Temporal decorrelations in compressible isotropic turbulence

Temporal decorrelations in compressible isotropic turbulence are studied using the space-time correlation theory and direct numerical simulation. A swept-wave model is developed for dilatational components, while the classic random sweeping model is proposed for solenoidal components. The swept-wave model shows that the temporal decorrelations in dilatational fluctuations are dominated by two physical processes: random sweeping and wave propagation. These models are supported by the direct numerical simulation of compressible isotropic turbulence, in the sense that all curves of normalized time correlations for different wave numbers collapse into a single one using the normalized time separations. The swept-wave model is further extended to account for a constant mean velocity.

Figure 1

Normalized time correlations of solenoidal components vs time separations for $k=15,30,45,60,75$.

Figure 2

Normalized time correlations of solenoidal components vs normalized time separations ${\tau }_V=Vk\tau$ for $k=15,30,45,60,75$.

Figure 3

Normalized time correlations of dilatational components vs time separations for $k=15,30,45,60,75$.

Figure 4

Normalized time correlations vs normalized time separations ${\tau }_V=Vk\tau$ for $k=15,30,45,60,75$.

Figure 5

Rescaled correlation functions vs normalized time separations ${\tau }_a=\overline{a}k\tau$ for $k=15$.