Stationary solutions in thermodynamics of stochastically forced fluids

We study the full Navier–Stokes–Fourier system governing the motion of a general viscous, heat-conducting, and compressible fluid subject to stochastic perturbation. The system is supplemented with non-homogeneous Neumann boundary conditions for the temperature and hence energetically open. We show that, in contrast with the energetically closed system, there exists a stationary solution. Our approach is based on new global-in-time estimates which rely on the non-homogeneous boundary conditions combined with estimates for the pressure.

Numerical investigation of flows with condensation in micronozzles

The paper considers the numerical simulation of the flow of argon with account for the condensation process in the micronozzle and behind it. To describe phase transitions, the initial mathematical model of viscous heat-conducting gas flow is supplemented with the equation of formation and growth of condensation nuclei in the flow. The developed mathematical model allows for simulating the process of gas condensation at low pressures and temperatures. It is shown that the condensate mass fraction in the flow is not less than 1% at the pressure and temperature of 5 bar and 200 K, respectively, when argon flows out of a micronozzle to the environment with the pressure of 0.01 Pa. At the nozzle exit, the size of condensed particles reaches 80 angstroms. The obtained results confirm the necessity to take into account the condensation phenomenon in micronozzle flows of inert gases.

ON THE TURBULENCE IN A VISCOUS HEAT-CONDUCTING GAS

The problem of the emergence of turbulence is one of the unsolved problems of physics and technology of the 20th century. It is noted that in order to understand the emergence of turbulence in a viscous heat-conducting gas, it is necessary to take into account the compressibility of the medium. A definition of turbulence in a viscous heat-conducting gas is given, which is a cyclically repeating process of the emergence and decay of coherent vortex structures described by a vector wave equation. The decay of vortex structures is accompanied by an explosive, asymptotic increase in pressure pulsations, which triggers a new cycle of turbulence generation. The emergence and decay of coherent vortex structures in the boundary layer on a plate and in a round jet is considered.

Decay rate of generalized solutions for equations of a viscous heat-conducting gas

The large time behavior is considered for the solutions of the Navier-Stokes equations for one-dimensional viscous polytropic ideal gas in unbounded domains. Using the local anti-derivatives functions technique, we obtain the power type decay estimates for the generalized solutions as time goes to infinity