Steady state existence of passive vector fields under the Kraichnan model

Abstract

The steady state existence problem for Kraichnan advected passive vector models is considered for isotropic and anisotropic initial values in arbitrary dimension. The model includes the magnetohydrodynamic (MHD) equations, linear pressure model (LPM) and linearized Navier-Stokes (LNS) equations. In addition to reproducing the previously known results for the MHD and linear pressure model, we obtain the values of the Kraichnan model roughness parameter $\xi$ for which the LNS steady state exists.

Improved text & figures, added references & other corrections

References in corpus (8)

• Turbulence with Pressure: Anomalous Scaling of a Passive Vector Field
• Anomalous scaling, nonlocality and anisotropy in a model of the passively advected vector field
• Pressure and intermittency in passive vector turbulence
• Anomalous scaling of passively advected magnetic field in the presence of strong anisotropy
• Scaling, renormalization and statistical conservation laws in the Kraichnan model of turbulent advection
• Anomalous scaling and anisotropy in models of passively advected vector fields
• Dynamo effect in the Kraichnan magnetohydrodynamic turbulence
• Universality in passively advected hydrodynamic fields: the case of a passive vector with pressure

Cited by in corpus (3)

• Anomalous scaling and large-scale anisotropy in magnetohydrodynamic turbulence: Two-loop renormalization-group analysis of the Kazantsev--Kraichnan kinematic model
• Logarithmic violation of scaling in strongly anisotropic turbulent transfer of a passive vector field
• Helical turbulent Prandtl number in the $A$ model of passive advection: Two loop approximation