Bulletin of the American Physical Society
75th Annual Meeting of the Division of Fluid Dynamics
Volume 67, Number 19
Sunday–Tuesday, November 20–22, 2022; Indiana Convention Center, Indianapolis, Indiana.
Session L27: Waves: Internal and Interfacial Waves |
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Chair: Kianoosh Yousefi, Columbia; Peter Diamessis, Cornell University Room: 235 |
Monday, November 21, 2022 8:00AM - 8:13AM |
L27.00001: Reflection and transmission of internal waves over topography in the presence of a barotropic tide Michael Allshouse, Manikandan Mathur, Sai Saandeep Sampatirao Internal waves are ubiquitous in the ocean and understanding how these waves change as they pass over topography provides insight into the ocean’s energy budget. Some are generated as a result of barotropic tides passing over topography and radiate away from their generation site, with mode-1 internal waves propagating the furthest. As these mode-1 waves pass over another topographic feature, some of the energy is converted into higher modes, which more rapidly dissipates, while the rest remains in a mode-1 wave that either reflects off the topographic feature or transmits past it. This process is complicated by the persisting barotropic tide, which continues generating internal waves off this second topographic feature. We investigate, analytically and numerically, the modal decomposition of the reflection and transmission process of an incoming mode-1 wave passing over a topographic feature in the presence of a background barotropic tide. Interestingly, despite using a low amplitude mode-1 wave and barotropic tide, the resulting wave field is not simply a superposition of the fields that would have resulted if these features were modeled in isolation. The resulting reflection and transmission of the mode-1 wave depends on its phase difference with the barotropic tide. |
Monday, November 21, 2022 8:13AM - 8:26AM |
L27.00002: Lagrangian transport by convectively breaking shoaling internal solitary waves with recirculating turbulent cores. Tilemachos Bolioudakis, Peter J Diamessis, Theodoros Diamantopoulos, Greg N Thomsen, Ren-Chieh Lien, Kevin G Lamb, Gustaaf B Jacobs, Bjoern F Klose This presentation discusses the first set of results on Lagrangian particle entrainment, transport, and detrainment, during internal solitary wave (ISW) shoaling over realistic gentle bathymetric slopes in the South China Sea. The shoaling ISWs are subject to convective breaking and, in conjunction with the near-surface shear structure of the background current, develop a subsurface recirculating core. The present work-in-progress focuses on the one-way coupling of a high-accuracy/resolution massively parallel 3D non-linear non-hydrostatic flow solver (Diamantopoulos et al. (Ocean Modelling, 2022)) with a high-accuracy particle-tracking scheme of Jacobs et al. (Journal of Computational and Applied Mathematics, 2007). Preliminary results shown here aim to identify the trajectories of neutrally buoyant Lagrangian particles in both 2-D and 3-D simulations and link them to Eulerian analysis of the structure of the turbulent core. Particular attention will be devoted to a qualitative-based outline of the recirculating core as contrasted to the classic umax/c metrics. |
Monday, November 21, 2022 8:26AM - 8:39AM |
L27.00003: The development of turbulence in convectively breaking internal solitary waves of depression shoaling over gentle slopes in the South China Sea Peter J Diamessis, Theodoros Diamantopoulos, Tilemachos Bolioudakis, Ren-Chieh Lien, Kevin G Lamb, Gustavo A Rivera-Rosario, Greg N Thomsen We report on results from three-dimensional turbulence-resolving simulations of shoaling internal solitary waves (ISWs) over a gentle bathymetric slope and background stratification/current profiles directly sampled in the South China Sea. Under the realistic constraint of normal-to-isobath wave propagation, the massively parallel simulations leverage a custom-designed hybrid high-order spectral-element/Fourier-Galkerin flow solver (Diamantopoulos et al. 2022). Three values of initial ISW amplitude (max. isopycnal displacement) of 136m, 143m and 150m are considered. The O(1km)-long waves propagate from 900m to 350m depth waters over a distance of 75km. As soon as the ISW arrives at the steepest slope of the propagation track, a distinct convective instability develops with the outer waveform of the ISW remaining, nevertheless, distinctly symmetric. The isopycnal plunging from the rear of the wave during the onset of this instability effectively drives a turbulent gravity-current-like feature which propagates through the ISW interior. The rear half of the wave core is mixed giving rise to values of the Richardson number at the wave trough which are sufficiently low to trigger a shear-instability. The distinct Kelvin-Helmholtz billows which emerge, in the form of 15-20m overturns, are advected through the pycnocline out of the rear of the wave. In the case of the 150m-amplitude wave, the shear instability produces dramatically high levels of turbulent kinetic energy and gives rise to a visible wake of patchy turbulence and, apparently dispersive, lower-amplitude waves behind the ISW. The presentation concludes with the examination of the correlation of the along-propagation-track turbulent kinetic energy intensity with wave-scale properties and a discussion of the potential for marginal instability in the simulated ISWs. |
Monday, November 21, 2022 8:39AM - 8:52AM |
L27.00004: Transmission and Reflection of Three-Dimensional Anelastic Internal Gravity Wave Packets in Nonuniform Retrograde Shear Flow Alain D Gervais, Gordon E Swaters, Bruce R Sutherland Internal gravity wave packets (IGWPs) propagate horizontally and vertically within stably stratified fluids. Linear theory predicts that a small amplitude IGWP propagating upward against a retrograde background shear flow will be Doppler-shifted until its Doppler-shifted frequency equals the background buoyancy frequency. The `reflection level' (RL) at which this occurs is the height at which the incident IGWP reflects, resulting in a downward-propagating IGWP. Anelastic amplitude growth allows IGWPs to evolve nonlinearly: wave-wave interactions induce an order amplitude-squared mean flow that locally accelerates the ambient fluid. Simulated Boussinesq 3-D IGWPs (Gervais et al, PRFluids, under review) were shown to transmit partially above the RL, provided the magnitude of the shear associated with their induced mean flow was locally greater than that of the background shear. We study the anelastic evolution of an initially small amplitude 3-D IGWP initialized with its predicted induced mean flow superimposed as it propagates into a nonuniform retrograde shear flow. Simulations are initialized with a range of amplitudes and vertical wavenumbers. We quantify wave transmission using the ratio of upward-propagating pseudomomentum above the RL to the total (conserved) pseudomomentum. |
