On the Spectrum and Decay of Random Two-Dimensional Vorticity Distributions at Large Reynolds Number

The hypothesis is made that the vorticity distribution in a field of random two-dimensional vorticity (two-dimensional turbulence) develops discontinuities. The energy spectrum is then calculated and shown to behave like k^(−4) for large values of the wave-number k. The rates of decay of mean square vorticity and velocity are estimated. An expression for the growth of length scale is obtained and it is noted that the size of turbulent trailing vortices is apparently well fitted by the formula