Internal wave resonance, surges, and strong nonlinear damping differentiated in two elongated lakes with the aid of an original Green's function

Abstract

AbstractWhile the analogy between the wind‐pumped internal seiche in a lake and the driven damped‐harmonic oscillator is recognized, use of a damped‐oscillator model to understand internal‐wave behavior is seldom attempted due to the irregular waveforms arising from variable winds, and to the presence of nonlinear waves like surges. Using a new variable‐frequency Green's function derived for a damped oscillator within the context of the two‐layer model of a stratified basin, we examine internal wave behaviors in Seneca and Owasco Lakes, two elongated lakes in New York state with very different lengths and depths. Our approach reproduces the measured undulations of the lowest horizonal‐mode internal‐seiche with surprising fidelity. It also yields the seiche's seasonal variation of frequency, primarily due to changes in the stratification intensity and thermocline depth. Notably, our model also estimates the seiche amplitude decay‐time, a key quantity difficult to obtain for a constantly agitated seiche. The decay time matches the computed surge‐formation time, which limits seiche lifetimes to as little as one seiche period. Surges also strongly affect the undulating internal‐wave waveforms in a manner consistent with tank experiments. Finally, we find that the internal seiche in Owasco Lake exhibits a uniquely well‐defined resonance with the diel wind pattern, and, for Seneca Lake, that surges propagate bidirectionally, augmenting an oft‐cited report of surges traveling only in one direction.