Bulletin of the American Physical Society
67th Annual Meeting of the APS Division of Fluid Dynamics
Volume 59, Number 20
Sunday–Tuesday, November 23–25, 2014; San Francisco, California
Session D16: Free-Surface Flows II: Waves |
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Room: 2000 |
Sunday, November 23, 2014 2:15PM - 2:28PM |
D16.00001: Shallow fluids meets Einstein: an experimental geodesic flow on a curved space Jay Johnson, Jean-Luc Thiffeault When a shallow layer of inviscid fluid flows over a smoothly-patterned substrate, the fluid particle trajectories are, to leading order in the layer thickness, geodesics on the two-dimensional curved space of the substrate. We use 3D-printed substrates to show that the pattern made by a jet striking a bumpy surface is described by the geodesic equation. Because the geodesic equation is fourth order, the geodesics are chaotic even for simple substrates. [Preview Abstract] |
Sunday, November 23, 2014 2:28PM - 2:41PM |
D16.00002: Controlled Pattern Selection of Free Surface Waves Chun-Ti Chang, Susan Daniel, Paul H. Steen In this experimental study, we investigate the resonance of surface waves subject to different geometric constraints. For liquid puddles with different footprints and depths, we experimentally probe and compare their dynamics of pattern selection. From the scientific perspective, the comparison relates resonance of sessile drops to Faraday waves. For technological development, the study provides guidelines for applications such as ordered self-assembly of nanoparticles, droplet transport, drop atomization, enhanced mixing, and suspension collection. [Preview Abstract] |
Sunday, November 23, 2014 2:41PM - 2:54PM |
D16.00003: Capillary Korteweg-de Vries solitons on a levitated cylinder Chi-Tuong Pham, Stephane Perrard, Charles Duchene, Luc Deike A water cylinder is deposited on a straight channel heated far above boiling temperature so that the water levitates above its own vapor owing to Leidenfrost effect. Our setup allows us to study the one-dimensional propagation of surface waves. We show that the dispersion relation of linear waves follows that of gravity-capillary waves under a dramatically reduced gravity (up to a factor 30), yielding an effective capillary length larger than one centimeter. Nonlinear capillary depression solitary waves propagate without deformation and undergo mutual collisions and reflections at the boundaries of the domain. Their typical width and their amplitude-dependent velocity are in very good agreement with theoretical predictions based on Korteweg-de Vries equation. [Preview Abstract] |
Sunday, November 23, 2014 2:54PM - 3:07PM |
D16.00004: Mach-like capillary-gravity wakes Marc Rabaud, Frederic Moisy We determine experimentally the angle $\alpha$ of maximum wave amplitude in the far-field wake behind a vertical surface-piercing cylinder translated at constant velocity $U$ for Bond numbers $Bo_D = D / \lambda_c$ ranging between 0.1 and 4.2, where $D$ is the cylinder diameter and $\lambda_c$ the capillary length. In all cases the wake angle is found to follow a Mach-like law at large velocity, $\alpha \sim U^{-1}$, but with different prefactors depending on the value of $Bo_D$. For small $Bo_D$ (large capillary effects), the wake angle approximately follows the law $\alpha \simeq c_{\rm g,min} / U$, where $c_{\rm g,min}$ is the minimum group velocity of capillary-gravity waves. For larger $Bo_D$ (weak capillary effects), we recover the law $\alpha \sim \sqrt{gD}/U$ found for ship wakes at large velocity. Using the general property of dispersive waves that the characteristic wavelength of the wavepacket emitted by a disturbance is of order of the disturbance size, we propose a simple model that describes the transition between these two Mach-like regimes as the Bond number is varied. This model, complemented by numerical simulations of the surface elevation induced by a moving Gaussian pressure disturbance, is in good agreement with experimental measurements. [Preview Abstract] |
Sunday, November 23, 2014 3:07PM - 3:20PM |
D16.00005: ABSTRACT WITHDRAWN |
Sunday, November 23, 2014 3:20PM - 3:33PM |
D16.00006: Dynamic square superlattice of Faraday waves Lyes Kahouadji, Jalel Chergui, Damir Juric, Seungwon Shin, Laurette Tuckerman Faraday waves are computed in a 3D container using BLUE, a code based on a hybrid Front-Tracking/Level-set algorithm for Lagrangian tracking of arbitrarily deformable phase interfaces. A new dynamic superlattice pattern is described which consists of a set of square waves arranged in a two-by-two array. The corners of this array are connected by a bridge whose position oscillates in time between the two diagonals. [Preview Abstract] |
