Exact relations for energy transfer in simple and active binary fluid turbulence

Area of Science:

• Fluid dynamics
• Turbulence theory
• Statistical mechanics

Background:

• Fully developed turbulence in binary fluids presents complex energy transfer dynamics.
• Understanding inertial range energy transfer is crucial for predicting turbulent behavior.

Purpose of the Study:

• To derive exact relations for inertial range energy transfer in 3D binary fluid turbulence.
• To compare these relations with those in incompressible magnetohydrodynamic turbulence.
• To explore the possibility of inverse energy cascades.

Main Methods:

• Utilizing statistical homogeneity assumption.
• Applying two-point statistics, including two-point increments and correlators.
• Deriving exact relations for energy cascade.

Main Results:

• Exact relations for energy cascade in binary fluid turbulence were derived, differing from incompressible magnetohydrodynamics.
• The study speculates on inverse energy cascades under specific conditions.
• An alternative exact relation using "upsilon" variables was found.

Conclusions:

• The energy cascade in binary fluid turbulence exhibits unique characteristics.
• The interplay between velocity and composition gradients influences energy transfer.
• A phenomenology predicting a k^{-3/2} energy spectrum law is proposed.