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

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.

Drive Signal Frequency-Lock Method Based on 90° Phase Shift for Quartz Angular-Rate Sensor

A drive signal frequency-lock method for quartz angular-rate sensor is presented. The calculation result obtained by the equivalent volume force analytic method indicated that when taking the inherent frequency of the drive tines as the drive signal frequency the phase of the reference vibration is 90° behind that of the drive signal, and the square of amplitude is less than that of the maximal amplitude by 1/(4Q~2_d) merely. The curves derived from the finite element analytic method proved that near the inherent frequency the phase shift of the feedback voltage is identical to that of the reference vibration, and the amplitude is proportional to that of the reference vibration, and the phase shift is linear approximatively with the frequency shift. The frequency shift could be calculated according to the phase shift obtained by quadrature correlation detection, so the drive signal frequency could be locked at the inherent frequency of the drive tines by means of iteration.