Abstract
Abstract Stability properties of a two-layer model of homogeneous and incompressible fluid subject to gravity and rotation are investigated by the small-perturbation method. The upper and lower fluids correspond, respectively, to warm and cold air. The interface between the warm and cold layers intersects the ground and forms the surface front. The model has been used to investigate the development of frontal cyclones. Linearized equations of warm and cold layers are solved as an eigenvalue problem to find solutions growing exponentially with time using a finite-difference technique. For prescribed values of the density ratio ϵ of warm and cold layers, the north-south extent D of the frontal interface, the Coriolis parameter f, the external gravity wave speed C0, and the basic state cold air velocity ū1, we vary the values of the wavenumber k of perturbations and the basic state warm air velocity ū2, through the use of the Rossby number [Ro≡½(ū2&minusū1)k/f] and the Richardson number [Ri≡C0(1−∈)/(ū2&minus...
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