New Methods for Applying Statistical State Dynamics to Problems in Atmospheric Turbulence

Abstract:

Adopting the perspective of statistical state dynamics (SSD) has led to a number of recent advances in
understanding and simulating atmospheric turbulence at both boundary layer and planetary scale. Traditionally, realizations 
have been used to study turbulence and if a statistical quantity was needed it was obtained by averaging.
However, it is now becomimg more widely appreciated that there are important advantages to studying the
statistical state dynamics (SSD) directly. In turbulent systems statistical quantities are often the most useful
and the advantage of obtaining these quantities directly as state variables is obvious. Moreover, quantities such as
the probability density function (pdf) are often difficult to obtain accurately by sampling state trajectories. 
In the event that the pdf is itself time dependent or even chaotic, as is the case in the turbulence of the planetary boundary
layer, the pdf can only be obtained as a state variable. However, perhaps the greatest advantage of the SSD approach is that
it reveals directly the essential cooperative mechanisms of interaction among spatial and temporal scales that underly the
turbulent state. In order to exploit these advantages of the SSD approach to geophysical turbulence, new analytical and computational
methods are being developed. Example problems in atmospheric turbulence will be presented in which these new
SSD analysis and computational methods are used.