Bulletin of the American Physical Society
73rd Annual Meeting of the APS Division of Fluid Dynamics
Volume 65, Number 13
Sunday–Tuesday, November 22–24, 2020; Virtual, CT (Chicago time)
Session Q11: Waves: Internal and Interfacial Waves and General (3:55pm - 4:40pm CST)Interactive On Demand
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Q11.00001: Soft-mode and Anderson-like localization in two-phase disordered media (Edmond) Tingtao Zhou, Dimitrios Fraggedakis, Fan Wang Wave localization is ubiquitous in disordered media -- from amorphous materials, where soft-mode localization is closely related to materials failure, to semi-conductors, where Anderson localization leads to metal-insulator transition. Our main understanding, though, is based on discrete models. Here, we provide a continuum perspective on the wave localization in two-phase disordered elastic media by studying the scalar wave equation with heterogeneous modulus and/or density. At low frequencies, soft modes arise as a result of disordered elastic modulus, which can also be predicted by the localization landscape. At high frequencies, Anderson-like localization occurs due to disorder either in density or modulus. For the latter case, we demonstrate how the vibrational dynamics changes from plane waves to diffusons with increasing frequency. Finally, we discuss the implications of our findings on the design of architected soft materials. [Preview Abstract] |
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Q11.00002: Propagation and Overturning of Three-Dimensional Boussinesq Wavepackets with Rotation Alain Gervais, Quinlan Ede, Gordon Swaters, Ton van den Bremer, Bruce Sutherland Internal gravity waves (IGWs) propagate horizontally and vertically within stably stratified fluids. As IGWs propagate vertically, nonlinear effects can lead to instabilities that may cause the waves to overturn and eventually break, irreversibly depositing their energy to the background flow. Even before breaking, moderately large amplitude IGW packets induce a mean flow that interacts nonlinearly with the waves, Doppler shifting their frequency, and altering the height at which the waves would have otherwise overturned. Here we derive explicit integral formulae for the flows induced by 3D IGW packets influenced by Coriolis forces. Numerical simulations of quasi-monochromatic wave packets with a range of initial amplitudes and vertical wavenumbers are initialized with the predicted induced flow superimposed. In simulations with moderately large initial amplitudes -- but still smaller than the overturning amplitudes predicted by linear theory -- interactions between the waves and their induced flow caused the waves eventually to overturn. In all cases shear instability did not play a role in driving the waves to overturn. The influence of the wave-induced flow acting upon IGWs interacting with retrograde shear is also examined as it affects wave reflection and transmission. [Preview Abstract] |
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Q11.00003: Self-generation of axisymmetric internal wave super-harmonics Samuel Boury, Thomas Peacock, Philippe Odier Numerous studies have been devoted to non-linear phenomena involving internal waves, particularly to the generation, from a primary wave field, of waves at lower (sub-harmonics) or higher (super-harmonics) frequencies, often associated with other wave numbers and therefore other scales to which energy can be transferred. For plane waves considered in a Cartesian geometry, non-linear self-interaction terms are null, preventing super-harmonics from existing in linearly stratified fluids. Super-harmonics are thus only expected to appear in non-linear stratifications. In axisymmetric geometry, however, the description of the wave field in terms of Bessel functions yields non-zero self-interaction terms, even in a linear stratification, and theory therefore predicts spontaneous generation of super-harmonics. We present an experimental observation of super-harmonics generated by self-interacting axisymmetric internal waves in linear stratified fluids. Excited at sufficiently low frequency, the wave field and its first harmonic are both propagating waves: we show that they remain axisymmetric and can be described by modes, or by a combination of modes. The selection of these modes is controlled by boundary conditions from the doubly confined (lateral and vertical) geometry. [Preview Abstract] |
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Q11.00004: The subcritical transition to turbulence of standing Faraday waves Benoit-joseph Gréa, Mathilde Cavelier, Antoine Briard, Louis Gostiaux We study the breaking process leading to turbulence of interfacial standing waves between miscible fluids of small density contrast. In our experiment, a primary wave is generated by a time-periodic acceleration via the Faraday instability (see \footnote{Briard et al., \emph{J. Fluid Mech.} \textbf{883} (2020)}. As the standing wave amplitude grows, a secondary destabilization process occurs and produces turbulent mixing at the nodes. We explain this phenomenon as a subcritical parametric instability at small scales and propose a criterion derived from local or global stability analysis to predict when and for which amplitude it appears. This theory is then assessed with various numerical and experimental data varying the frequencies and amplitude of the forcing acceleration. [Preview Abstract] |
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Q11.00005: Onset, mixing and saturation of the turbulent Faraday instability Antoine Briard, Benoît-Joseph Gréa, Louis Gostiaux, Mathilde Cavelier When a system of two miscible fluids in stable configuration is destabilised by a periodic vertical acceleration, a turbulent mixing zone may grow in size as a result of parametric resonances between internal gravity waves. With the growth of this layer, enhanced by turbulent diffusion, the intensity of the mean density gradient decreases, and the natural frequency of the system can no longer be excited, which eventually leads to saturation of the instability. The final size of the mixing zone was predicted to be $L_{sat} = 2 A g_0 (2F + 4)/\omega^2$, where $A$ is the Atwood number, $g_0$ the gravitational acceleration, and $F$ and $\omega$ the intensity and pulsation of the periodic forcing. This prediction was well assessed numerically and experimentally for a wide range of parameters. In addition, a whole variety of wavelengths were observed at onset that match a simple inviscid prediction when the instability is initiated from a sharp interface. Additionally, a model was derived to take into account an initial width for the miscible interface, along with viscous effects. A remarkable feature is the observation of a spontaneous change of wavelength that can occur during the instability: this phenomenon can be explained by the linear inhomogeneous theory. [Preview Abstract] |
