Three‐dimensional simulation of high‐frequency nonlinear internal wave dynamics in <scp>C</scp>ayuga <scp>L</scp>ake

Abstract

Abstract Three‐dimensional (3‐D) hydrostatic and nonhydrostatic versions of the MITgcm were applied to simulate the dynamics of the internal wave field (basin‐scale seiches, nonlinear surges, and high‐frequency nonlinear internal waves, NLIWs) in Cayuga Lake, NY. The simulations were performed using up to 226 million computational cells with several horizontal grid resolutions, varying from 450 × 450 m to 22 × 22 m. Vertical grid spacing was not varied and ranged from 0.5 to 2.95 m. The 22 × 22 m nonhydrostatic grid reproduced qualitatively the formation, propagation, and shoaling of observed NLIWs using &gt;10 grid points along the wavelength and a grid lepticity λ of O (1). This ensured, respectively, that the waves were not aliased and physical dispersion predominated over numerical dispersion. Using a sensitivity analysis, we generalize that correctly simulating NLIWs in real domains, using second‐order discretization, requires grid resolutions that are an order of magnitude smaller than the wavelength and amplitude with λ ∼ 2; consistent with published work on idealized domains. Local gyre‐like circulation was simulated, near midbasin headlands, and transverse shoaling of NLIW packets on lateral boundaries was associated with topographic reflection and refraction, in agreement with published field observations from estuaries, which show NLIW propagation in long narrow quasi‐2‐D systems (e.g., Finger Lakes, lochs, fjords, estuaries, and straits) is fundamentally 3‐D. These results, therefore, help fill the gap in understanding and correctly modeling the multiscale 3‐D dynamics of NLIWs in complex natural systems.