skip to main content


Title: Wave propagation studies in numerical wave tanks with weakly compressible smoothed particle hydrodynamics
Generation and propagation of waves in a numerical wave tank constructed using Weakly Compressible Smoothed Particle Hydrodynamics (WCSPH) are considered here. Numerical wave tank simulations have been carried out with implementations of different Wendland kernels in conjunction with different numerical dissipation schemes. The simulations were accelerated by using General Process Graphics Processing Unit (GPGPU) computing to utilize the massively parallel nature of the simulations and thus improve process efficiency. Numerical experiments with short domains have been carried out to validate the dissipation schemes used. The wave tank experiments consist of piston-type wavemakers and appropriate passive absorption arrangements to facilitate comparisons with theoretical predictions. The comparative performance of the different numerical wave tank experiments was carried out on the basis of the hydrostatic pressure and wave surface elevations. The effect of numerical dissipation with the different kernel functions was also studied on the basis of energy analysis. Finally, the observations and results were used to arrive at the best possible numerical set up for simulation of waves at medium and long distances of propagation, which can play a significant role in the study of extreme waves and energy localizations observed in oceans through such numerical wave tank simulations.  more » « less
Award ID(s):
1854532
NSF-PAR ID:
10232181
Author(s) / Creator(s):
;
Date Published:
Journal Name:
Journal of marine science and engineering
Volume:
9
ISSN:
2077-1312
Page Range / eLocation ID:
233
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Abstract

    Acoustic wave heating is believed to contribute significantly to the missing energy input required to maintain the solar chromosphere in its observed state. We studied the propagation of waves above the acoustic cutoff in the upper photosphere into the chromosphere with ultraviolet and optical spectral observations interpreted through comparison with 3D radiative magnetohydrodynamic Bifrost models to constrain the heating contribution from acoustic waves in the solar atmosphere. Sit-and-stare observations taken with the Interface Region Imaging Spectrograph and data from the Interferometric BIdimensional Spectrograph were used to provide the observational basis of this work. We compared the observations with synthetic observables derived from the Bifrost solar atmospheric model. Our analysis of the Bifrost simulations show that internetwork and enhanced-network regions exhibit significantly different wave-propagation properties, which are important for accurate wave flux estimates. The inferred wave energy fluxes based on our observations are not sufficient to maintain the solar chromosphere. We point out that the systematics of the modeling approaches in the literature lead to differences which could determine the conclusions of this type of study, based on the same observations.

     
    more » « less
  2. Abstract

    We present an investigation of the azimuthal bimodality of the wind-wave spectrum for waves shorter than the dominant scale comparing numerical model solutions of developing waves from idealized experiments using WAVEWATCH III (WW3). The wave solutions were forced with the “exact” Webb–Resio–Tracy (WRT) nonlinear energy fluxes and the direct interaction approximation (DIA) with three different combinations of wind input and breaking dissipation parameterizations. The WRT gives larger azimuthal bimodal amplitudes compared to the DIA regardless of wind input/dissipation. The widely used wind input/dissipation parameterizations (i.e., ST4 and ST6) generally give narrow directional distributions with relatively small bimodal amplitudes and lobe separations compared to field measurements. These biases are significantly improved by the breaking dissipation of Romero (R2019). Moreover, the ratio of the resolved cross- to downwind mean square slope is significantly lower for ST4 and ST6 compared to R2019. The overlap integral relevant for the prediction of microseisms is several orders of magnitude smaller for ST4 and ST6 compared to R2019, which nearly agrees with a semiempirical model.

    Significance Statement

    Spectral gravity wave models generally cannot accurately predict the directional distribution which impacts their ability to predict the resolved down- and crosswind mean square slopes and the generation of microseisms. Our analysis shows that a directionally narrow spectral energy dissipation, accounting for long-wave–short-wave modulation, can significantly improve the directional distribution of the wind-wave spectrum by coupling to the nonlinear energy fluxes due to wave–wave interactions, which has important implications for improved predictions of the mean square slopes and the generation of microseisms.

