Quantitative analysis of production of turbulent kinetic energy by using catastrophe method for the whole process of turbulence formation

The whole process of turbulence formation was quantitatively studied by the catastrophe method. The change law of the production of turbulent kinetic energy and its spectral distribution with the transformation of wave number and time factor are mainly studied. In addition, the distribution and production of turbulent kinetic energy in Karman vortex street model are studied by numerical simulation. The results show that the production of turbulent kinetic energy first increases and then decreases with the time factor, and the spectrum at different wave numbers follows this trend. When the time factor g(t) = -1.8, the maximum value appears. In the Karman vortex street model, the simulation results are consistent with our derived values.