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These files contain data supporting all results reported in Lloret et al. "A robust numerical method for the generation and propagation of periodic finite-amplitude internal waves in natural waters using high-accuracy simulations". In Lloret et al. we found: The design and implementation of boundary conditions for the robust generation and simulation of periodic finite-amplitude internal waves is examined in a quasi two-layer continuous stratification using a spectralelement-method-based incompressible flow solver. The commonly used Eulerian approach develops spurious, and potentially catastrophic small-scale numerical features near the wave-generating boundary in a non-linear stratification when the parameter A/(δc) is sufficiently larger than unity; A and δ are measures of the maximum wave-induced vertical velocity and pycnocline thickness, respectively, and c is the linear wave propagation speed. To this end, an Euler–Lagrange approach is developed and implemented to generate robust high-amplitude periodic deep-water internal waves. Central to this approach is to take into account the wave- induced (isopycnal) displacement of the pycnocline in both the vertical and (effectively) upstream directions. With amplitudes not restricted by the limits of linear theory, the Euler–Lagrange-generated waves maintain their structural integrity as they propagate away from the source. The advantages of the high-accuracy numerical method, whose minimal numerical dissipation cannot damp the above near-source spurious numerical features of the purely Eulerian case, can still be preserved and leveraged further along the wave propagation path through the robust reproduction of the non-linear adjustments of the waveform. The near- and far-source robustness of the optimized Euler–Lagrange approach is demonstrated for finite-amplitude waves in a sharp quasi two- layer continuous stratification representative of seasonally stratified lakes. The findings of this study provide an enabling framework for two-dimensional simulations of internal swash zones driven by well-developed non- linear internal waves and, ultimately, the accompanying turbulence-resolving three-dimensional simulations. Please cite as: Lloret, P., Diamessis, P., Stastna, M., & Thomsen, G. N. (2024). Data and scripts from: A robust numerical method for the generation and propagation of periodic finite-amplitude internal waves in natural waters using high-accuracy simulations [Data set]. Cornell University eCommons Repository. https://doi.org/10.7298/5VKW-0303 

Abstract. The design and implementation of boundary conditions for the robust generation and simulation of periodic finite-amplitude internal waves is examined in a quasi two-layer continuous stratification using a spectral-element-method-based incompressible flow solver. The commonly used Eulerian approach develops spurious, and potentially catastrophic small-scale numerical features near the wave-generating boundary in a non-linear stratification when the parameter A/(δc) is sufficiently larger than unity; A and δ are measures of the maximum wave-induced vertical velocity and pycnocline thickness, respectively, and c is the linear wave propagation speed. To this end, an Euler–Lagrange approach is developed and implemented to generate robust high-amplitude periodic deep-water internal waves. Central to this approach is to take into account the wave-induced (isopycnal) displacement of the pycnocline in both the vertical and (effectively) upstream directions. With amplitudes not restricted by the limits of linear theory, the Euler–Lagrange-generated waves maintain their structural integrity as they propagate away from the source. The advantages of the high-accuracy numerical method, whose minimal numerical dissipation cannot damp the above near-source spurious numerical features of the purely Eulerian case, can still be preserved and leveraged further along the wave propagation path through the robust reproduction of the non-linear adjustments of the waveform. The near- and far-source robustness of the optimized Euler–Lagrange approach is demonstrated for finite-amplitude waves in a sharp quasi two-layer continuous stratification representative of seasonally stratified lakes. The findings of this study provide an enabling framework for two-dimensional simulations of internal swash zones driven by well-developed non-linear internal waves and, ultimately, the accompanying turbulence-resolving three-dimensional simulations. 

Abstract Shoaling internal solitary waves (ISWs) were observed at three mooring sites on the upper continental slope in the northern South China Sea over a period of 5–11 months at water depths of 600, 430, and 350 m. Their properties exhibit a fortnightly variation because of their origination from internal tides. ISW amplitudes, current speeds, and propagation speeds are greater and wave widths narrower in summer than in winter, consistent with the effect of increased stratification in summer, as confirmed by Dubreil‐Jacotin‐Long (DJL) solutions. As ISWs propagate up the slope, the differential response of current and propagation speeds to bottom topography provides an opportunity for convective breaking of ISWs. Convective breaking occurs mostly between 430 and 600‐m depths and exhibits a marginal convective instability status such that (a) the maximum current speed remains nearly equal to the propagation speed and (b) for large‐amplitude waves the current speed and propagation speed decrease at nearly the same rate between 600 and 430‐m depths. The marginal convective instability occurs because ISWs adjust gradually to the gently sloping bottom and preserve their structural integrity after the onset of breaking. Vertical velocity variances behind the leading ISWs, which serve as a surrogate for the number of trailing waves, increase when ISWs reach the convective breaking limit, suggesting that convective breaking may accelerate the fission process in leading ISWs or that convective breaking is accompanied by an enhanced nonlinear dispersion of waves trailing ISWs generated by internal tides. 

The formation of a recirculating subsurface core in an internal solitary wave (ISW) of depression, shoaling over realistic bathymetry, is explored through fully nonlinear and nonhydrostatic two-dimensional simulations. The computational approach is based on a high-resolution/accuracy deformed spectral multidomain penalty-method flow solver, which employs the recorded bathymetry, background current, and stratification profile in the South China Sea. The flow solver is initialized using a solution of the fully nonlinear Dubreil–Jacotin–Long equation. During shoaling, convective breaking precedes core formation as the rear steepens and the trough decelerates, allowing heavier fluid to plunge forward, forming a trapped core. This core-formation mechanism is attributed to a stretching of a near-surface background vorticity layer. Since the sign of the vorticity is opposite to that generated by the propagating wave, only subsurface recirculating cores can form. The onset of convective breaking is visualized, and the sensitivity of the core properties to changes in the initial wave, near-surface background shear, and bottom slope is quantified. The magnitude of the near-surface vorticity determines the size of the convective-breaking region, and the rapid increase of local bathymetric slope accelerates core formation. If the amplitude of the initial wave is increased, the subsequent convective-breaking region increases in size. The simulations are guided by field data and capture the development of the recirculating subsurface core. The analyzed parameter space constitutes a baseline for future three-dimensional simulations focused on characterizing the turbulent flow engulfed within the convectively unstable ISW.