An exact derivation of the dissipation rate correlation exponent μ in fully-developed turbulence
نویسنده
چکیده
We derive for the Navier-Stokes equation an exact equation satisfied by the dissipation rate correlation function, 〈ǫ(~x+~r, t+ τ)ǫ(~x, t)〉. In the equal time limit, for the homogeneous, isotropic state of fullydeveloped turbulence, we show that the correlation function behaves as Ar1 +Br2 with μ1 = 2−ζ6 and μ2 = z ′′ 4−ζ4 for r in the inertial range; the ζ’s are exponents of velocity structure functions and z 4 is a dynamical exponent characterizing the 4th order dynamical structure function. This provides the first direct derivation of the exponents of the dissipation-rate correlation. PACS numbers: 0.5.45.+b, 47.10.+g
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