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 G19: Surface Waves IIFree Surface
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Chair: Simen Ellingsen, Norwegian University of Science and Technology Room: 702 |
Monday, November 20, 2017 10:35AM - 10:48AM |
G19.00001: The hydraulic analogy revisited Patrick Sprenger, Mark Hoefer The so-called ``hydraulic analogy" between supercritical shallow water flow and supersonic compressible gas flow was leveraged though a table-top water table experiment to understand the interaction of supersonic flow with stationary objects. However, surface water waves are intrinsically dispersive and the wave patterns generated were, in fact, dispersive shock waves, wholly different from their previously assumed viscous shock counterparts. In this talk, the water table experiment is studied as a dispersive hydraulic analogy, akin to other nonlinear dispersive media such as superfluids and intense laser light propagation. The steady, oblique dispersive shock waves resulting from a supercritical flow impinging on a wedge obstacle will be examined theoretically and experimentally. [Preview Abstract] |
Monday, November 20, 2017 10:48AM - 11:01AM |
G19.00002: Coherent Structures and Evolution of Vorticity in Short-Crested Breaking Surface Waves James Kirby, Morteza Derakhti We employ a multi-phase LES/VOF code to study turbulence and coherent structures generated during breaking of short-crested surface water waves. We examine the evolution of coherent vortex structures evolving at the scale of the width of the breaking event, and their long-time interaction with smaller vortex loops formed by the local instability of the breaking crest. Long-time results are often characterized by the detachment of the larger scale vortex loop from the surface and formation of a closed vortex ring. The evolution of circulation for the vortical flow field is examined. The initial concentration of forcing close to the free surface leads to spatial distributions of both span-wise and vertical vorticity distributions which are concentrated close to the surface. This result, which persists into shallow water, is at odds with the basic simplicity of the Peregrine mechanism, suggesting that even shallow flows such as the surf zone should be regarded as being forced (in dissipative situations) by a wave-induced surface stress rather than a uniform-over-depth body force. The localized forcing leads to the development of a complex pattern of stream-wise vorticity, comparable in strength to the vertical and span-wise components, and also persist into shallow water. [Preview Abstract] |
Monday, November 20, 2017 11:01AM - 11:14AM |
G19.00003: Simulations of quasi-steady breaking waves: flow structure Kelli Hendrickson, Dick Yue Quasi-steady breaking waves are prominent and highly observable features in civil, environmental, ocean and naval engineering applications with direct impact on turbulent dissipation and air-sea interaction. We present high-resolution 3D direct numerical and implicit large eddy simulations of quasi-steady breaking waves of flow over a lifting body. The numerical method is Cartesian-grid based utilizing conservative Volume of Fluid (cVOF) for interface capturing and Boundary Data Immersion Method (BDIM) for the body geometry. We show the instantaneous and mean flow structure in the liquid bulk and air-water mixed-region over a range breaking strengths and orientations with the inflow. Our particular interest lies in understanding the near-surface shear layer and air entrainment for these waves in comparison to ship wakes and hydraulic jumps. [Preview Abstract] |
Monday, November 20, 2017 11:14AM - 11:27AM |
G19.00004: Dispersion relation for waves on arbitrarily depth-varying shear current: a numerical scheme Simen Å. Ellingsen, Yan Li In the coastal zone, currents can be strongly sheared in the vertical direction, which affect the dispersion properties of surface water waves in a complicated manner. Oceanographic wave models depend on accurate dispersion calculation, as do predictions of wave forces on vessels and structures. We present a new numerical method for calculating the dispersion relation of linear waves propagating on a horizontal shear current whose magnitude and direction may vary arbitrarily with depth. The method compares favourably with existing methods: it is more efficient and simpler to implement than the classical piecewise-linear approach, and has much higher and well controlled accuracy compared to semi-analytical approximation relations, at only moderately greater cost. We also present the theory by which any numerically calculated dispersion relation can be used to calculate waves from an arbitrary time-dependent surface pressure source. [Preview Abstract] |
Monday, November 20, 2017 11:27AM - 11:40AM |
G19.00005: Weakly nonlinear theory for the initial value problem of three-dimensional deep water surface waves in a uniform shear field Andreas Akselsen, Simen Ellingsen We investigate the weakly nonlinear dynamics of gravity ring waves at infinite depth under the influence of a shear current varying linearly with depth. Although this problem cannot be treated using potential theory, a solution is permitted via integration of the Euler equations. The linear initial value problem is extended to the weakly nonlinear regime using an Euler expansion mode coupling method. A particle trajectory approximation, including Stokes drift effects, is obtained in a similar manner. Although this technique generally generates expressions of a complexity too great for numerical evaluation, comparatively simple asymptotic approximations can be constructed using a two-dimensional method of stationary phase. Expressions for problems with a two-dimensional initial profile are also reasonably wieldy. Two-dimensional and asymptotic three-dimensional numerical results are presented to second order in wave steepness. From these the nonlinear effects induced by the shear are investigated. [Preview Abstract] |
