Large-scale features of rotating forced turbulence

Area of Science:

• Fluid dynamics
• Nonlinear dynamics
• Geophysics

Background:

• Understanding large-scale fluid behavior is crucial in fields like geophysics and astrophysics.
• The influence of rotation and random forcing on fluid dynamics presents complex challenges.
• Perturbation theory offers a method to analyze systems with small parameters.

Purpose of the Study:

• To investigate the effects of random isotropic forcing and fluid rotation on large-scale fluid dynamics.
• To identify and characterize modifications to the fluid equations of motion under these conditions.
• To analyze the nature and implications of emergent effective forces and viscosities.

Main Methods:

• Perturbation theory was applied, considering first-order effects of random force amplitude and angular velocity.
• The study focused on incompressible and unbounded rotating fluid systems.
• Analysis involved examining the fluid equation of motion and the properties of inertial waves.

Main Results:

• Two primary modifications to the fluid equations were identified.
• Molecular shear viscosity was transformed into a rotation-independent effective viscosity.
• A new, large-scale, nondissipative force proportional to angular velocity emerged in the slow rotation regime.

Conclusions:

• The dynamically generated effective viscosity and nondissipative force align with components of the general axisymmetric viscosity tensor for Newtonian fluids.
• The findings provide insights into the behavior of rotating fluids under external forcing.
• This work contributes to a deeper understanding of large-scale fluid phenomena and wave propagation.