Nonlinear stability of multilayer quasi-geostrophic flow

New nonlinear stability theorems are derived for disturbances to steady basic flows in the context of the multilayer quasi-geostrophic equations. These theorems are analogues of Arnol’d's second stability theorem, the latter applying to the two-dimensional Euler equations. Explicit upper bounds are obtained on both the disturbance energy and disturbance potential enstrophy in terms of the initial disturbance fields. An important feature of the present analysis is that the disturbances are allowed to have non-zero circulation. While Arnol’d's stability method relies on the energy–Casimir invariant being sign-definite, the new criteria can be applied to cases where it is sign-indefinite because of the disturbance circulations. A version of Andrews’ theorem is established for this problem, and uniform potential vorticity flow is shown to be nonlinearly stable. The special case of two-layer flow is treated in detail, with particular attention paid to the Phillips model of baroclinic instability. It is found that the short-wave portion of the marginal stability curve found in linear theory is precisely captured by the new nonlinear stability criteria

Modeling and Optimal Control of Atmospheric Pollution Hazard in Nuclear and Chemical Disasters

AbstractNuclear and chemical disasters can cause heavy atmospheric pollution hazard and threat people's lives and health. In this paper, theory and application for modeling and optimal control of such hazard is studied. The modeling is based on the simulation and visualization of atmospheric dispersion of pollutants, the source term estimation of nuclear and chemical disasters, and the risk evaluation of hazardous substances. The optimal control is based on Natural Cybernetics theory, effective and economic cost evaluation of control techniques, and optimization methods. Some applications and illustrations of modeling and optimal control are reported