Nonlinear Triad Interactions and the Mechanism of Spreading in Drift-Wave Turbulence

We present the results of a derivation of the fluctuation energy transport matrix for the two-field Hasegawa-Wakatani model of drift wave turbulence. The energy transport matrix is derived from a two-scale direct interaction approximation assuming weak turbulence. We examine different classes of triad interactions and show that radially extended eddies, as occurs in penetrative convection, are the most effective in turbulence spreading. We show that in the near-adiabatic limit internal energy spreads faster than the kinetic energy. Previous theories of spreading results are discussed in the context of weak turbulence theory.

Figure 1

The manifold of wave numbers that interact resonantly with a $p_x=0$ mode. In a full spectrum one should integrate over the other two wave numbers of the triad to compute the diffusion coefficients [as in Eqs. (4, 5, 6)], only taking the resonant interactions into account. This can be achieved by computing the integrals along the resonance manifold as shown (up to a wave-number dependent coefficient).

Figure 2

The resonance manifold for the interaction involving a $q_y=0$ mode.

Figure 3

The resonance manifold for the interaction involving a hydrodynamic streamer [i.e., $(k_x,k_{\parallel })\to 0$].