i am new to this field of CFD. i have some small quires. 1. can we express the turbulent viscosity for 3D flow using prandtls mixing length model? if so how can it be expressed? 2. in k-e model for turbulence, if k is a function of x,y,z,t and similarly for e, dont u think it there should be 3 equations each for k and e, for complete mathematical closure of the model.?

(1). I think there is a popular algebraic turbulence model called "Baldwin-Lomax model", you can take a look at it. (2). If it is a function of x,y,z,t, then it is four dimensional. The variable is a function (x,y,z,t), and the equation will have derivative terms such as dkdx, dkdy, dkdz, and dkdt,etc.... (3). K and epsilon are not vectors, so each requires only one equation.