Abstract:The dynamics of relaxation and transformation of the structure of convective flows of a weakly stratified liquid are investigated by optical methods in the case of uniform lateral heating. The experiments were carried out for different (small (S = 0.22%) and high (6.5%) basic-salinity values, for which the main parameters of the medium (the thermal expansion coefficient, the saline compression coefficient, the kinematic viscosity, the thermal diffusivity, and the salt diffusion coefficient) differ somewhat. It… Show more
“…We consider the steady nonperturbed distributions of temperature T 0 (z) , salinity S 0 (z) , and density 0 (z) characterized by constant scales [10] …”
The methods of perturbation theory and integral representations are used to analyze the general properties of a system of equations of the mechanics of inhomogeneous fluids including the equations of momentum, 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 perturbed and singularly perturbed solutions of the system. In the case of reduction or degeneration of solutions, 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 nonlinear, 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 variables capable of the reliable characterization of the physical properties of the media and the parameters of currents were selected and the fundamental equations aimed at the description of the mechanics and thermodynamics 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 versions of turbulence theory in the hydroaerodynamics of the environment [3] and the theories of boundary layer in the engineering hydromechanics [4]) whose symmetry differs from the symmetry of the fundamental equations [5]. The fact that the constitutive models are not closed stimulated the development of more detailed investigations of the fundamental system of equations and its subsystems. In [6], the analysis of the mechanisms of adaptation of physical fields to rapidly varying external conditions is performed under the assumption of existence 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 [6].
“…We consider the steady nonperturbed distributions of temperature T 0 (z) , salinity S 0 (z) , and density 0 (z) characterized by constant scales [10] …”
The methods of perturbation theory and integral representations are used to analyze the general properties of a system of equations of the mechanics of inhomogeneous fluids including the equations of momentum, 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 perturbed and singularly perturbed solutions of the system. In the case of reduction or degeneration of solutions, 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 nonlinear, 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 variables capable of the reliable characterization of the physical properties of the media and the parameters of currents were selected and the fundamental equations aimed at the description of the mechanics and thermodynamics 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 versions of turbulence theory in the hydroaerodynamics of the environment [3] and the theories of boundary layer in the engineering hydromechanics [4]) whose symmetry differs from the symmetry of the fundamental equations [5]. The fact that the constitutive models are not closed stimulated the development of more detailed investigations of the fundamental system of equations and its subsystems. In [6], the analysis of the mechanisms of adaptation of physical fields to rapidly varying external conditions is performed under the assumption of existence 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 [6].
“…Most measurements are for the sphere. Larsen (1969) and Hurlen (2006) used big spheres with relatively small from to , while Levitskii & Chashechkin (1999), Chashechkin & Levitskii (2003) and Prikhod'ko & Chashechkin (2006) used smaller spheres with larger from to , say. The comparison with theory, shown in figures 3 and 4, does not exhibit any systematic effect of .…”
Section: Free Oscillationsmentioning
confidence: 99%
“…Figure 3.Comparison of inviscid (blue lines) and viscous (brown lines) theories with the data (circles) in figure 2 of Larsen (1969) and figure 4.3 of Hurlen (2006). Parameters values are given in table 1.Figure 4.Same as figure 3 for the data in figures 2 and 7 of Levitskii & Chashechkin (1999), figure 5 of Chashechkin & Levitskii (2003) and figure 2 of Prikhod'ko & Chashechkin (2006). Figure 5.Same as figure 3 for the data in figures 1 and 2 of Vasil'ev & Chashechkin (2009).…”
Section: Free Oscillationsmentioning
confidence: 99%
“…Same as figure 3 for the data in figures 2 and 7 of Levitskii & Chashechkin (1999), figure 5 of Chashechkin & Levitskii (2003) and figure 2 of Prikhod'ko & Chashechkin (2006). …”
Section: Free Oscillationsmentioning
confidence: 99%
“…For a linearly stratified fluid, the experiments of Larsen (1969) and Winant (1974) for a buoyant sphere had been focused on the motion of the sphere. Further attention was paid to the flow around it by Levitskii & Chashechkin (1999), Chashechkin & Levitskii (1999, 2003), Prikhod'ko & Chashechkin (2006), Chashechkin & Prikhod'ko (2006, 2007) and Vasil'ev & Chashechkin (2009), while Prikhod'ko & Chashechkin (2006) and Chashechkin & Prikhod'ko (2006) also considered a finite-length horizontal or vertical circular cylinder, and Biró et al. (2008) a smaller sphere dropped at the surface and observed over hundreds of oscillation periods.…”
The oscillations of buoyant bodies in stratified fluids are deduced from the variations of their added mass. Three configurations are considered: a body displaced from its neutral level then released; a Cartesian diver set into oscillation by a modulation of the hydrostatic pressure, then released; and a body attached to a pendulum to which an impulse is applied. The first configuration is related to the dynamics of Lagrangian floats in the ocean. Two particular bodies are considered: an elliptic cylinder of horizontal axis, typical of two-dimensional bodies; and a spheroid of vertical axis, typical of three-dimensional bodies. The ultimate motion of the body consists of oscillations at the buoyancy frequency with an amplitude decaying algebraically with time. Before that, the resonant response of the system is observed, either aperiodic exponential decay when the system has no intrinsic dynamics, or exponentially damped oscillation otherwise. Comparison with available measurements demonstrates the need to include viscous dissipation in the analysis. At high Stokes number, dissipation comes from the Basset–Boussinesq memory force and is affected negligibly by the stratification; at low Stokes number, dissipation comes from Stokes resistance and exhibits a significant effect of the stratification.
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