7TROPICAL An Introduction to the OMEGA-Tendency Equation: Its Application to Weather Analyses and Understanding of Hurricane Eye Dynamics

A new equation, herein called the omega-tendency equation, has been derived by the author. The derivation involved combining the divergence equation with the continuity equation. The new equation reveals a dynamical link between the time tendency of omega (or “vertical motion tendency”) together with the ageostrophic vorticity term and a solid body rotation term from the divergence equation. Further mathematical analyses reveal that the two aforementioned terms would cancel each other if the horizontal wind components are in exact gradient wind balance. This implies that the super/sub-gradient winds would have a direct dynamical response to induce vertical motion tendency in an air parcel. Since the derivation involves the continuity equation in pressure coordinates, hydrostatic balance is an underlying assumption in this omega-tendency equation.

Since vertical motion is an important quantity in the studies of various meteorological phenomena, this newly derived omega tendency equation could find numerous applications in weather analyses and numerical weather forecasts. Preliminary interpretations indicate that this equation can be applied to the diagnosis of convection initiation, jet-stream dynamics, as well as toward a better understanding of the internal dynamics of intense atmospheric vortices, such as tornado inner-core and hurricane-eye dynamics.

The derivation of the omega-tendency equation and its physical interpretations as well as applications to weather analyses will be presented in the conference.