The study of fundamental aspects of atmospheric systems is made difficult by the fact that these systems are nonlinear and sometimes chaotic in nature. Accordingly, numerical systems (known as low order models; LOMs) that lend themselves to relatively simple mathematical solutions while still maintaining the fundamental characteristics of the atmospheric flows are valuable research tools for understanding the underlying physics.
Preliminary studies by the Principal Investigators indicate that low order models of atmospheric phenomena may be presented in the form of mathematical systems known in classical mechanics as Volterra gyrostats. A building block approach for the construction of LOMs of atmospheric circulations is proposed, whereby simple well-understood components are used to construct models of complex phenomena. These possess fundamental conservation properties of fluid dynamic equations and have various fluid dynamic interpretations, the celebrated Lorenz model among them.
The proposed research will address the problem of developing physically sound low-order models of atmospheric circulations with particular attention to modeling mesoscale shallow convection (MSC). MSC results from a complex mix of various processes whose roles in the evolution of MSC remain unclear. The goal is to eventually assemble a model of MSC from gyrostats, or blocks of gyrostats, responsible for particular processes.