TL;DR: In this paper, the Clausius-Duhem inequality for the mean turbulent motion of an incompressible fluid is formulated and thermodynamics of the mean field fluid is studied, and several thermodynamical relationships are developed.
Abstract: The averaged basic balance laws for the mean turbulent motion of an incompressible fluid are considered. The Clausius-Duhem inequality for the mean motion is formulated and thermodynamics of the mean field fluid is studied. The free energy and the coldness functions for the mean turbulent motion are introduced and several thermodynamical relationships are developed. Based on the averaged entropy inequality an anisotropic rate-dependent constitutive equation for the turbulent stress tensor is formulated, and the constraints on material coefficients are described. Thermodynamically consistent transport equations for time, frequency and dissipation scales of turbulence are also developed. It is shown that the resulting model contains the available ratedependent algebraic stress models as special limiting cases.
TL;DR: In this paper, free convection motion induced by a travelling thermal wave in a horizontal porous layer is studied analytically assuming the validity of the Brinkman model under Boussinesq and long-wave approximations.
TL;DR: In this article, the motion in a circular orbit of a thin, homogeneous, unstretched viscoelastic ring in a central Newtonian gravitational field is investigated, and an approximate non-linear system of differential equations is written out which describe the quasistatic state of motion of the ring relative to the centre of mass.