A tentative study of the transport of energy and other scalar quantities in forced turbulence driven by ▽n A-type volume forces

作者：Wei Zhao; Guiren Wang

来源：水动力学研究与进展 B辑, 2021, 33(6): 1271-1281.

• Forced turbulence
• scalar based volume force
• cascade of kinetic energy
• cascade of scalar variance

The transport of the energy and other scalar quantities in turbulence can be controlled by scalar-based volume forces,e.g.,the buoyancy in the turbulent thermal convection or the electric body force in the electrokinetic(EK)turbulence,and expressed as▽n A,with A being a control scalar.This paper presents a unified theoretical framework for the transport of the energy and other scalar quantities in the turbulence driven by scalar-based volume forces.Several isolated results that have previously been reported in relation to the turbulent thermal convection(related to n=0)and the EK turbulence(related to n=1)are unified in this theoretical framework.With the theory,the following interesting results are predicted:(1)When n＜2/3,the transport of the kinetic energy is dominated by the Kolmogorov scale η and another small scale lA.When n＞2/3,the transport of the kinetic energy is controlled by three characteristic small scales:lK,lηK and lA.(2)The scaling law range can be divided into an inertial subrange and a volume-force-dominated subrange.(3)In the latter case,the exponents of the power spectra of the velocity and the relevant scalar quantity are ηu=(4n-11)/5,ηA=-(2n+7)/5,respectively.(4)In the equilibrium state,n cannot exceed 4.(5)The positive exponent of lA～0.024Ra0.107±0.016A,ln is confirmed in the turbulent thermal convection.

• 单位
  西北大学