TURBULENCE AMPLIFICATION BY A SHOCK-WAVE AND RAPID DISTORTION THEORY

Amplification of turbulent kinetic energy in an axial compression is e xamined in the frame of homogeneous rapid distortion theory (RDT) by u sing the Craya-Herring formalism. By separating the turbulent field in to solenoidal and dilatational modes (Helmholtz decomposition), one ca n show the dilatational mode is mediated by the parameter DELTAm0=D0/a 0k0, which corresponds to the initial ratio between the acoustic time scale (a0k0)-1 and the compression time scale D0(-1), with D0 the comp ression rate. It is shown here that amplification of total kinetic ene rgy is then limited by two analytical solutions obtained for DELTAm0=0 (purely solenoidal-acoustical regime) and for DELTAm0 much greater th an 1 (''pressure released'' regime), respectively. The results of the theory are first compared to results of direct numerical simulations ( DNS) on homogeneous axial compression. The applicability of this homog eneous approach to the shock wave turbulence interaction, is then disc ussed. Considering a shock-induced compression at given Mach number, i t is shown that the corresponding amplification factors predicted by h omogeneous RDT largely differs from that obtained from Ribner's linear interaction analysis and DNS on the shock problem.