Monday, November 21, 2022 8:52AM - 9:05AM |
L27.00005: Aspects of the spectral-element-based simulation of a model internal swash zone Pierre Lloret, Peter J Diamessis, Marek Stastna We examine the design and implementation of a numerically simulated internal swash zone (ISZ) in a two-layer continuous stratification, in two-dimensions. An ISZ operates over slower timescales and is forced by longer internal wavelengths as compared to its surface counterpart (Emery and Gunnerson 1973). Moreover, such waves drives mixing of near-boundary fluid and energizes the bottom boundary layer. |
Monday, November 21, 2022 9:05AM - 9:18AM |
L27.00006: Determining reflection coefficients when internal waves reflect from solid boundaries Bruce E Rodenborn, Luke Payne, Yichen Guo, Michael Allshouse Instabilities and other nonlinear processes may cause local dissipation of internal wave beams when they reflect from solid boundaries. We analyze this problem using the reflection coefficient, the ratio of the outgoing propagating energy to the incoming wave beam energy: R≡Eout /Ein. We have developed a method to independently measure losses due to viscous decay, boundary dissipation and harmonic generation when calculating R. We use a 2D pseudo-spectral and a 2D finite volume code to solve the Navier-Stokes equations in the Boussinesq limit, along with low Reynolds number experiments to find values of R for different conditions. We compare results from no-slip boundaries, free-slip boundaries, rough surfaces, and from turning depths. The reflection coefficient for a turning depth in the numerical simulations is similar to that of a free slip boundary and so provides a mechanism to create a quasi-free-slip boundary in experiments. We apply our method to a sloping boundary to evaluate the different mechanisms that cause decay of the reflected wave beam. We find that R is minimized when the wave beam and slope angle are the same, as is common on continental slopes in the ocean. |
Monday, November 21, 2022 9:18AM - 9:31AM |
L27.00007: Internal Wave Generation by Multiple Peak Topographies Natasha Wilson, Julie Crockett Tidal flow over topography in the ocean is a common method of internal wave generation. As more dense fluid is moved up over topography, an oscillation is initiated that propagates away from the source. The local density gradient as well as the topography shape define the amplitude and wavelengths in the generated internal wave field. For uniform or simple topographic shapes these relationships are well known. However, for more complex shapes these relationships have not been thoroughly investigated. This work focuses on characterizing the impact of multiple Gaussian peaks on topography, compared with a single peak. Specifically, the tidally generated internal wavefield will be characterized. Experiments exploring these waves were run using topographies with peak counts ranging from one to six where all peaks were defined by Gaussian profiles. The generated internal wavefield is defined by both the overall topography length and the smaller peaks present on top of the topography. As the number of peaks increases, the kinetic energy in the component of the wavefield generated by peaks decreases. |
Monday, November 21, 2022 9:31AM - 9:44AM |
L27.00008: The role of a soft-gel on the natural frequencies and in the evolution of Faraday waves at the free surface of a fluid layer Mradul Varshney, Dinesh Bhagavatula The natural frequency of a fluid layer overlying on a rigid wall depends on the density of the fluid, surface tension at the free surface and the waveform that evolves at the free surface. However, the presence of a soft-gel layer underneath the fluid layer is expected to alter the natural frequency of the fluid layer. In this work, a linear stability analysis is carried out to show that the natural frequency of the fluid layer is altered by the elasticity of the compliant soft-gel layer. As a consequence of a shift in the natural frequency, linear stability calculations shown that there is also a shift in the instability regions when the fluid layer lying on the soft-gel is subjected to Faraday forcing. This indicates that the soft-gel layer either has a stabilizing effect or a destabilizing effect because the presence of a deformable soft-gel layer either raises or lowers the Faraday threshold to induce an instability. |
Monday, November 21, 2022 9:44AM - 9:57AM |
L27.00009: A high-order spectral method for effective simulation of surface waves interacting with an internal wave of large amplitude Xuanting Hao, Jie Wu, Justin S Rogers, Oliver B Fringer, Lian Shen We propose a new method for simulating complex surface waves interacting with a large amplitude internal solitary wave. Our model is based on a high-order spectral method for surface waves with the bottom boundary conditions computed from an internal wave solver. We first test the convergence of the model using an internal wave case without surface waves. We then perform simulations of a canonical nonlinear wave interaction case, and the initial energy growth rate of the resonant wave component is found to agree with the analytical solution. The model is also validated against the two-layer model for the interaction between surface waves and a weakly nonlinear internal wave. Finally, we show the application of our model in a multiscale nested modeling framework, where the internal wave parameters are extracted from the mesoscale simulation using a nonhydrostatic ocean model. The evolution of the spatial variations of the surface roughness is captured and the surface wave orbital velocity also changes in space owing to the surface motions induced by the internal wave. Our phase-resolved model provides a computationally efficient tool for simulating complex surface wave fields in the background of internal waves of large amplitudes. |
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