     
    more » « less
  3. Abstract

    Oceanic mixing, mostly driven by the breaking of internal waves at small scales in the ocean interior, is of major importance for ocean circulation and the ocean response to future climate scenarios. Understanding how internal waves transfer their energy to smaller scales from their generation to their dissipation is therefore an important step for improving the representation of ocean mixing in climate models. In this study, the processes leading to cross-scale energy fluxes in the internal wave field are quantified using an original decomposition approach in a realistic numerical simulation of the California Current. We quantify the relative contribution of eddy–internal wave interactions and wave–wave interactions to these fluxes and show that eddy–internal wave interactions are more efficient than wave–wave interactions in the formation of the internal wave continuum spectrum. Carrying out twin numerical simulations, where we successively activate or deactivate one of the main internal wave forcing, we also show that eddy–near-inertial internal wave interactions are more efficient in the cross-scale energy transfer than eddy–tidal internal wave interactions. This results in the dissipation being dominated by the near-inertial internal waves over tidal internal waves. A companion study focuses on the role of stimulated cascade on the energy and enstrophy fluxes.

     
    more » « less
  4. Abstract

    Large-amplitude internal solitary waves were recently observed in a coastal plain estuary and were hypothesized to evolve from an internal lee wave generated at the channel–shoal interface. To test this mechanism, a 3D nonhydrostatic model with nested domains and adaptive grids was used to investigate the generation of the internal solitary waves and their subsequent nonlinear evolution. A complex sequence of wave propagation and transformation was documented and interpreted using the nonlinear wave theory based on the Korteweg–de Vries equation. During the ebb tide a mode-2 internal lee wave is generated by the interaction between lateral flows and channel–shoal topography. This mode-2 lee wave subsequently propagates onto the shallow shoal and transforms into a mode-1 wave of elevation as strong mixing on the flood tide erases stratification in the bottom boundary layer and the lower branch of the mode-2 wave. The mode-1 wave of elevation evolves into an internal solitary wave due to nonlinear steepening and spatial changes in the wave phase speed. As the solitary wave of elevation continues to propagate over the shoaling bottom, the leading edge moves ahead as a rarefaction wave while the trailing edge steepens and disintegrates into a train of rank-ordered internal solitary waves, due to the combined effects of shoaling and dispersion. Strong turbulence in the bottom boundary layer dissipates wave energy and causes the eventual destruction of the solitary waves. In the meantime, the internal solitary waves can generate elevated shear and dissipation rate in local regions.

    Significance Statement

    In the coastal ocean nonlinear internal solitary waves are widely recognized to play an important role in generating turbulent mixing, modulating short-term variability of nearshore ecosystem, and transporting sediment and biochemical materials. However, their effects on shallow and stratified estuaries are poorly known and have been rarely studied. The nonhydrostatic model simulations presented in this paper shed new light into the generation, propagation, and transformation of the internal solitary waves in a coastal plain estuary.

     
    more » « less
  5. The YBJ equation (Young & Ben Jelloul, J. Marine Res. , vol. 55, 1997, pp. 735–766) provides a phase-averaged description of the propagation of near-inertial waves (NIWs) through a geostrophic flow. YBJ is obtained via an asymptotic expansion based on the limit $\mathit{Bu}\rightarrow 0$ , where $\mathit{Bu}$ is the Burger number of the NIWs. Here we develop an improved version, the YBJ + equation. In common with an earlier improvement proposed by Thomas, Smith & Bühler ( J. Fluid Mech. , vol. 817, 2017, pp. 406–438), YBJ + has a dispersion relation that is second-order accurate in $\mathit{Bu}$ . (YBJ is first-order accurate.) Thus both improvements have the same formal justification. But the dispersion relation of YBJ + is a Padé approximant to the exact dispersion relation and with $\mathit{Bu}$ of order unity this is significantly more accurate than the power-series approximation of Thomas et al. (2017). Moreover, in the limit of high horizontal wavenumber $k\rightarrow \infty$ , the wave frequency of YBJ + asymptotes to twice the inertial frequency $2f$ . This enables solution of YBJ + with explicit time-stepping schemes using a time step determined by stable integration of oscillations with frequency $2f$ . Other phase-averaged equations have dispersion relations with frequency increasing as $k^{2}$ (YBJ) or $k^{4}$ (Thomas et al. 2017): in these cases stable integration with an explicit scheme becomes impractical with increasing horizontal resolution. The YBJ + equation is tested by comparing its numerical solutions with those of the Boussinesq and YBJ equations. In virtually all cases, YBJ + is more accurate than YBJ. The error, however, does not go rapidly to zero as the Burger number characterizing the initial condition is reduced: advection and refraction by geostrophic eddies reduces in the initial length scale of NIWs so that $\mathit{Bu}$ increases with time. This increase, if unchecked, would destroy the approximation. We show, however, that dispersion limits the damage by confining most of the wave energy to low  $\mathit{Bu}$ . In other words, advection and refraction by geostrophic flows does not result in a strong transfer of initially near-inertial energy out of the near-inertial frequency band. 
    more » « less