turbulence dissipation rate in DNS

Shaohua Wu

Hello,

I am trying to calculate the dissipation rate in my DNS code for decaying turbulence. I calculate the dissipation rate, epslon, in spectrum sapce

1) epslon=2*nu*int(k*k*E(k)dk), E(k) is the 3D spectrum,

and in physical space,

2) epslon=4*nu*<SijSij>, Sij=0.5*(dui/dxj+duj/dxi)

I calculate Sij with 4th order central difference scheme. But the results of 1) and 2) are different. I am confused about the results, can anyone gave me some guidance?