Two-dimensional, turbulent plasma flows in the topside equatorial F region ionosphere associated with fully developed equatorial spread F are analyzed and simulated numerically. In the inertially dominated flow regime, the governing equations of motion resemble the Navier Stokes equation but are cubicly nonlinear. Large amplitude density irregularities are prerequisite for inertial effects to be important, but when these are present, the third-order nonlinear effects become significant, mean-squared velocity and vorticity cease to be conserved by nonlinear mode coupling, and the foundations of the turbulent cascade theory of Kraichnan <1967> are undermined. Nonetheless, one-dimensional, angle-averaged velocity spectra computed from simulated flows exhibit similarity ranges with k-5/3 and k-3 power laws, resembling inertial ranges and suggesting turbulent cascades. Invariants of the flow (quantities conserved by nonlinear mode coupling) are found which are generalizations of the quadratic forms of kinetic energy and enstrophy and which are dimensionally equivalent to them. Statistical properties of the flow appear to permit turbulent cascades to arise.