Statistical analysis and numerical modeling of shoaling internal waves offshore of La Jolla, CA*

High-frequency internal wave (IW) trains with a period of approximately 10 min are observed at certain phases of the internal tide offshore of La Jolla, CA. The shoaling IWs structure is captured by an L-shaped temperature fiber optic sensing array. Despite the distinctive structure of the IWs, their intermittent and stochastic nature complicates the analysis. We apply conditional statistics to extract solitary wave characteristics like the dominant velocity (0.8 m/s), wave period (∼ 8 min), and wave propagation angle (∼15° to shore normal). Next, we demonstrate that wave trains with these characteristics are generated as solutions to the two-dimensional weakly nonlinear Kadomtsev–Petviashvili (KP) wave equation with cross-shore-varying bathymetry. The initial condition is, informed by the data, chosen as a 15° angled solitary wave of finite alongshore span. For a fixed initial wave amplitude, the density stratification is varied to investigate the evolution of the shoaling waves that are generated by the dispersion and advection of the initial soliton solution.