摘要
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 scaleηand another small scale l_(A).When n>2/3,the transport of the kinetic energy is controlled by three characteristic small scales:l_(K),l_(ηK) and l_(A).(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 areη_(u)=(4n-11)/5,η_(A)=-(2n+7)/5,respectively.(4)In the equilibrium state,n cannot exceed 4.(5)The positive exponent of l_(A)∼0.024Ra^(0.107±0.016)_(A.l_(0)) is confirmed in the turbulent thermal convection.
基金
Projects supported by the National Natural Science Foundation of China(Grant No.11672229).
