Measures of intermittency in driven supersonic flows.

Area of Science:

• Fluid dynamics
• Turbulence research
• Computational physics

Background:

• Understanding turbulence in supersonic flows is crucial for astrophysical and engineering applications.
• Previous studies often focused on incompressible or low Mach number flows, leaving supersonic regimes less explored.
• Supersonic flows introduce compressibility and shock waves, significantly altering turbulent behavior.

Purpose of the Study:

• To compute scaling exponents for structure functions of velocity, density, and entropy in driven supersonic flows.
• To analyze the impact of compressibility and shocks on turbulence scaling.
• To compare findings with existing theories like the Kolmogorov refined similarity hypothesis.

Main Methods:

• Numerical simulations using the piecewise parabolic method (PPM) algorithm.
• Utilizing high-resolution grids up to 512(3) points for accuracy.
• Employing driving mechanisms with one or three orthogonal shear waves.

Main Results:

• Compressible velocity components are approximately 6 times weaker than solenoidal components in the statistically steady regime.
• Longitudinal and transverse velocity scaling exponents are similar to incompressible flows and robust to shocks.
• Density and entropy structure functions show significant deviations from linear scaling.

Conclusions:

• Supersonic turbulence exhibits distinct scaling properties compared to incompressible turbulence, particularly for passive scalars like density and entropy.
• The solenoidal component of velocity dominates in driven supersonic flows.
• The study provides insights into energy transfer and turbulence characteristics under supersonic conditions.