Non-Kolmogorov dissipation in a turbulent planar jet

A turbulent planar jet is analyzed theoretically by adopting the Lie theory of continuous transformation groups on turbulent statistical model equations. We show that at the infinite-Reynolds-number limit, the planar jet, in analogy to the turbulent axisymmetric wake, obeys the non-Kolmogorov dissipation law is an element of similar to C-is an element of((k) over bar)(3)(/2)/l, where the dissipation coefficient C-is an element of varies with the local and global Reynolds numbers Re-l and Re-0, respectively. In the planar jet, C-is an element of similar to (Re-0/Re-l)(m), with m = -2 + 2a(1)/a(2) preferably lying in [-2, 1], where a(1) and a(2) are dilation symmetry group parameters. When m is an element of [-2, 0) boolean OR (0, 1], the planar jet follows nontrivial power-law similarity scalings, while when m = -2 it may scale exponentially. The production P of turbulent kinetic energy (k) over bar in this study is considered as P = -(u' v') over bar partial derivative(u) over bar/partial derivative y - ((u'(2)) over bar - (v'(2)) over bar partial derivative(u) over bar/partial derivative x, where -(u' v') over bar, -(u'(2)) over bar, and -(v'(2)) over bar are Reynolds stresses. Thus, the laws support (k) over bar similar to ((u) over bar)(2) not similar to -(u' v') over bar when m not equal 0, (u) over bar being the mean streamwise velocity. The power-law scaling of the turbulent jet half-width and centerline mean streamwise velocity for m = 1 agree well with the recent experimental results. The entrainment coefficient, which is constant in streamwise distance when m = 0 (Kolmogorov dissipation), varies with streamwise distance when m is an element of [-2, 0) boolean OR (0, 1]. It scales nonlinearly as an exponent -1/3 of streamwise distance for m = 1, which agrees with the recent experimental observation of Cafiero and Vassilicos.