Inter-Relations between Scale Invariance and Mixing Length Theory based on g and Rippling Mode Turbulent Transports

When the transport coefficient based on the mixing length theory, D^M, does not include a poloidal mode number, m, it is exactly the same as the scale invariance result, D_s. For the g mode turbulence in stellarators, D_M and D_s corresponding to the con-vective and the collisionless stochastic transport coincide with each other. For the rippling mode turbulence in tokamaks, D_M includes m and disagrees with D_s as well as the collisional stochastic transport in the g mode case. However, by taking account the scale transformation for the poloidal mode number into the expression of D_M, the coincidence is recovered. It is examined how the bootstrap current produced by the electrostatic turbulence changes the transport in the g mode case. A possibility is pointed out that the Kolmogorov spectrum appears in the g mode and the rippling mode turbulence.