Drag reduction in homogeneous turbulence by scale-dependent effective viscosity

Area of Science:

• Fluid Dynamics
• Turbulence Research
• Polymer Physics

Background:

• Drag reduction is a critical phenomenon in fluid dynamics, particularly in turbulent flows.
• Understanding the interaction between polymer dynamics and fluid velocity fields is key to explaining drag reduction mechanisms.

Purpose of the Study:

• To demonstrate that drag reduction in homogeneous turbulence can be effectively modeled using a scale-dependent effective viscosity.
• To provide an equivalent single-field (velocity) model for polymer-turbulence interactions.
• To distinguish drag reduction mechanisms in homogeneous versus wall-bounded turbulent flows.

Main Methods:

• Utilizing suitable shell models to simulate homogeneous turbulence.
• Developing an "equivalent" equation of motion for the velocity field alone.
• Introducing a scale-dependent effective viscosity to represent polymer-velocity coupling.

Main Results:

• Homogeneous turbulence drag reduction is usefully described by a scale-dependent effective viscosity.
• The proposed model successfully recaptures the essence of drag reduction seen in coupled velocity-polymer field models.
• Key differences between drag reduction in homogeneous and wall-bounded flows are clarified.

Conclusions:

• A scale-dependent effective viscosity provides a concise and powerful way to understand drag reduction in homogeneous turbulence.
• This approach simplifies complex polymer-fluid interactions into a single-field framework.
• The study highlights distinct physical mechanisms governing drag reduction in different flow configurations.