Bulletin of the American Physical Society
70th Annual Meeting of the APS Division of Fluid Dynamics
Volume 62, Number 14
Sunday–Tuesday, November 19–21, 2017; Denver, Colorado
Session M19: Internal and Interfacial Waves IIInterfacial
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Chair: Scott Wunsch, Johns Hopkins University Room: 702 |
Tuesday, November 21, 2017 8:00AM - 8:13AM |
M19.00001: Fate of internal waves on a shallow shelf Kristen Davis, Robert Arthur, Emma Reid, Thomas DeCarlo, Anne Cohen Internal waves strongly influence the physical and chemical environment of coastal ecosystems worldwide. We report novel observations from a distributed temperature sensing (DTS) system that tracked the transformation of internal waves from the shelf break to the surf zone over a shelf-slope region of a coral atoll in the South China Sea. The spatially-continuous view of the near-bottom temperature field provided by the DTS offers a perspective of physical processes previously available only in laboratory settings or numerical models. These processes include internal wave reflection off a natural slope, shoreward transport of dense fluid within trapped cores, internal ``tide pools'' (dense water left behind after the retreat of an internal wave), and internal run-down (near-bottom, offshore-directed jets of water preceding a breaking internal wave). Analysis shows that the fate of internal waves on this shelf -- whether they are transmitted into shallow waters or reflected back offshore -- is mediated by local water column density and shear structure, with important implications for nearshore distributions of energy, heat, and nutrients. [Preview Abstract] |
Tuesday, November 21, 2017 8:13AM - 8:26AM |
M19.00002: Internal tide dissipation: triadic resonant instability and evenescent waves Oceane Richet, Caroline Muller, Jean-Marc Chomaz Several previous numerical studies suggest the presence of a critical latitude corresponding to an enhanced energy dissipation associated to mixing and a strong latitudinal dependence of the local energy dissipation. The purpose of this study is to understand mechanisms behind this latitudinal dependence. We separate the evolution of the energy dissipation with latitude in two parts: before the critical latitude, where internal waves are propagative and after the critical latitude, where internal waves can be evanescent. Before the critical latitude, we propose a mechanism in 3 stages involving triadic resonant instability. At the critical latitude, the peak of energy dissipation is explained by inertial waves with small vertical scales. After the critical latitude, the presence of near-inertial evanescent waves generated by the parametric subharmonic instability explains dissipation on several degrees of latitude after the critical latitude. The study combines theoretical results and 2D idealized numerical simulations. [Preview Abstract] |
Tuesday, November 21, 2017 8:26AM - 8:39AM |
M19.00003: Coalescence and Interaction of Solitons in the Coupled Korteweg--de Vries System Wai Choi Chung, Kwok Wing Chow There are many physical systems which are governed by the classical Korteweg--de Vries equation. One of the prominent examples is the shallow water wave in fluid dynamics. In recent years, a coupled Korteweg--de Vries system has been proposed to describe fluids in a two-layer flow, and coherent structures in terms of solitons are found. We studied the coupled Korteweg--de Vries system by means of the Hirota bilinear method. Soliton and breather solutions are constructed. Localized pulses which result from the coupling of waves can be formed. The structure of the localized pulses becomes asymmetric as the control parameter varies. The coalescence and interaction of solitons in the coupled Korteweg--de Vries system will be discussed. [Preview Abstract] |
Tuesday, November 21, 2017 8:39AM - 8:52AM |
M19.00004: Utilizing a Coupled Nonlinear Schr\"{o}dinger Model to Solve the Linear Modal Problem for Stratified Flows Tianyang Liu, Hiu Ning Chan, Roger Grimshaw, Kwok Wing Chow The spatial structure of small disturbances in stratified flows without background shear, usually named the `Taylor-Goldstein equation', is studied by employing the Boussinesq approximation (variation in density ignored except in the buoyancy). Analytical solutions are derived for special wavenumbers when the Brunt-V\"{a}is\"{a}l\"{a} frequency is quadratic in hyperbolic secant, by comparison with coupled systems of nonlinear Schr\"{o}dinger equations intensively studied in the literature. Cases of coupled Schr\"{o}dinger equations with four, five and six components are utilized as concrete examples. Dispersion curves for arbitrary wavenumbers are obtained numerically. The computations of the group velocity, second harmonic, induced mean flow, and the second derivative of the angular frequency can all be facilitated by these exact linear eigenfunctions of the Taylor-Goldstein equation in terms of hyperbolic function, leading to a cubic Schr\"{o}dinger equation for the evolution of a wavepacket. The occurrence of internal rogue waves can be predicted if the dispersion and cubic nonlinearity terms of the Schr\"{o}dinger equations are of the same sign. [Preview Abstract] |
Tuesday, November 21, 2017 8:52AM - 9:05AM |
