero and degenerate systems in
which the variations of density or some other variables are neglected. We analyze both regularly per-
turbed and singularly perturbed solutions of the system. In the case of reduction or degeneration of solu-
tions, the order of the system decreases. In this case, regularly perturbed solutions are preserved (with
certain modifications) but the number of singularly perturbed components participating in the formation
of the boundary layers on contact surfaces and their analogs in the bulk of the fluid, i.e., the elongated
high-gradient interlayers, decreases. The interaction between all components of the currents is nonlin-
ear, despite the fact that their characteristic scales are different.
Together with the experimental and numerical methods, the analytic methods remain one of the basic tools
in the investigation of the nature of currents in fluids. In the course of their development, the information vari-
ables capable of the reliable characterization of the physical properties of the media and the parameters of cur-
rents were selected and the fundamental equations aimed at the description of the mechanics and thermodynam-
ics of fluids were deduced [1, 2]. However, the analysis of the behavior of the entire system and the properties
of separate equations, as well as the construction of partial solutions encounter serious difficulties due to the
presence of multiscale processes and the nonlinearity of equations and the corresponding boundary and initial
conditions. Numerous important results in the theory of slow (as compared with the sound velocity) currents in
low-viscous weakly stratified fluids were obtained by the methods of perturbation theory [1, 2].
Parallel with the fundamental equations, the researchers extensively use constitutive models (various ver-
sions of turbulence theory in the hydroaerodynamics of the environment  and the theories of boundary layer
in the engineering hydromechanics ) whose symmetry differs from the symmetry of the fundamental equa-
tions . The fact that the constitutive models are not closed stimulated the development of more detailed in-
vestigations of the fundamental system of equations and its subsystems. In , the analysis of the mechanisms
of adaptation of physical fields to rapidly varying external conditions is performed under the assumption of exis-
tence of stationary dynamic states of inhomogeneous rotating fluids including the state of rest. The transient
wave processes are analyzed in the linear approximation, and the effect of dissipative factors (viscosity, thermal
diffusivity, and diffusion) is neglected .
Ishlinskii Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, Russia; e-mail: firstname.lastname@example.org.
Translated from Morskoi Gidrofizicheskii Zhurnal, No.
3–10, September–October, 2010. Original article submitted February 3,
0928–5105/11/2005–0317 © 2011 Springer Science+Business Media, Inc. 317