Application to real weather systems
Adjustment theory is most useful for understanding model behavior and how data impact the model forecast, but it also helps some in understanding the real atmosphere.
Big picture
The Rossby radius in the tropics is very large. Consequently, most mesoscale to synoptic-scale features are short-lived and the wind field is more important than the mass field in determining their future evolution. Monsoons and planetary-scale features such as the Madden-Julian Oscillation (MJO) are large enough to have longevity and for the mass field to be more important in the forecast. Hurricanes have sufficiently high vorticity to greatly reduce the Rossby radius.
The Rossby radius in mid-latitudes is smaller than the long-wave ridges and troughs, which are controlled by the mass field. Mobile short-wave troughs are a mixture, depending on their strength and wavelength. Mass and wind information are both important in determining the evolution of mobile troughs. Features in an anticyclonic environment have to be larger than features in a cyclonic environment to have longevity.
Real-world differences from theory
The real atmosphere usually has fairly smooth evolution rather than a sudden imposition of disturbances followed by wave pulses and an adjustment process. However, potent, rapidly developing systems sometimes do undergo fairly sudden changes in which gravity waves may play a role in an adjustment process.
Gravity waves are ubiquitous in the real atmosphere, caused by fronts, cumulus clouds, flow over hills, cold air drainage, and many other things. Typically they are of small amplitude and short horizontal wavelength, propagating their energy vertically rather than spreading energy over large horizontal distances. They do not accomplish much (if any) geostrophic adjustment.
The theory is based on barotropic conditions — no phase tilt or change in perturbation sign with height. A baroclinic wave has a phase tilt while a hurricane has an anticyclone sitting on top of the cyclone. These kinds of complications make application sometimes less than straightforward.
Nonetheless, the essence of the theory — the longevity of a feature and whether it is controlled primarily by the wind field or the mass field — does hold up. The atmosphere is always being thrown out of balance — by mountains, convection, turbulence, jet streaks accelerating parcels through regions of near zero absolute vorticity, movement of sharp boundaries created by geography (like elevated mixed-layer plumes), etc. Usually the forcing throwing things out of balance gradually ramps up and secondary circulations form in response, somewhat lagged. Thus, the atmosphere can be thought of as always undergoing an adjustment.
Practical forecast application
Suppose an event occurs, creating some disturbance, and then its forcing dissipates. It might be an MCC
mid-level vortex and upper-level outflow jet, it might be a cutoff 500 hPa cold pocket, it might be
a warm, elevated, mixed-layer plume.
LR?If it measures up as "large," expect it will retain its characteristic temperature perturbations for a considerable time (modified, of course, by radiation and other physical processes) and the winds will come into balance with the heights. If it measures up as "small," expect it will disperse, the weakened remnants will retain some of the original vorticity perturbation, and the heights will come into balance with the remaining winds.