Sunday, November 23, 2014 3:33PM - 3:46PM |
D16.00007: A theory for stationary polygonal hydraulic jumps Aslan Kasimov When a vertical jet of viscous fluid strikes a horizontal plate, a circular hydraulic jump occurs at some distance from the jet impact point. Under certain conditions, the circular symmetry of the jump breaks and gives rise to stationary or rotating polygonal patterns. We describe experimental observations of the symmetry breaking and propose a model for the structure of the polygonal jumps. [Preview Abstract] |
Sunday, November 23, 2014 3:46PM - 3:59PM |
D16.00008: Hydraulic jumps in partially closed containers Andrew Belmonte, Vishal Vasan We present results of experiments investigating the effect of far field boundary conditions on the hydraulic jump in water. The classic hydraulic jump is an axisymmetric flow characterized by a single radial transition of the fluid height, for which the far field depth of the water is a key parameter. With suitable choices of the flow parameters, the circular jump exhibits symmetry breaking, transitioning into polygonal jumps among other possibilities. Here we study the transition between the jumps by suitably controlling the far field condition. This permits the flow to sustain a quasi-steady transition state between circular and polygonal jumps. Further, we investigate the effect of non-axisymmetric boundary conditions on the jump and its stability. [Preview Abstract] |
Sunday, November 23, 2014 3:59PM - 4:12PM |
D16.00009: Reovering water-wave profiles from bottom pressure measurements Vishal Vasan, Katie Oliveras, Diane Henderson, Bernard Deconinck Accurate measurements of the surface elevation are essential for understanding flow along coastlines. Often surface elevation is measured indirectly through pressure gauges situated on the bottom bed using linear theory. The full relationship between pressure and surface elevation is however significantly more complicated. In this talk we present a fully nonlinear formula that recovers the surface elevation profile of a traveling water-wave from measurements of the pressure beneath the wave. This is the first analytical investigation to take full nonlinearity into account. From this new relation, we derive a variety of different asymptotic formulas. Surface profile reconstructions from bottom pressure, measured using pressure gauges, are compared to actual heights obtained from surface capacitance gauges. Our comparisons indicate that a new asymptotic reconstruction formula affords significant gains over the traditional approach. Further, it is rapid and easy to implement, requiring only three Fourier transforms. [Preview Abstract] |
Sunday, November 23, 2014 4:12PM - 4:25PM |
D16.00010: Quantification and prediction of rare events in nonlinear waves Themistoklis Sapsis, Will Cousins, Mustafa Mohamad The scope of this work is the quantification and prediction of rare events characterized by extreme intensity, in nonlinear dispersive models that simulate water waves. In particular we are interested for the understanding and the short-term prediction of rogue waves in the ocean and to this end, we consider 1-dimensional nonlinear models of the NLS type. To understand the energy transfers that occur during the development of an extreme event we perform a spatially localized analysis of the energy distribution along different wavenumbers by means of the Gabor transform. A stochastic analysis of the Gabor coefficients reveals i) the low-dimensionality of the intermittent structures, ii) the interplay between non-Gaussian statistical properties and nonlinear energy transfers between modes, as well as iii) the critical scales (or Gabor coefficients) where a critical energy can trigger the formation of an extreme event. The unstable character of these critical localized modes is analysed directly through the system equation and it is shown that it is defined as the result of the system nonlinearity and the wave dissipation (that mimics wave breaking). These unstable modes are randomly triggered through the dispersive ``heat bath'' of random waves that propagate in the nonlinear medium. Using these properties we formulate low-dimensional functionals of these Gabor coefficients that allow for the prediction of extreme event well before the strongly nonlinear interactions begin to occur. The prediction window is further enhanced by the combination of the developed scheme with traditional filtering schemes. [Preview Abstract] |
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