Anomalous hydrodynamic fluctuations during the development of thermal convection

Abstract

The spectral functions of the fluctuations of the hydrodynamic variables in an inhomogeneously heated liquid in the region of Rayleigh numbers close to the threshold of convective stability have been calculated using the equations of the correlation theory of thermal fluctuations in non-equilibrium statistical systems. It is shown that anomalous fluctuations, which form the structure of the flow in the regions of supercritical values of the Rayleigh number are of an essentially non-equilibrium nature and are completely accounted for by the long wavelength part of the correlation functions. The results of the calculations are used to analyse the effect of large-scale fluctuations on the Rayleigh scattering of radiation. It is is shown that, in a region where thermal convection develops, they are responsible for a phenomenon which is analogous to the critical opalescence of light during equilibrium phase transitions of the second kind. The investigation of the dependence of the spectral functions of thermal hydrodynamic fluctuations on the degree of non-equilibrium in statistical systems is of great significance in the development of optical methods for the noise diagnostics of inhomogeneous flows of liquids and gases. Systems which are far removed from thermodynamic equilibrium and, in particular, the fluctuation mechanisms of processes involving the self-organization of flow structures when there is loss of stability are of special interest. A large number of papers (/1–4/, for example) have been concerned with the study of the anomalous hydrodynamic fluctuations which develop close to the thermal convection threshold in a liquid which is heated from below. However, the results obtained in the majority of these papers are contradictory as for example, in /1/ and /2/. This is explained by the previously discussed /5–7/ incompleteness of the theories of non-equilibrium hydrodynamic fluctuation theories which were employed. In this paper an analysis of the anomalous fluctuations during the development of thermal convection is carried out using the solution of the equations of the theory in /6/ which enables one to evaluate the results which have previously been obtained from common positions.