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Q11.00006: Lee Waves in Shear Flow Yue Wu, Amala Mahadevan, Eric Kunze, Amit Tandon Numerical simulations of internal lee waves generated by a bottom-intensified geostrophic jet over topography have been conducted to investigate lee-wave generation, dissipation and re-absorption into mean shears. Roughly 1 TW of wind-work drives the ocean circulation, out of which up to 20-75\% might be dissipated through internal lee-wave generation. Lee-wave energy was thought to be lost to turbulence locally near their generation, but recent observations suggest suppression of turbulence, with dissipation rates one order of magnitude below predicted values. Wave action conservation suggests that internal waves can exchange energy with the sheared mean flow, which might explain this discrepancy. We revisit Reynolds-decomposed energy conservation equations and numerically examine whether a fraction of lee-wave energy is re-absorbed back into sheared mean flow. This research quantifies the role of topographic lee waves in dissipating versus redistributing balanced energy in the ocean. [Preview Abstract] |
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Q11.00007: Experimental study on super-harmonic wave generation by resonant interaction between internal wave modes Dheeraj Varma, Pauline Husseini, Thierry Dauxois, Sylvain Joubaud, Philippe Odier, Manikandan Mathur We present an experimental study of resonant generation of super-harmonic internal waves as a result of interaction between horizontally propagating vertical internal wave modes m and n at frequency $\omega $ in a uniformly stratified finite-depth fluid. Theoretical studies have shown that modes m and n at frequency $\omega $ and mode-p $=$ \textbar m-n\textbar at frequency 2$\omega $ are in triadic resonance at specific values of $\omega $. To demonstrate the occurrence of this triadic resonance, a primary wave field of modes m and n at various $\omega $ is forced using a novel internal wave generator, and the spontaneous growth (or lack thereof) of the super-harmonic mode-p $=$ \textbar m-n\textbar at frequency 2$\omega $ is measured. A super-harmonic wave field with a predominantly mode-p $=$ \textbar m-n\textbar structure is observed over a finite range of frequency ($\Delta \omega \simeq $0.03N) around the resonant value, where N is the uniform buoyancy frequency. The observed spatial growth of the super-harmonic wave field is then quantitatively compared with the predictions from amplitude evolution equations at resonance at various forcing amplitudes, thereby validating this model. [Preview Abstract] |
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Q11.00008: The discrete and continuous spectrum of a stratified liquid layer Patibandla Ramana, Saswata Basak, Palas Farsoiya, Ratul Dasgupta, Anubhab Roy We study the temporal spectrum of perturbations in a layer of viscous, density-stratified liquid of infinite depth with a free surface. In this scenario, the canonical set of discrete eigenfunctions, from normal mode analysis, lack completeness. A vorticity patch located at depths larger than the decay length scales of the discrete modes will have its projection predominantly on the continuous spectrum modes. The existence of this continuous spectrum, and the completeness thereof, is ascertained by carrying out a linearized initial value problem(IVP). We validate these findings, using direct numerical simulations(DNS) conducted using an open-source code(basilisk.fr) for solving the incompressible, Navier-Stokes equations for immiscible phases. Further, by using the same methods, we show the absence of the viscous continuous spectrum and the completeness of discrete spectrum in the liquid layer of finite depth. Qualitatively similar results are obtained even with constant density, in a viscous liquid layer of finite/infinite depth. However, for an inviscid fluid of finite extent, we find that the continuous spectrum is essential for the completeness of eigenfunctions in both stratified/unstratified scenarios. [Preview Abstract] |
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Q11.00009: Pressure and wave-flux optical analysis of 3D focusing internal waves compared between laboratory experiments and SOMAR Pierre-Yves Passaggia, Vamsi K. Chalamalla, Edward Santilli, Alberto Scotti Stratified flows driven by internal waves are particularly challenging to diagnose in lab experiments. Non-intrusive measurements techniques offer a viable way to obtain pressure which is notably difficult to measure in such flows. In this talk, we present an experimental procedure coupling Particle Image Velocimetry (PIV) with Synthetic Schlieren (SS) to reconstruct simultaneously velocity and density. Using these two time-resolved quantities, pressure can be estimated to establish energy budgets. We compare combined time-resolved PIV-SS measurements with direct numerical simulations (DNS) in the case of three-dimensional internal waves focusing on top of a Gaussian ring. The ring is forced by a barotropic-like tidal motion which drives a mode-1 type beam-like structure focusing at the center of the domain and the results from PIV and SS for velocity, density and pressure are compared with DNS using a newly implemented low-dissipation-type scheme of the numerical code SOMAR. In addition, we show that approaches based on PIV alone or SS alone can be flawed in the focusing region and that combined PIV and SS measurements provide an accurate comparison with the DNS. [Preview Abstract] |
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Q11.00010: Abstract Withdrawn
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Q11.00011: The Effect of Discrete Resonant Manifold Structure on Discrete Wave Turbulence Yulin Pan, Alexander Hrabski We consider the long-term dynamics of nonlinear dispersive waves in a finite periodic domain. The purpose of the work is to show that the statistical properties of the wave field rely critically on the structure of the discrete resonant manifold (DRM). To demonstrate this, we simulate the two-dimensional Majda, McLaughlin, Tabak (MMT) equation on rational and irrational tori, resulting in remarkably different power-law spectra and energy cascades at low nonlinearity levels. The difference is explained in terms of different structures of the DRM, which makes use of the recent number theory results. [Preview Abstract] |
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