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Fabian October 16, 2001 10:27

"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?

John C. Chien October 16, 2001 14:35

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.

kalyan October 19, 2001 12:52

Re: "Pseudo" Dissipation

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

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