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Updated: Jul 25, 2026
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Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow
Published on: February 27, 2016
Burgers' turbulence with self-consistently evolved pressure
1Physics Department, University of California at San Diego, La Jolla, California 92093, USA.
Summary
This study extends the Burgers
Area of Science:
- Fluid Dynamics
- Plasma Physics
- Magnetohydrodynamics
Background:
- The Burgers' model is a fundamental tool for studying nonlinear phenomena in fluid dynamics.
- Extending this model to include pressure back-reaction is crucial for understanding compressible systems.
- This work bridges concepts in adiabatic gas dynamics and compressible magnetohydrodynamics.
Purpose of the Study:
- To develop a minimal model of compressible fluid dynamics with pressure back-reaction.
- To investigate energy transfer mechanisms, specifically 'Alfvenization,' in a simplified magnetohydrodynamic system.
- To analyze the behavior of turbulence, termed 'Burgerlence,' under varying transport coefficients.
Main Methods:
- Coupling Burgers' equation with a pressure gradient to an advection-diffusion equation for pressure.
- Analytical investigation for the integrable case of equal viscosity and diffusivity.
- Renormalized perturbation theory to determine effective transport coefficients for non-integrable cases.
- Numerical simulations to validate theoretical predictions.
Main Results:
- The system models adiabatic gas dynamics and compressible magnetohydrodynamics, exhibiting 'Alfvenization'.
- For equal transport coefficients, the system is integrable, decoupling into two Burgers' equations.
- Energy equidissipation, not equipartition, characterizes the turbulent state.
- Energy and dissipation concentrate in shock-like structures, stabilized by small-scale forcing and pressure effects.
Conclusions:
- The extended Burgers' model provides a minimal yet comprehensive framework for compressible fluid and magnetohydrodynamic turbulence.
- Pressure back-reaction and small-scale forcing play key roles in stabilizing shock structures.
- The findings are supported by theoretical predictions and numerical simulations, advancing the understanding of turbulent energy transfer.
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