nonhydrostatic

Nonhydrostatic refers to fluid flows in which vertical accelerations are non-negligible, so the hydrostatic balance between vertical pressure gradient and gravity does not hold exactly. In atmospheric and oceanic modeling, nonhydrostatic formulations resolve vertical momentum and pressure variations that are neglected in hydrostatic models, enabling more accurate representation of small-scale vertical motions.

Governing equations in nonhydrostatic models typically use the full compressible Navier–Stokes equations (or a Boussinesq approximation) with the complete vertical momentum equation and a nonzero vertical pressure gradient term. In hydrostatic models, the vertical momentum equation is simplified to the hydrostatic relation dp/dz = -ρg, removing vertical accelerations from the dynamics. Nonhydrostatic formulations retain the term for vertical acceleration, allowing significant vertical motions such as deep convection, strong updrafts, and internal gravity waves to influence the flow.

Applications of nonhydrostatic modeling include high-resolution weather prediction at convective and mesoscale ranges, cloud-resolving simulations, and the study of orographic and atmospheric gravity waves. In oceanography, nonhydrostatic models are employed to resolve small-scale processes near coastlines and in shallow regions, where vertical accelerations and interactions with bathymetry drive important dynamics such as breaking waves and stratified mixing.

Computational considerations accompany nonhydrostatic use: solving the full vertical momentum equation increases computational cost and can impose stricter time-step and grid requirements. Consequently, nonhydrostatic models are favored when vertical motions are essential to the phenomena of interest, while hydrostatic models remain adequate for large-scale, slowly varying flows.