Chapter 12 - Epilogue

Abstract

This chapter discusses thermally excited hydrodynamic fluctuations in fluids and fluid mixtures that are either in a thermodynamic equilibrium state or in a stationary quiescent nonconvective nonturbulent nonequilibrium state. There is a qualitative difference between thermal fluctuations in fluids in equilibrium and in nonequilibrium states. With the exception of states near a critical point, temperature and/or concentration fluctuations in fluids in thermodynamic equilibrium are generally uncorrelated at hydrodynamic length scales. The corresponding real-space hydrodynamic correlation functions in equilibrium are proportional to a delta function of the distance variable. It is observed that to extend the theory of fluctuating hydrodynamics to fluctuations in nonequilibrium fluids we have assumed that the noise correlation functions are still given by a local application of the FDT. It is found that the mode-coupling effects incorporated in fluctuating hydrodynamics yield an amplitudes of the wave-number-dependent nonequilibrium fluctuations near the onset of Rayleigh–Bénard convection, which differ from the those found from traditional hydrodynamic instability analysis.