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Particle clustering in a temperature stratified turbulence with small but still finite correlation time is studied. It is shown that 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 considerably 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. The temperature fluctuations produce the pressure fluctuations and cause particle clustering in regions with increased pressure fluctuations. The ratio of growth rates of the tangling and inertial clustering instabilities is proportional to √Re (l0 /LT )^2 /(3Ma)^4 , 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 was 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 tangling clustering instability may be effective, e.g., in atmospheric turbulence with temperature inversions.
Author(s):
Tov Elperin
Ben-Gurion University of the Negev
Israel
Nathan Kleeorin
Ben-Gurion University of the Negev
Israel
Misha Liberman
Department of Physics and Astronomy, Uppsala University
Sweden
Igor Rogachevskii
Ben-Gurion University of the Negev
Israel