Abstract: In a series of numerical experiments, Williamson and Temperton demonstrated that the interaction of the high-frequency gravity waves with the low-frequency Rossby waves in a three-dimensional adiabatic model is very weak. ...

Abstract: Current meteorological observational networks are capable of observing only a limited number of the dependent variables that describe the state of the atmosphere. For example, the large-scale temperature and horizontal ...

Abstract: We consider smooth solutions of the shallow water equations restricted only by the assumption that the magnitude of the deviation of the geopotential from the mean is small relative to that mean. For such solutions we find ...

Abstract: Pressure oscillations with amplitudes of the deviations from the horizontal mean and periods considerably less than those for the large-scale case have been observed in a number of summer and winter storms. However, there ...

Abstract: Large-amplitude high-frequency motions can appear in the solution of a hyperbolic system containing multiple time scales unless the initial conditions are suitably adjusted through a process called initialization. We observe ...

Abstract: The time step for the leapfrog scheme for a symmetric hyperbolic system with multiple timescales is limited by the Courant-Friedlichs-Lewy condition based on the fastest speed present. However, in many physical cases, most ...

Abstract: The bounded derivative theory (BDT) for hyperbolic systems with multiple timescales was originally applied to the initialization problem for large-scale shallow-water flows in the midlatitudes and near the equator. Concepts ...

Abstract: A mathematical theory was recently developed on the relationship between the dominant and gravity wave components of the slowly varying in time solutions (solutions varying on the advective timescale) corresponding to ...

Abstract: Recently, a mathematical theory has been developed that proves that there are two main components of the solution of the forced dynamical system that describes a mesoscale storm driven by cooling and heating processes. The ...