Compressible turbulence: the cascade and its locality

Area of Science:

• Fluid Dynamics
• Turbulence Physics
• Computational Physics

Background:

• Compressible turbulence involves complex energy transfer mechanisms across various scales.
• The direct transfer of kinetic energy from large to dissipation scales, particularly into shocks, is a commonly held belief.
• Understanding energy cascade pathways is crucial for accurate turbulence modeling.

Purpose of the Study:

• To investigate the dominant mechanisms of interscale kinetic energy transfer in compressible turbulence.
• To challenge the prevailing notion of direct energy transfer from large to dissipation scales.
• To establish the existence and characteristics of an inertial range in compressible turbulence.

Main Methods:

• Analysis of kinetic energy transfer based on weak assumptions on structure function scaling.
• Investigation of pressure dilatation cospectrum properties.
• Derivation of energy budgets for kinetic and internal energy components.

Main Results:

• Interscale kinetic energy transfer is predominantly governed by local interactions.
• Direct transfer from large to dissipation scales, including shocks, is precluded in high Reynolds number turbulence.
• Mean kinetic and internal energy budgets statistically decouple beyond a transitional conversion range.
• An inertial range is established where the mean subgrid scale kinetic energy flux is constant and scale-independent.

Conclusions:

• Local interactions dominate kinetic energy transfer in compressible turbulence.
• The concept of a direct cascade to dissipation scales is revised for high Reynolds number flows.
• A scale-independent inertial range exists, characterized by local and conservative kinetic energy cascades.