DYNAMICAL STRUCTURE FACTORS IN MODELS OF TURBULENCE

We investigate the dynamical scaling behavior of the rime-dependent st ructure functions, S-q(r,tau) =<[u(r,tau)-u(0,0)](q) >, in the one-dim ensional, stochastic: Burgers equation as a function-of the: exponent beta that characterizes the scale of noise correlations. We present an d analyze the exact equations satisfied by S-2(r,tau) and a related co rrelation function to argue that (a) partial derivative S-2(r, tau)/pa rtial derivative tau exhibits a discontinuity at tau=0 With an effecti ve dynamical exponent given by 1+beta/3 and (b) the dynamical scaling exponent z is unity for intermediate times (a result equivalent to Tay lor's hypothesis). Various numerical checks of these results are prese nted. Finally, the corresponding exact equations for the structure fun ctions in the case of the Navier-Stokes equation are presented, and by analogy with the one-dimensional Burgers equation it is shown how Tay lor's hypothesis can arise in homogeneous turbulence.