Three-Dimensional Dynamics of Nonlinear Internal Waves

Abstract

The three-dimensional (3D) baroclinic response of Cayuga Lake to surface wind forcing was investigated using the fully nonhydrostatic MITgcm. The model was validated against observed temperature data using a hydrostatic 450 m (horizontal) grid and both qualitative and quantitative methods. The model correctly reproduces the basin-scale dynamics (e.g., seiche with horizontal mode-one period T1 = 80 h) with a basin-wide root-mean-square error of 1.9 C. Nonlinear internal surges were visualized to evolve due to (i) a wind-induced locally downwelled thermocline (wind duration Twind < T1/4), (ii) a basin-scale wind-induced upwelled thermocline (Twind > T1/4), (iii) internal hydraulic jumps (IHJs). Results from a 113 m grid and field observations were used to characterize the basin-scale internal wave field according to composite Froude number (G2), Wedderburn number (WN), and Lake number (LN). The typical Cayuga Lake response is a surge when ~ 1 < WN (LN) < ~ 2-12 and a surge with emergent nonlinear internal waves (NLIWs) when WN or LN < ~ 2, in agreement with published laboratory studies. An observed shock front was simulated to be an IHJ, occurring at mid-basin during strong winds when WN < 0.8. This is the first simulation of a mid-basin seiche-induced IHJ due to super critical conditions (G2 > 1) in a lake. The topographic-induced IHJs were also shown to form when the surges interact with a sill-contraction topographic feature. Both high-resolution hydrostatic and nonhydrostatic models were used to investigate the evolution, propagation and shoaling of NLIWs at medium lake-scale. A nonhydrostatic 22 m grid with lepticity λ ~ 1 ensures minimal numerical relative to physical dispersion, qualitatively reproducing observed dispersive NLIWs using ~ 2.3E+8 grid cells. Solitary waves evolve with almost unchanged wavelengths upon grid refinement from 40 m (λ ~ 2) to 22 m; suggesting model convergence to the correct solution. Corresponding hydrostatic grids were shown to produce a packet of narrower spurious solitary-like motions with different wavelengths, representing a balance between nonlinear steepening and numerical dispersion. Local gyre-like patterns and secondary transverse NLIW packets were visualized to result from wave-topography interaction, suggesting that NLIW propagation in long narrow lakes, where the bottom topography has irregularities is fundamentally 3D.