Tangling clustering instability for small particles in temperature stratified turbulence

Abstract

We study tangling clustering instability of inertial particles in a temperature stratified turbulence with small finite correlation time. It is shown that the tangling mechanism in the temperature stratified turbulence strongly increases the degree of compressibility of particle velocity field. This results in the strong decrease of the threshold for the excitation of the tangling clustering instability even for small particles. The tangling clustering instability in the temperature stratified turbulence is essentially different from the inertial clustering instability that occurs in non-stratified isotropic and homogeneous turbulence. While the inertial clustering instability is caused by the centrifugal effect of the turbulent eddies, the mechanism of the tangling clustering instability is related to the temperature fluctuations generated by the tangling of the mean temperature gradient by the velocity fluctuations. Temperature fluctuations produce pressure fluctuations and cause particle accumulations in regions with increased instantaneous pressure. It is shown that the growth rate of the tangling clustering instability is by \documentclass[12pt]{minimal}\begin{document}$\sqrt{\rm Re} \, (\ell _0 / L_T)^2 / (3 {\rm Ma})^4$\end{document} Re (ℓ0/LT)2/(3 Ma )4 times larger than that of the inertial clustering instability, where Re is the Reynolds number, Ma is the Mach number, ℓ0 is the integral turbulence scale, and LT is the characteristic scale of the mean temperature variations. It is found that depending on the parameters of the turbulence and the mean temperature gradient there is a preferential particle size at which the particle clustering due to the tangling clustering instability is more effective. The particle number density inside the cluster after the saturation of this instability can be by several orders of magnitude larger than the mean particle number density. It is also demonstrated that the evaporation of droplets drastically changes the tangling clustering instability, e.g., it increases the instability threshold in the droplet radius. The tangling clustering instability is of a great importance, e.g., in atmospheric turbulence with temperature inversions.