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 \(Ri~h_e/L\le 1\). 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.

内波是在稳定的密度分层流体中的传播扰动。内部seiche振幅通常是通过基于Bulk Richardson数（Ri）。然而，大多数理论表述忽略了可能影响内部神学发展的次要影响。由于这些波已被指出是垂直混合的最重要过程，影响了分层盆地中的生物地球化学通量，因此错误的估计可能会对系统动力学的预测产生若干影响。这项研究特别关注了可能对盆地规模内波振幅起主要作用的次要影响的重要性，特别是与内波与湖泊边界之间的相互作用，内波深度以及湍流引起的混合过程有关。基于包括自相关和互相关，光谱分析和数学模型在内的一系列方法，我们分析了总水深，风共振，以及垂直模式对幅度增长的影响。我们的分析基于从两个小型热分层盆地获得的水下温度测量值和气象数据，并辅以数值模拟。我们在这里介绍了一种新的参数化方法，该方法考虑了总水深（H），湖泊长度（L），epi生厚度（\（h_e \））以及共振效应。我们观察到\（Ri〜h_e / L \ le 1 \）时，与线性理论相比，幅度增长的速率降低。在这些情况下，我们认为先前的理论高估了内部seiche振幅，而忽略了由于弱稳定性和波浪相互作用而在波峰附近产生的不稳定性。但是，在较浅的温跃层条件下，由于上层的额外压力，垂直位移可能会比线性理论所预测的高。