Shock-driven transition to turbulence: emergence of power-law scaling

TL;DR

This study investigates shock-induced turbulence from shock-cylinder interactions, revealing power-law scaling in flow structures and analyzing how vorticity and turbulence evolve with different shock angles and Mach numbers.

Contribution

It provides the first detailed analysis of power-law behavior in shock-driven turbulence for both 2D and 3D vorticity fields across varying shock angles and Mach numbers.

Findings

Power-law scaling observed in flow structure functions.

Scaling behavior consistent across Mach numbers 1.1 to 2.0.

Flow properties depend on shock angle and vorticity dimensionality.

Abstract

We consider two cases of interaction between a planar shock and a cylindrical density interface. In the first case (planar normal shock), the axis of the gas cylinder is parallel to the shock front, and baroclinic vorticity deposited by the shock is predominantly two-dimensional (directed along the axis of the cylinder). In the second case, the cylinder is tilted, resulting in an oblique shock interaction, and a fully three-dimensional shock-induced vorticity field. The statistical properties of the flow for both cases are analyzed based on images from two orthogonal visualization planes, using structure functions of the intensity maps of fluorescent tracer pre-mixed with the heavy gas. At later times, these structure functions exhibit power-law-like behavior over a considerable range of scales. Manifestation of this behavior is remarkably consistent in terms of dimensionless time defined based on Richtmyer's linear theory within the range of Mach numbers from 1.1 to 2.0 and the range of gas cylinder tilt angles with respect to the plane of the shock front (0 to 30 degrees).