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Entropy in Exact 2D Navier-Stokes and 3D Burgers Gas Flows
1Department of Mathematical and Physical Sciences, La Trobe University, Bundoora, VIC 3086, Australia.
Entropy (Basel, Switzerland)
|February 27, 2026
Summary
Researchers developed exact solutions for viscous compressible gas dynamics, detailing a steady vortex and a shock-like radial solution. These findings provide insights into fluid behavior and entropy production in complex systems.
Area of Science:
- Fluid Dynamics
- Computational Physics
Background:
- Understanding complex fluid behavior is crucial in various scientific and engineering fields.
- Exact solutions are valuable for validating numerical methods and theoretical models.
Purpose of the Study:
- To construct novel exact solutions for viscous compressible gas dynamics in 2D and 3D.
- To analyze the properties of these solutions, including entropy production.
Main Methods:
- Solving the full Navier-Stokes equations for a steady vortex flow.
- Deriving a time-dependent radial solution for the 3D vector Burgers' equation.
Main Results:
- Explicit solutions for velocity, density, temperature, and pressure of a steady vortex.
- A shock-like radial solution for low Reynolds numbers, featuring a constant injection rate.
- Expressions for local entropy production density in both solutions.
Conclusions:
- The study provides new exact solutions for complex gas dynamics problems.
- These solutions offer benchmarks for further research in fluid mechanics and shock phenomena.
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