Ionospheric turbulence: Interchange instabilities and chaotic fluid behavior

We develop a set of mode coupling equations which describe the nonlinear evolution of the Rayleigh‐Taylor and gradient drift instabilities which are relevant to the ionosphere. We show that for a three mode system, the nonlinear equations describing these instabilities correspond exactly to the Lorenz equations which approximately describe the Rayleigh‐Benard instability. It is shown that the three mode system can exhibit a strange attractor with chaotic behavior. Ion inertia plays a critical role in this phenomenon in that if it is neglected, as in the collisional limit, the three mode system does not exhibit chaos and a stable convection pattern results.