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07. Turbulence and Flow Instabilities

Solenoidal and dilatational velocity statistics for a planar shock wave propagating in turbulence

A planar shock wave propagating through homogeneous isotropic turbulence is investigated using direct numerical simulations. Detailed analyses focus on the local shock wave front geometries of the shock wave, evaluated using the mean curvature (H) and Gaussian curvature (K). These parameters help classify the geometries into elliptic convex, elliptic concave, saddle convex, and saddle concave shapes. The fluid velocity is also decomposed into dilatational and solenoidal components through Helmholtz decomposition. Conditional statistics based on (H, K) for the decomposed velocity components reveal relationships between the local shock wave front geometry and shock wave behavior. The convex shape typically appears in flow regions where the direction of the solenoidal velocity vector aligns with the shock propagation direction. Conversely, a solenoidal velocity in the opposite direction correlates with a concave shape. The dilatational velocity in the shock normal direction exhibits a significantly large jump across the shock wave with a concave shape, indicating strong compression. In contrast, weak compression is observed in regions with a convex shape. These relationships suggest that local shock wave front geometry alterations, driven by solenoidal velocity fluctuations in turbulence, influence the strength of the shock wave.

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Author Information

Amane Kusuhata
Ms.
Corresponding author, Presenting author
Kento Tanaka
Dr.
Tomoaki Watanabe
Dr.
Koji Nagata
Prof.
Akihiro Sasoh
Prof.