Anomalous Transport Arising From Nonlinear Resistive Pressure Driven Modes in a

Satoshi Hamaguchi

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) - Pq - ' —5 (7-20) (Y-1) /Tq ^2 near D - D^^. Here we used Eqs. (3-20) and (3-26) to relate to . Equation (7-20) gives the dependence of the anomalous heat flux -Pq on the parameter D, which we have been after in this section.
In summary, we have derived the dependence of the anomalous heat flux on the parameter D, which is proportional to the mean pressure gradient p^. Since this derivation is based on a small amplitude expansion, the result is correct only when D is slightly larger than t...he linear stability limit D^. In this region, it is found that the anomalous heat flux is linear with (D-D^^). The dependence on other parameters R, M and x af"e, however, not apparent in our results since the expression of the anomalous heat transport given in Eq. (7-20) is a functional of the linear marginal modes, which depend on R, M and x implicitly.
When the parameter D is much larger than the linear stability limit D^^, the nonlinearity of the system is so strong that we need numerical calculations to estimate the anomalous heat transport.

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