On the relation between 'mixing length' and 'direct interaction approximation' theories of turbulence

The capabilities of direct interaction approximations (DIA) and weak-coupling approximations (WCA) in modeling turbulence in plasma physics studies are examined. DIA and WCA formalisms are reviewed and a DIA expression for homogeneous incompressible hydrodynamics is simplified to derive an energy sp...

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Bibliographic Details
Published in:The Physics of fluids (1958) 1985-06, Vol.28 (6), p.1702-1718
Main Authors: Sudan, R. N., Pfirsch, D.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Fluid Mechanics And Heat Transfer
Physics
Physics of gases, plasmas and electric discharges
Physics of plasmas and electric discharges
Waves, oscillations, and instabilities in plasmas and intense beams
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Summary:The capabilities of direct interaction approximations (DIA) and weak-coupling approximations (WCA) in modeling turbulence in plasma physics studies are examined. DIA and WCA formalisms are reviewed and a DIA expression for homogeneous incompressible hydrodynamics is simplified to derive an energy spectrum in an arbitrary wavenumber space. A solution is defined for the expression when applied to long wavelength phenomena generated by an instability. The equation is further generalized to yield a transport equation for modeling the spectrum generated by homogeneous turbulence in a linearly unstable system undergoing nonlinear interaction. Finally, the technique is applied to two-dimensional turbulence in a low pressure, weakly ionized plasma embedded in a homogeneous magnetic field and experiencing instabilities caused by electron density and electric potential gradients, such as found in the ionospheric E region.
ISSN:0031-9171
2163-4998
DOI:10.1063/1.864963