"Pseudo" Dissipation
 

In most scientific articles dealing with turbulence a dissipation rate of the turbulent kinetic energy is defined as: \epsilon=\nu \cdot \frac{\partial u_i}{\partial x_j} \frac{\partial u_i}{\partial x_j}. In only a handful of articles the dissipation rate of turbulent kinetic energy is defined as: \epsilon = [( \frac{\partial u_i}{\partial x_j} + \frac{\partial u_j}{\partial x_i}) \cdot ( \frac{\partial u_i}{\partial x_j} + \frac{\partial u_j}{\partial x_i}) ] and the above mentioned definition is titled "pseudo dissipation". Can somebody explain the difference in the two terms and why do most scientific articles refer to the simplified definition of the dissipation?

Re: "Pseudo" Dissipation
 

(1). In Hinze's book, p-65-, eq.(1-98), term-V, it is nu * mean of { [(dui/dxj) + (duj/dxi)] * (duj/dxi) }.(2). In Wilcox's book, p-104-, eq.(4.5), it is nu * mean of { (dui/dxk) * (dui/dxk) }. (3). There is a short explanation on p-105-. (4). So, if you have to be right, use the long form. Or take 2% error by using the short form.

Re: "Pseudo" Dissipation
 

Fabian,

I have addressed this issue in reply to your other question about dissipation and pressure drop in DNS my Mansour et al.