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Published on: October 5, 2018
Fluctuating hydrodynamics and turbulence in a rotating fluid: universal properties
Abhik Basu1, Jayanta K Bhattacharjee
1Theoretical Condensed Matter Physics Division, Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata, Calcutta 700064, India. abhik.basu@saha.ac.in
Summary
This study analyzes 3D turbulence in rotating fluids, revealing distinct statistical behaviors parallel and perpendicular to rotation. Results suggest rotating flows differ from 2D turbulence, with specific scaling laws observed.
Area of Science:
- Fluid Dynamics
- Turbulence Theory
- Statistical Mechanics
Background:
- Understanding the statistical properties of turbulent flows is crucial in fluid dynamics.
- Rotating fluids introduce complex dynamics, deviating from simpler non-rotating systems.
- Characterizing three-dimensional (3D) turbulence under rotation requires advanced theoretical tools.
Purpose of the Study:
- To analyze the statistical properties of 3D turbulence in a rotating fluid.
- To derive exact hierarchical equations for velocity structure functions under arbitrary angular velocity.
- To investigate the behavior of these relations in the limit of large rotation.
Main Methods:
- Introduction of a generating functional to study the velocity field's statistical properties.
- Derivation of the master equation from the Navier-Stokes equation in a rotating frame.
- Obtaining differential forms for analogs of the von Karman-Howarth relation.
Main Results:
- Dissimilar statistical behavior and scaling observed along directions parallel and perpendicular to the angular velocity (Ω).
- Evidence that flows in large rotation are not identical to pure two-dimensional (2D) flows.
- Kolmogorov scaling (q(-5/3)) for velocity components parallel to Ω, and q(-3) for other components in the inertial range.
Conclusions:
- The statistical nature of 3D turbulence in rotating fluids is anisotropic.
- The derived hierarchical relations provide strong evidence against the identity of large-rotation flows with 2D turbulence.
- Results are testable via experiments and direct numerical simulations of rotating Navier-Stokes equations.
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