The realizable Markovian closure. I. General theory, with application to three-wave dynamics

Journal Article · Fri Oct 01 04:00:00 EDT 1993 · Physics of Fluids B; (United States)

DOI:https://doi.org/10.1063/1.860829· OSTI ID:6190821

Bowman, J C; Krommes, J A; Ottaviani, M ^[1]

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1. Plasma Physics Laboratory, Princeton University, P.O. Box 451, Princeton, New Jersey 08543 (United States)

A type of eddy-damped quasinormal Markovian (EDQNM) closure is shown to be potentially [ital nonrealizable] in the presence of linear wave phenomena. This statistical closure results from the application of a fluctuation--dissipation (FD) ansatz to the direct-interaction approximation (DIA); unlike in phenomenological formulations of the EDQNM, both the frequency and the damping rate are renormalized. A violation of realizability can have serious physical consequences, including the prediction of negative or even divergent energies. A new statistical approximation, the realizable Markovian closure (RMC), is proposed as a remedy. An underlying Langevin equation that makes no assumption of white-noise statistics is exhibited. Even in the wave-free case the RMC, which is based on a nonstationary version of the FD ansatz, provides a better representation of the true dynamics than does the EDQNM closure. The closure solutions are compared numerically against the exact ensemble dynamics of three interacting waves.

• DOE Contract Number: AC02-76CH03073
• OSTI ID: 6190821
• Journal Information: Physics of Fluids B; (United States), Journal Name: Physics of Fluids B; (United States) Vol. 5:10; ISSN 0899-8221; ISSN PFBPEI
• Country of Publication: United States
• Language: English

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INSTABILITY GROWTH RATES
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MARKOV PROCESS
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