Anisotropy in homogeneous rotating turbulence

Area of Science:

• Fluid dynamics
• Turbulence theory
• Rheology

Background:

• Homogeneous turbulent rotating fluids exhibit anisotropic effective stress tensors.
• Understanding these anisotropies is crucial for accurate fluid modeling.

Purpose of the Study:

• To derive the most general axisymmetric four-rank viscosity tensor for a Newtonian fluid.
• To identify new terms in the large-scale turbulent effective force arising from this tensor.
• To explore axisymmetry constraints on response functions and velocity correlations.

Main Methods:

• Derivation of the general axisymmetric four-rank viscosity tensor.
• Analysis of the resulting turbulent effective force terms, including couplings to vorticity.
• Investigation of angular momentum nonconserving effects in the rotating frame.
• Application of axisymmetry constraints to response functions and two-point velocity correlations.

Main Results:

• The effective stress tensor in homogeneous turbulent rotating fluids is anisotropic.
• New terms in the large-scale turbulent effective force arise from the generalized viscosity tensor.
• Some terms exhibit couplings to vorticity, while others are angular momentum nonconserving.
• Axisymmetry imposes specific constraints on the response function and velocity correlations.

Conclusions:

• The generalized axisymmetric viscosity tensor provides a more complete description of turbulent rotating fluids.
• The identified new force terms and nonconserving effects are significant for large-scale dynamics.
• Comparison with existing models highlights the advancements in describing anisotropic turbulence.