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Application of Kraichnan's direct interaction approximation to kinematic dynamo theory. III. Solution of the Kraichnan equations under Parker's ``short‐sudden'' conditions

### Abstract

Using Parker's ``short‐sudden'' conditions, we solve the Kraichnan equations*exactly*. We find that the normal modes of the ensemble average magnetic field have very different properties in this case than when the velocity turbulence is static, which situation was investigated in earlier papers in this series. We have done this calculation for two reasons: first because exact solutions of the Kraichnan equations are few in number, and second because the nonlinearity and singularity of the Kraichnan equations is such as to emphasize the physical difference in the properties of the normal modes of the average magnetic field under a small change in the prescription of the turbulent velocity field.

© 1973 The American Institute of Physics

Received 04 May 1973
Published online 03 November 2003