Modelling Turbulent Time Series by BSS-Processes

Incremental similarity and turbulence

“…[11]. And a recent study [10] of the Helium data discussed in Section 2, based on exponential LSS processes, has revealed a new type of universality for the energy dissipation.…”

Some Recent Developments in Ambit Stochastics

“…The remaining parameters for the kernel g and the constant β can then be estimated from the second and third order structure function, that is, the second and third order moments of velocity increments. In [35] it is shown that the second order structure function is excellently reproduced and that the details of the third order structure function are well captured. It is important to note that the model is completely specified from the energy dissipation statistics and the second and third order structure functions.…”

“…Within the context of turbulence, BSS-processes have been shown to be able to reproduce many key features of turbulence, see [35] and the following subsection for a recent example. The extent to which BSS-processes in general possess universality is still ongoing research [20] but results indicate that BSS-processes and in general LSS-process are good candidates for models where parsimony and universality are desired features.…”

“…Recently this analysis has been extended to a quantitative comparison with turbulent data [31,35]. More specifically, based on the results for the energy dissipation oulined in Sect.…”

“…More specifically, based on the results for the energy dissipation oulined in Sect. 4.1, BSS processes have been analyzed and compared in detail to turbulent velocity time series in [35] by directly estimating the model parameters from data. Here we briefly summarize this analysis.…”