Chrystal and Proudman resonances simulated with three numerical models

The aim of this work was to study Chrystal and Proudman resonances in a simple closed basin and to explore and compare how well the two resonant mechanisms are reproduced with different, nowadays widely used, numerical ocean models. The test case was based on air pressure disturbances of two commonly used shapes (a sinusoidal and a boxcar), having various wave lengths, and propagating at different speeds. Our test domain was a closed rectangular basin, 300 km long with a uniform depth of 50 m, with the theoretical analytical solution available for benchmark. In total, 2250 simulations were performed for each of the three different numerical models: ADCIRC, SCHISM and ROMS. During each of the simulations, we recorded water level anomalies and computed the integral of the energy density spectrum for a number of points distributed along the basin. We have successfully documented the transition from Proudman to Chrystal resonance that occurs for a sinusoidal air pressure disturbance having a wavelength between one and two basin lengths. An inter-model comparison of the results shows that different models represent the two resonant phenomena in a slightly different way. For Chrystal resonance, all the models showed similar behavior; however, ADCIRC model providing slightly higher values of the mean resonant period than the other two models. In the case of Proudman resonance, the most consistent results, closest to the analytical solution, were obtained using ROMS model, which reproduced the mean resonant speed equal to 22.00 m/s— i.e., close to the theoretical value of 22.15 m/s. ADCIRC and SCHISM models showed small deviations from that value, with the mean speed being slightly lower—21.97 m/s (ADCIRC) and 21.93 m/s (SCHISM). The findings may seem small but could play an important role when resonance is a crucial process producing enhancing effects by two orders of magnitude (i.e., meteotsunamis).