Many oceanographers have postulated that internal wave form inversion would take place at the turning point where the thickness of the upper and bottom layer are equal in a stratified two-layer fluid system. This implies that an internal wave of depression may convert into elevation as the wave propagates over a continental margin comprising continental slope and shelf. Laboratory experiments were conducted on the propagation of a depression ISW over a trapezoidal obstacle in a stratified two-layer fresh/brine water system in a steel framed wave tank of 12m long with cross section of 0.7m high by 0.5m wide. The relative difference in water depth between the upper and lower layer and the initial ISW amplitude were the main controlling parameters, among others. The water depth in the stratified two-layer system on the horizontal plateau of the trapezoid obstacle fell into one of the following case: (1) the upper layer larger than lower (H1>¢Ö2'); or (2) equal depth in the upper and lower layer (H1=¢Ö2'); or (3) the upper layer less than lower layer (H1<¢Ö2'). In addition of the depth ratio, the difference in the length of the horizontal plateau and the thickness of the phycnocline above if were also parameters affecting the outcome of the experiments. In these experiments, three different type of the height and length of the trapezoidal obstacle were used, including long (4.8x0.37m), medium (1x0.35m) and short (0.5x0.35m) types. A full account on the characteristics of the ISW evolution observed during this experimental study is presented in this thesis. As an ISW propagated on the fronting slope, were run-down, vortex motion, internal hydraulic jump (IHJ) and run-up were occurred. Once the wave passed the turning point (where the depth of upper and lower layer equal), the wave form became elevation on the plateau above the obstacle. Based on the laboratory data available, the effect on internal wave evolution can be evaluated by the relative fluid thickness (H1/¢Ö2') on the plateau. The outcome can be classified into three categories: (1) H1>¢Ö2', the relative layer thickness on the plateau unfits for depression ISW propagation and waveform behaves like elevation type; (2) H1=¢Ö2', wave boluses containing mixed fluid propagating on the plateau after breaking on the slope; (3) H1<¢Ö2', ISW propagated over trapezoidal obstacle subjected to shoaling and viscosity effect, without change in waveform. As a depression ISW propagated over the variable length of the plateau, another important factor affecting the intensity of the internal hydraulic jump was the water volume drawn from the plateau. In the case of long horizontal plateau, the interaction range was large, and the IHJ was strong. Consequently, the thickness of the increased which caused the IHJ to move upward along the fronting slope. However, the amplitude and phase speed of the resulting internal wave decreased as if propagated further.

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. / Thesis (Ph.D, Civil Engineering) -- Queen's University, 2012-12-14 12:45:21.727