Vol 58, No 7 (2017)

We discuss the molecular diffusion transport in infinitely dilute liquid solutions under nonisothermal conditions. This discussion is motivated by an occurring misinterpretation of thermodynamic transport equations written in terms of chemical potential in the presence of temperature gradient. The transport equations contain the contributions owned by a gauge transformation related to the fact that chemical potential is determined up to the summand of form (AT + B) with arbitrary constants A and B, where constant A is owned by the entropy invariance with respect to shifts by a constant value and B is owned by the potential energy invariance with respect to shifts by a constant value. The coefficients of the cross-effect terms in thermodynamic fluxes are contributed by this gauge transformation and, generally, are not the actual cross-effect physical transport coefficients. Our treatment is based on consideration of the entropy balance and suggests a promising hint for attempts of evaluation of the thermal diffusion constant from the first principles. We also discuss the impossibility of the “barodiffusion” for dilute solutions, understood in a sense of diffusion flux driven by the pressure gradient itself. When one speaks of “barodiffusion” terms in literature, these terms typically represent the drift in external potential force field (e.g., electric or gravitational fields), where in the final equations the specific force on molecules is substituted with an expression with the hydrostatic pressure gradient this external force field produces. Obviously, the interpretation of the latter as barodiffusion is fragile and may hinder the accounting for the diffusion fluxes produced by the pressure gradient itself.

The paper is devoted to specificities of the cascade processes in developed turbulence existing on a background of the density (temperature) gradient either parallel (turbulence in a stably stratified (SS) medium) or antiparallel (convective turbulence (CT)) to the gravitational force. Our main attention is paid to the Obukhov–Bolgiano (OB) regime, which presumes a balance between the buoyancy and nonlinear forces in a sufficiently extensive part of the inertial interval. Up to now, there has been no reliable evidence of the existence of the OB regime, although fragments of spectra with slopes close to–11/5 and–7/5 were detected in some works on the numerical simulations of convective turbulence. The paper presents a critical comparison of these data with the results obtained in this work using the cascade model of convective turbulence, which makes it possible to consider a wide range of control parameters. The cascade model is new and was obtained by the generalization of the class of helical cascade models to the case of turbulent convection. It is shown that, in developed turbulence, which is characterized by an interval with a constant spectral flux of kinetic energy, the buoyancy force cannot compete with nonlinear interactions and has no essential effect on the dynamics of the inertial interval. It is the buoyancy force that supplies the cascade process with energy in convective turbulence but only in the maximum scales. Under the SS conditions, the buoyancy forces reduce the energy of turbulent pulsations. In the case of stable stratification, the buoyancy force reduces the turbulence pulsation energy. The OB regime arises in none of these cases, but, in the scales beyond the inertial interval, Kolmogorov’s turbulence with the “–5/3” law, in which temperature behaves like a passive admixture, is established. The observed deviations from the “–5/3” spectrum, erroneously interpreted as the OB regime, are manifested in the case of insufficient separation of the macroscale of turbulence and the dissipative scale.

The paper presents an integral technique simulating all phases of a landslide-driven tsunami. The technique is based on the numerical solution of the system of Navier–Stokes equations for multiphase flows. The numerical algorithm uses a fully implicit approximation method, in which the equations of continuity and momentum conservation are coupled through implicit summands of pressure gradient and mass flow. The method we propose removes severe restrictions on the time step and allows simulation of tsunami propagation to arbitrarily large distances. The landslide origin is simulated as an individual phase being a Newtonian fluid with its own density and viscosity and separated from the water and air phases by an interface. The basic formulas of equation discretization and expressions for coefficients are presented, and the main steps of the computation procedure are described in the paper. To enable simulations of tsunami propagation across wide water areas, we propose a parallel algorithm of the technique implementation, which employs an algebraic multigrid method. The implementation of the multigrid method is based on the global level and cascade collection algorithms that impose no limitations on the paralleling scale and make this technique applicable to petascale systems. We demonstrate the possibility of simulating all phases of a landslide-driven tsunami, including its generation, propagation and uprush. The technique has been verified against the problems supported by experimental data. The paper describes the mechanism of incorporating bathymetric data to simulate tsunamis in real water areas of the world ocean. Results of comparison with the nonlinear dispersion theory, which has demonstrated good agreement, are presented for the case of a historical tsunami of volcanic origin on the Montserrat Island in the Caribbean Sea.

Based on a stepwise algorithm involving central finite differences for the approximation in time, a mathematical model is developed for elastoplastic deformation of cross-reinforced plates with isotropically hardening materials of components of the composition. The model allows obtaining the solution of elastoplastic problems at discrete points in time by an explicit scheme. The initial boundary value problem of the dynamic behavior of flexible plates reinforced in their own plane is formulated in the von Kármán approximation with allowance for their weakened resistance to the transverse shear. With a common approach, the resolving equations corresponding to two variants of the Timoshenko theory are obtained. An explicit “cross” scheme for numerical integration of the posed initial boundary value problem has been constructed. The scheme is consistent with the incremental algorithm used for simulating the elastoplastic behavior of a reinforced medium. Calculations of the dynamic behavior have been performed for elastoplastic cylindrical bending of differently reinforced fiberglass rectangular elongated plates. It is shown that the reinforcement structure significantly affects their elastoplastic dynamic behavior. It has been found that the classical theory of plates is as a rule unacceptable for carrying out the required calculations (except for very thin plates), and the first version of the Timoshenko theory yields reasonable results only in cases of relatively thin constructions reinforced by lowmodulus fibers. Proceeding from the results of the work, it is recommended to use the second variant of the Timoshenko theory (as a more accurate one) for calculations of the elastoplastic behavior of reinforced plates.

The dynamics of the formation of a surface phase in aqueous solutions of surfactants in a tray with the Langmuir barrier system during one compression–expansion cycle of the interface boundary is investigated both experimentally and theoretically. Organic salts of fatty acids such as potassium laurate, caprylate, and acetate, which are members of the same homologous series, were used as surfactants. It is experimentally determined that the dependence of the surface pressure increment measured under the maximum compression of the surface on the volume concentration has a maximum, the position of which is different for all the studied surfactant solutions. It is shown that the position of the maximum corresponds to the concentration value at which a saturated monolayer of surfactant molecules is formed at the interface boundary. A theoretical model that considers the effect of the forced convection arisen in the bulk of the solution upon changing the surface area is proposed for the interpretation of the experimental results. The model allows one to render the main kinetic characteristics of the adsorption/desorption processes involving the compounds under study. A good agreement between the theoretical and experimental results is observed, but there is a discrepancy between them when diffusion is considered to be the only way surfactant molecules are transferred into the bulk phase. Based on the data, a new method for determination of the Langmuir–Shishkovsky constant is proposed.