An empirical parametrization of internal seiche amplitude including secondary effects

An internal wave is a propagating disturbance within a stable density-stratified fluid. The internal seiche amplitude is often estimated through theories that describe the amplitude growth based on the Bulk Richardson number ( Ri ). However, most theoretical formulations neglect secondary effects that may influence the evolution of internal seiches. Since these waves have been pointed out as the most important process of vertical mixing, influencing the biogeochemical fluxes in stratified basins, the wrong estimation may have several impacts on the prediction of the system dynamics. This research paid particular attention to the importance of secondary effects that may play a major role on the basin-scale internal wave amplitude, especially related to the interaction between internal waves and lake boundaries, internal wave depth, and mixing processes due to turbulence. Based on a set of methods, which include auto- and cross-correlations, spectral analysis, and mathematical models, we analyzed the effect of total water depth, wind-resonance, and higher vertical modes on the amplitude growth. We based our analysis on underwater temperature measurements and meteorological data obtained from two small thermally-stratified basins, complemented with numerical simulations. We introduce here a new parametrization which takes into account the total water depth ( H ), lake length ( L ), epilimnion thickness ( h e ), as well as the resonance effect. We observed that the rate of amplitude growth decreases compared to linear theory when R i h e / L ≤ 1 . In these cases, we suggests that previous theories overestimate the internal seiche amplitude, neglecting the instabilities generated near the wave crest due to weak stability and wave interactions. However, under shallow thermocline conditions, due to extra pressure in the upper layer, the vertical displacement may be higher than that predicted by the linear theory.