Hi, I have a very fundamental question. Many turbulence papers use the word "degree of freedom(DOF)" as usual. But, what is the rigorous difinition of DOF of turbulence? What is the relation between DOF and number of grid points used in DNS? Will you show some literatures?

Thanks,

In general the number of degrees of freedom is the number of independent variables required to completely describe the state of a system. This means that once you have this much information of the system you can predict the future state of the system using whatever equations govern the system.

I understand it, Thank you. However, so that, what is the difinition of DOF of turbulence? Is it equivalent to the number of grid point? When we use spectral method, fewer grid point is needed to describe the flow field properly comparing to finite difference. I suppose DOF should not concern with the method. Umm, what is DOF?