SPECTRA OF FLUCTUATIONS OF VELOCITY, KINETIC-ENERGY, AND THE DISSIPATION RATE IN STRONG TURBULENCE

Following the ideas of operator product expansion, the velocity v, kin etic energy K = 1/2upsilon2, and dissipation rate epsilon=nu0(partial derivativeupsilon(i)/partial derivativex(j))2 are treated as independe nt dynamical variables, each obeying its own equation of motion. The r elations DELTAu(DELTAK)2BAR is-proportional-to r, DELTAU(DELTAepsilon) 2BAR is-proportional-to r0, and (DELTAu)5BAR almost-equal-to rDELTAeps ilonDELTAK are derived. If velocity scales as (DELTAupsilon)rms is-pro portional-to r(gamma/3)-1, then simple power counting gives (DELTAK)rm s is-proportional-to r1-(gamma/6) and (DELTAepsilon)rms is-proportiona l-to 1/square-root (DELTAupsilon)rms is-proportional-to r(1/2)-(gamma/ 6). In the Kolmogorov turbulence (gamma=4) the intermittency exponent mu = (gamma/3)-1 = 1/3 and (DELTAepsilon)2=O(Re1/4). The scaling relat ion for the epsilon fluctuations is a consequence of cancellation of u ltraviolet divergences in the equation of motion for the dissipation r ate.