| We consider the k - 3 model for the evolution of turbulent bursts: kt=ak2 3kx x-3 3t=bk 233x x-g32k where k is the turbulent kinetic energy, 3 is the dissipation rate of the turbulent energy, and a,b , and g are positive constants. After substituting k=A&d5;2 t2mfz ,3=A&d5; 2t2m+1g z,z= xA&d5;t1-m into the k - 3 model, where A > 0 is a free scaling parameter, we examine the Barenblatt self-similar k - 3 model for turbulence: af2g f''+ 1-mzf'+2m f-g=0,0a,3a>2b , and g>32 , we show the existence of m for which there is a positive solution to the system and corresponding boundary conditions by proving a series of lemmas. We also include graphs of solutions (f, g) obtained by using XPPAUT 5.85. |
