Ionospheric plasma cloud dynamics via regularized contour dynamics. I. Stability and nonlinear evolution of one‐contour models

The linear stability and nonlinear evolution of a regularized contour dynamical model of an ionospheric plasma cloud (or deformable dielectric) is examined. That is, the cloud is modeled by piecewise‐constant ion density regions; and the regularization is accomplished with a tangential diffusion operator that models aspects of the diffusion operator in two dimensions. A complete linear stability analysis of a circular cloud shows that a single‐mode excitation ‘‘cascades downward’’ in wavenumber as it grows in amplitude, a process that results from the symmetry‐breaking electric field. Approximate formulas are derived for the amplitude growth and cascade‐down phenomena and verified with precise numerical calculations. A simple rescaling shows that clouds with large λ (=cloud‐ion density/ambient‐ion density) evolve more slowly and appear more dissipative. The regularized contour‐dynamical algorithm for computations in the nonlinear regime is validated against the linear analysis and truncation errors are assessed by using different spatial resolutions. Calculations in the nonlinear regime show the experimentally observed ‘‘backside’’ striations. Furthermore, at long times, a secondary structure arises on the sides of the primary striations. A comparison of simulations with different λ shows that nonlinear effects arise sooner in normalized time (but longer in real time) if λ is larger.