Effects of hydrostatic approximation and resolution on the simulation of convective adjustment

A two-dimensional non-hydrostatic ocean model and a hydrostatic version of the same model are used to simulate convective adjustment, without the use of an instantaneous adjustment parameterization. The model geometry is a domain on the vertical plane of width 40 km and depth 500 m. Model results for four cases are examined: hydrostatic and non-hydrostatic, at 0.1 and 1 km spatial resolution. The convectively adjusted stable state obtained in all four cases are qualitatively similar; thus the hydrostatic approximation does not eliminate convective adjustment. The details of the simulated convective plumes depend on resolution and whether the hydrostatic approximation is made. The adjusted state has significant stratification which cannot be captured by the conventional instantaneous adjustment or diffusion-based parameterizations. We also compare the results to the case when an instantaneous adjustment parameterization is used.