Inertial Instability and Mesoscale Convective Systems. Part I: Linear Theory of Inertial Instability in Rotating Viscous Fluids

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Abstract
Observations of strong convective lines in middle latitudes indicate a close association of the lines with the presence of vertical shear of the large-scale horizontal wind. Under the premise that this shear is necessary to the maintenance of mesoscale circulations accompanying the lines, it is found that the susceptibility of the large-scale momentum, temperature and moisture fields to such circulations is related to the inertial stability of the flow. Part I contains a description of a variational solution of the linear equations governing two-dimensional perturbations in a bounded, fully viscous, adiabatic and Boussinesq rotating fluid with constant vertical and horizontal shears. The principal finding of this analysis is that the horizontal length scale of the most unstable normal mode is determined primarily by the depth of the unstable domain and the slope of isentropic surfaces rather than by the diffusive properties of the fluid. The effects of moisture and the conditions under which inertial circulations are likely to develop in the atmosphere are examined in Part II and compared with observations of mesoscale convective systems.

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