Some considerations about non-hydrostatic vs. hydrostatic simulation of short-period internal waves. A case study: The Strait of Gibraltar

Abstract

A 3-D nonlinear, finite-difference, high-resolution, hydrodynamic model, extended with a direct implementation of the non-hydrostatic pressure, is applied to study the influence of the non-hydrostatic contribution to the generation and propagation of short-period wave fronts (less than 1 h) in the domain of the Gibraltar Strait. The generation, rupture and propagation of these waves and their free surface manifestations are shown. Calculations of the model show its ability to generate surface wave fronts. However, differences in the period and wavelength of the generated baroclinic waves are evident when hydrostatic and non-hydrostatic results are compared. In particular, the non-hydrostatic contribution tends to generate short-period waves with longer wavelengths and periods with respect to the hydrostatic values. An increase of the non-hydrostatic short-period wavelengths from the Camarinal Sill towards the Mediterranean Sea is also plausible. This increase is induced by changes in the thickness of the deeper layer that influences the disintegration of wave fronts into wave trains and the imbalance of non-hydrostatic and non-linear contributions. Sensitivity analyses show that grid resolution is a key factor due to the potential generation of spurious non-hydrostatic processes, including numerical dispersion induced by a low grid resolution. It is shown that this numerical non-hydrostatic process could generate similar results in hydrostatic and non-hydrostatic simulations when the spatial resolution is comparable to the wavelengths. Results also show the ability of the direct implementation of the non-hydrostatic model to reproduce the main features in a real case, such as the Strait of Gibraltar.