Linearly forced isotropic turbulence at low Reynolds numbers

Area of Science:

• Fluid Dynamics
• Turbulence Research
• Nonlinear Systems

Background:

• Understanding the conditions for sustained fluid flow is crucial in various scientific and engineering fields.
• Linear forcing is a common method to introduce energy into fluid systems.

Purpose of the Study:

• To determine the critical Reynolds number (R_c) for sustaining flow under linear forcing.
• To develop and validate a model for predicting kinetic energy in such flows.
• To refine the model using insights from dissipation rate analysis and nonlinear transfer.

Main Methods:

• Theoretical analysis to define critical Reynolds number (R_c).
• Development of a simplified dissipation rate model.
• Direct numerical simulations (DNS) for validation.
• Two-point closure integrations for model assessment.

Main Results:

• A critical Reynolds number (R_c) was determined, dependent on system parameters.
• A closed-form expression for kinetic energy as a function of Reynolds number was derived.
• The model successfully reproduced low-Reynolds-number behavior (kinetic energy proportional to R-R_c).

Conclusions:

• The proposed dissipation model and kinetic energy predictions are validated by numerical simulations.
• The study provides a refined model for fluid flow under linear forcing.
• The findings offer insights into the relationship between forcing, dissipation, and kinetic energy in turbulent flows.