Recently I have been investigating the Wilcox k-w turbulence model, and I have a question that hopefully someone(s) can help me with.

Wilcox cites the A.A. Townsend approximation for k as k~t^(-n). I am unclear about what time span the "t" is referring to. Looks like the units don't match, though I'm not sure if they have to in this case.

An explanation of the equation and the "t" would be greatly appreciated.

Thanks in advance.

After reviewing the equation, my colleagues and I can only conclude that the "t" is actually a "Tau" or a stress tensor without subscripts, and not a time scale or time span. So at a minimum, its a confusing simplification, and possibly a typo. Any comments?

I'm assuming you're referring to Wilcox's turbulence and CFD book published by DCW industries.

They have a web page devoted to known typos, and reporting newly-discovered ones:

http://www.dcwindustries.com/typos.htm

I suggest you check it out! Good luck

After sharing e-mails with the author, I've learned that the equation is correct as written k~t^(-n) and t is indeed time. The time scale for this t is infinity and leads to the asymptotic solution for k.

Townsend gives the relation k~t^-n for the (initial) decaying (grid) turbulence and give n the value = 1.25+-0.06. Note that n rises to 2.5 in the final decay. This physical behaviour is one (good) reason for introducing turbulence govern (NOT y+) damping functions. Wilcox and others uses this relation to set the value of the coefficient for the destruction term (C_eps2, beta) in the epsilon/omega-equation.

/Jonas