M19.00005: On the interaction of vortices and internal waves in the dead-water problem. Eric Hester Dead water refers to a mysterious increase in resistance experienced by boats in density-stratified waters. The problem has been documented since ancient times, and studied scientifically for over a century. These investigations have revealed the role of internal waves in generating drag. However, analytical approaches neglect important vortex dynamics, which experiments fail to visualise. For the first time, we study the phenomenon using state-of-the-art numerical simulations. We reproduce the effect and show it is greatest in strongly nonlinear regimes poorly modelled by current theory. The most exciting development found a new trailing vortex coupled to the boat. This robust structure is consistent with sailors accounts, but has been missed in previous scientific studies. We expect these results to lead to actionable ways to mitigate dead water in the real world. [Preview Abstract] |
Tuesday, November 21, 2017 9:05AM - 9:18AM |
M19.00006: Axisymmetric capillary-gravity waves at the interface of two viscous, immiscible fluids - Initial value problem Palas Kumar Farsoiya, Ratul Dasgupta When the interface between two radially unbounded, viscous fluids lying vertically in a stable configuration (denser fluid below) at rest, is perturbed, radially propagating capillary-gravity waves are formed which damp out with time. We study this process analytically using a recently developed linearised theory (Farsoiya, Mayya and Dasgupta, J. Fluid Mech., In Press, 2017). For small amplitude initial perturbations, the analytical solution to the initial value problem, represented as a linear superposition of Bessel modes at time $t=0$, is found to agree very well with results obtained from direct numerical simulations of the Navier-Stokes equations, for a range of initial conditions. Our study extends the earlier work by John W. Miles (J. Fluid Mech., 1968) who studied this initial value problem analytically, taking into account, a single viscous fluid only. Implications of this study for the mechanistic understanding of droplet impact into a deep pool, will be discussed. Some preliminary, qualitative comparison with experiments will also be presented. [Preview Abstract] |
Tuesday, November 21, 2017 9:18AM - 9:31AM |
M19.00007: Internal Waves Generation from Tidal Currents Coupling with Existing Waves Yong Liang, Mohammad-Reza Alam Here we report a new mechanism for generation of internal gravity waves through resonance, owing to tidal currents coupling with existing waves. The new waves feature with the same wave number vectors as the existing ones and frequencies higher by the tidal frequency. They grow exponentially in time by continuously extracting energy from the tidal currents until wave breaking occurs. We prove that this mechanism is possible in any stratified ocean with smooth density profiles. [Preview Abstract] |
Tuesday, November 21, 2017 9:31AM - 9:44AM |
M19.00008: Interference of Locally Forced Internal Waves in Non-Uniform Stratifications Rohit Supekar, Thomas Peacock Several studies have investigated the effect of constructive or destructive interference on the transmission of internal waves propagating through non-uniform stratifications. Such studies have been performed for internal waves that are spatiotemporally harmonic. To understand the effect of localization, we perform a theoretical and experimental study of the transmission of two-dimensional internal waves that are generated by a spatiotemporally localized boundary forcing. This is done by considering an idealized problem and applying a weakly viscous semi-analytic linear model. Parametric studies using this model show that localization leads to the disappearance of transmission peaks and troughs that would otherwise be present for a harmonic forcing. Laboratory experiments that we perform provide a clear indication of this physical effect. Based on the group velocity and angle of propagation of the internal waves, a practical criteria that assesses when the transmission peaks or troughs are evident, is obtained. It is found that there is a significant difference in the predicted energy transfer due to a harmonic and non-harmonic forcing which has direct implications to various physical forcings such as a storm over the ocean. [Preview Abstract] |
Tuesday, November 21, 2017 9:44AM - 9:57AM |
M19.00009: Internal wave mode resonant triads in an arbitrarly stratified finite-depth ocean with background rotation Dheeraj Varma, Manikandan Mathur Internal tides generated by barotropic tides on bottom topography or the spatially compact near-inertial mixed layer currents excited by surface winds can be conveniently represented in the linear regime as a superposition of vertical modes at a given frequency in an arbitrarily stratified ocean of finite depth. Considering modes $(m,n)$ at a frequency $\omega$ in the primary wave field, we derive the weakly nonlinear solution, which contains a secondary wave at $2\omega$ that diverges when it forms a resonant triad with the primary waves. In nonuniform stratifications, resonant triads are shown to occur when the horizontal component of the classical RTI criterion $\vec{k}_1+\vec{k}_2+\vec{k}_3=0$ is satisfied along with a non-orthogonality criterion. In nonuniform stratifications with a pycnocline, infinitely more pairs of primary wave modes $(m,n)$ result in RTI when compared to a uniform stratification. Further, two nearby high modes at around the near-inertial frequency often form a resonant triad with a low mode at $2\omega$, reminiscent of the features of PSI near the critical latitude. The theoretical framework is then adapted to investigate RTI in two different scenarios: low-mode internal tide scattering over topography, and internal wave beams incident on a pycnocline. [Preview Abstract] |
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