Multiscale Bounded Derivative Initialization for an Arbitrary Domain

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 from the theory also have been used to prove the existence of a simple reduced system that accurately describes the dominant component of a midlatitude mesoscale storm forced by cooling and heating. Recently, it has been shown how the latter results can be extended to tropospheric flows near the equator. In all of these cases, only a single type of flow was assumed to exist in the domain of interest in order to better examine the characteristics of that flow. Here it is shown how BDT concepts can be used to understand the dependence of developing mesoscale features on a balanced large-scale background flow. That understanding is then used to develop multiscale initialization constraints for the three-dimensional diabatic equations in any domain on the globe.