Search

Records of turbulent velocity fluctuations from both laboratory flumes and rivers exhibit the Hurst phenomenon, R/S ∽ sH, where R is the range of the cumulative sum of departures from the mean for a time series of length s, S is the standard deviation of the time series, and 0.5 ≤ H ≤ 1. The Hurst phenomenon suggests long-term persistence in a time series. The implications in turbulent flows are that the integral time scales do not exist and, rather, that the turbulent velocity fluctuations have the properties of fractional Gaussian noise. Some indirect evidence from dispersion studies supports these implications.

Now we shall apply to the case of the MS a method used by Csiszar and Longo in the case of a DMS. We shall prove the exponential behaviour of \({\text{P}}_e^{\left( n \right)}\), without being able, however, to find the expression for the exponent. Further investigation on this will be carried out in the sequel.