How Stochastic Structural Stability Theory Relates to Traditional Statistical Closures

Physics

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The stochastic structural stability theory (SSST) is a technique ootnotetextB. F. Farrell and P. J. Ioannou, J. Atmos. Sci. 60, 2101 (2003). that can be used for understanding the statistical behavior of drift-wave--zonal-flow systems. ootnotetextB. F. Farrell and P. J. Ioannou, Phys. Plasmas 16, 112903 (2009). The method involves parameterizing the nonlinear DW--DW interactions as white noise while keeping the correct behavior of the DW--ZF interactions. The SSST can be interpreted as an intermediate step between the fundamental amplitude equations and conventional statistical closures. Unlike typical closures which describe only the mean-square ZF, the SSST retains a ZF amplitude. We discuss the relationship between the SSST and more traditional closures of the DW--ZF problem. ootnotetextJ. A. Krommes and C.-B. Kim, Phys. Rev. E. 62, 8508 (2000). In particular, we examine the physical content of a closure of the SSST equations, illustrating with the Generalized Hasegawa--Mima equation. Studies are also made of the Hasegawa--Wakatani system, extending and clarifying the work of Ref. 3. The ideas are relevant for the ultimate control of microturbulence.

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