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: The semi-implicit time-stepping scheme is often applied to the terms responsible for fast waves in large-scale global weather prediction and general circulation models to remove the time step restrictions associated with ...

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 vorticity method is applied to determine horizontal divergence using the dynamical balance of terms in the vorticity equation. The viability of the method is analyzed in terms of dynamical approximations, sensitivity ...

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 time-dependent model that simulates the interaction of a thunderstorm with its electrical environment is introduced. The model solves the continuity equation of the Maxwell current density that includes conduction, ...

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 ...