Monday, November 20, 2017 11:40AM - 11:53AM |
G19.00006: Stability of Surface Gravity Waves on Constant Vorticity Current James Steer, Dimitris Stagonas, Eugeny Buldakov, Alistair Borthwick, Ton van den Bremer Nonlinear surface gravity waves are subject to an instability that can lead to the generation of spectral-sidebands and the eventual break-up of the waves known as modulational (or Benjamin-Feir) instability (Benjamin {\&} Feir, 1967, J. Fluid Mech.). The instability is captured by the nonlinear Schr\"{o}dinger equation. The stability of unidirectional surface waves on a sheared current with constant vorticity may be described by deriving a relevant non-linear Schr\"{o}dinger equation (the vor-NLS equation), as derived by Thomas, Kharif {\&} Manna (2012, Phys. Fluids). We report on experiments examining the stability of modulated periodic wavetrains in a laboratory flume, where the waves are superimposed on a vertically sheared current with a constant vorticity. We keep the shear profile constant along the length of the tank and are able to observe stabilisation of instabilities compared to the case without shear. We obtain estimates of the observed growth rate of the sidebands to predictions based on the vor-NLS equation. [Preview Abstract] |
Monday, November 20, 2017 11:53AM - 12:06PM |
G19.00007: Existence of non-dispersion niches of long perturbation waves in the plane Poiseuille flow. Impact on wave packets morphology. Federico Fraternale, Gabriele Nastro, Daniela Tordella We consider the dispersion of 3D wavy perturbations in the plane Poiseuille flow. We focus on the wavenumbers-Reynolds numbers map. By considering the long-term evolution of these linear traveling waves, we found a sub-region nested in the dispersive part of the map where dispersion is abruptly inhibited. This region is observed at the bottom right dial of the map (Re$>$29840 and k$<$0.35) and includes non-dispersive waves moving as the basic flow. Two other regions were observed with a dispersion substantially different with respect to the surroundings. In one case, the dispersion level measured as the difference between the group speed and the phase speed is enhanced. In the other, the dispersion level is damped. Such regions contain waves with higher phase speed than waves in the surrounding area of the parameter space. This study builds on a previous one (PRE 93, 2016) where, by moving in the map from small to high wavenumbers, we show that a dispersive-to-nondispersive transition occurs in sheared flows under fixed flow conditions. The transition takes place at a specific wavenumber threshold, which splits the map in two main regions: the lower one, the dispersive one, being that hosting the nested regions above. An inference on the morphology of wave packets is presented. [Preview Abstract] |
Monday, November 20, 2017 12:06PM - 12:19PM |
G19.00008: Abstract Withdrawn
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Monday, November 20, 2017 12:19PM - 12:32PM |
G19.00009: Leaky GFD problems Lyubov Chumakova, Andrew Rzeznik, Rodolfo R. Rosales In many dispersive/conservative wave problems, waves carry energy outside of the domain of interest and never return. Inside the domain of interest, this wave leakage acts as an effective dissipation mechanism, causing solutions to decay. % In classical geophysical fluid dynamics problems this scenario occurs in the troposphere, if one assumes a homogeneous stratosphere. % In this talk we present several classic GFD problems, where we seek the solution in the troposphere alone. Assuming that upward propagating waves that reach the stratosphere never return, we demonstrate how classic baroclinic modes become leaky, with characteristic decay time-scales that can be calculated. We also show how damping due to wave leakage changes the classic baroclinic instability problem in the presence of shear. This presentation is a part of a joint project. The mathematical approach used here relies on extending the classical concept of group velocity to leaky waves with complex wavenumber and frequency, which will be presented at this meeting by A. Rzeznik in the talk ``Group Velocity for Leaky Waves''. [Preview Abstract] |
Monday, November 20, 2017 12:32PM - 12:45PM |
G19.00010: Almost analytical Karhunen-Loeve representation of irregular waves based on the prolate spheroidal wave functions Gibbeum Lee, Yeunwoo Cho We present an almost analytical new approach to solving the matrix eigenvalue problem or the integral equation in Karhunen-Loeve (K-L) representation of random data such as irregular ocean waves. Instead of solving this matrix eigenvalue problem purely numerically, which may suffer from the computational inaccuracy for big data, first, we consider a pair of integral and differential equations, which are related to the so-called prolate spheroidal wave functions (PSWF). For the PSWF differential equation, the pair of the eigenvectors (PSWF) and eigenvalues can be obtained from a relatively small number of analytical Legendre functions. Then, the eigenvalues in the PSWF integral equation are expressed in terms of functional values of the PSWF and the eigenvalues of the PSWF differential equation. Finally, the analytically expressed PSWFs and the eigenvalues in the PWSF integral equation are used to form the kernel matrix in the K-L integral equation for the representation of exemplary wave data; ordinary irregular waves and rogue waves. We found that the present almost analytical method is better than the conventional data-independent Fourier representation and, also, the conventional direct numerical K-L representation in terms of both accuracy and computational cost. [Preview Abstract] |
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