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Published on: December 4, 2017
Hydrodynamic fluctuations in the Kolmogorov flow: linear regime
1Limburgs Universitair Centrum, B-3590 Diepenbeek, Belgium.
Summary
Landau-Lifshitz fluctuating hydrodynamics reveals Kolmogorov flow
Area of Science:
- Fluid dynamics
- Statistical mechanics
- Nonlinear dynamics
Background:
- Kolmogorov flow is a fundamental model in fluid dynamics.
- Understanding fluctuations is crucial for predicting fluid behavior near instability.
- Linearized analysis simplifies complex hydrodynamic systems.
Purpose of the Study:
- To investigate the statistical properties of linearized Kolmogorov flow using Landau-Lifshitz fluctuating hydrodynamics.
- To analyze the fluctuation spectrum across different regimes, from near equilibrium to the convective instability threshold.
- To compare theoretical predictions with numerical simulations.
Main Methods:
- Application of Landau-Lifshitz fluctuating hydrodynamics.
- Detailed spectral analysis of flow fluctuations.
- Numerical simulations of nonlinear fluctuating hydrodynamic equations.
Main Results:
- Kolmogorov flow exhibits incompressible behavior in the long-time limit, irrespective of the Reynolds number.
- Short-time behavior deviates from incompressibility, affecting static correlation functions except near instability.
- Theoretical predictions align with numerical simulation results.
Conclusions:
- The study clarifies the role of incompressibility in Kolmogorov flow dynamics.
- Fluctuating hydrodynamics provides accurate predictions for flow behavior, especially near instability.
- Numerical simulations validate the theoretical framework for complex fluid systems.
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