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 A19: Free Surface Flows: GeneralFree Surface
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Chair: Kelli Hendrickson, Massachusetts Institute of Technology Room: 702 |
Sunday, November 19, 2017 8:00AM - 8:13AM |
A19.00001: Capillary waves with surface viscosity Li Shen, Fabian Denner, Neal Morgan, Berend van Wachem, Daniele Dini Experiments over the last 50 years have suggested a correlation between the surface (shear) viscosity and the stability of a foam or emulsion. With recent techniques allowing more accurate measurements of the elusive surface viscosity, we examine this link theoretically using small-amplitude capillary waves in the presence of the Marangoni effect and surface viscosity modelled via the Boussinesq-Scriven model. The surface viscosity effect is found to contribute a damping effect on the amplitude of the capillary wave with subtle differences to the effect of the convective-diffusive Marangoni transport. The general wave dispersion is augmented to take into account the Marangoni and surface viscosity effects, and a first-order correction to the critical damping wavelength is derived. [Preview Abstract] |
Sunday, November 19, 2017 8:13AM - 8:26AM |
A19.00002: Two-dimensional gravity--capillary solitary waves on deep water: Generation and transverse instability. Beomchan Park, Yeunwoo Cho Two-dimensional (2-D) gravity--capillary solitary waves are generated using a moving pressure jet from a 2-D narrow slit as a forcing onto the surface of deep water. The forcing moves horizontally over the surface of deep water with speeds close to the minimum phase speed $c_{\min } =$23$\mbox{cm/s}$. Four different states are observed according to forcing speeds. At relatively low speeds below $c_{\min } $, small-amplitude depressions are observed and they move steadily just below the moving forcing. As the forcing speed increases towards $c_{\min } $, nonlinear 2-D gravity--capillary solitary waves are observed, and they move steadily behind the moving forcing. When the forcing speed is very close to $c_{\min } $, periodic shedding of local depressions is observed behind the moving forcing. Finally, at relatively high speeds above $c_{\min } $, a pair of short and long linear waves is observed, respectively, ahead of and behind the moving forcing. In addition, we observe the transverse instability of free 2-D gravity--capillary solitary waves and, further, the resultant formation of 3-D gravity--capillary solitary waves. These experimental observations are compared with numerical results based on a model equation that admits gravity--capillary solitary wave solutions near $c_{\min } $and they agree with each other very well. [Preview Abstract] |
Sunday, November 19, 2017 8:26AM - 8:39AM |
A19.00003: Variational data assimilation for the shallow water equations Nicholas Kevlahan, Ramsha Khan, Bartosz Protas The shallow water equations (SWE) are a widely used model for the propagation of surface waves. In particular, the SWE are used to model the propagation of tsunami waves in the open ocean. We consider the associated data assimilation problem of optimally determining the initial conditions for the one-dimensional SWE equations from a small set of observations of the sea surface height. We derive variational data assimilation methods for both the linear and nonlinear SWE and implement them numerically. In the linear case we solve the assimilation equations analytically and prove a theorem giving sufficient conditions for convergence to the true initial conditions. At least two observation points must be used and at least one pair of observation points must be spaced more closely than half the effective minimum wavelength of the energy spectrum of the initial conditions. We confirm our analysis in numerical implementations of the both the linear and nonlinear SWE assimilation problems. At least three observation points are required for the practically useful results. This paper is a first step in understanding the conditions for observability of the SWE for multiple observation points in more physically realistic settings. [Preview Abstract] |
Sunday, November 19, 2017 8:39AM - 8:52AM |
A19.00004: Experimental study on the bubble-induced gravity--capillary jet-like surface waves. Youn J. Kang, Yeunwoo Cho We experimentally study on the jet-like wave motion of a free surface caused by the motion of an electric-spark-generated underwater bubble near the free surface. The overall length scale of the bubble-induced free-surface jet is on the order of a few \textit{mm}, where both the gravity and the surface tension are important. Three different motions of the gravity--capillary jet-like surface waves are observed depending on the inception position of the bubble ($d)$ from the free surface, the maximum radius of the bubble ($R_{\mathrm{m}})$ and the maximum height of the gravity--capillary surface jet ($h)$ before pinch-off if any. When $d$/$R_{\mathrm{m}}$\textgreater 1.2, the surface jet shows a simple smooth hump (case 1). When 0.7\textless $d$/$R_{\mathrm{m}}$\textless 1.2, a single or multiple droplets are pinched off sequentially or simultaneously at the tip or from some points of the surface jet (case 2). Finally, when $d$/$R_{\mathrm{m}}$\textless 0.7, a series of squirting {\&} jetting phenomena are observed at the top of the surface jet (case 3). In particular, for cases 1 and 2 ($d$/$R_{\mathrm{m}}$\textgreater 0.7), we experimentally found the linearly proportional relationship between $h$/$R_{\mathrm{m\thinspace }}$and ($d$/$R_{\mathrm{m}})^{\mathrm{-4}}$. This proportional relationship is proven semi-analytically using a scaling argument and conservation of mass, momentum, and energy. [Preview Abstract] |
Sunday, November 19, 2017 8:52AM - 9:05AM |
A19.00005: Surfactants non-monotonically modify the onset of Faraday waves Stephen Strickland, Michael Shearer, Karen Daniels When a water-filled container is vertically vibrated, subharmonic Faraday waves emerge once the driving from the vibrations exceeds viscous dissipation. In the presence of an insoluble surfactant, a viscous boundary layer forms at the contaminated surface to balance the Marangoni and Boussinesq stresses. For linear gravity-capillary waves in an undriven fluid, the surfactant-induced boundary layer increases the amount of viscous dissipation. In our analysis and experiments, we consider whether similar effects occur for nonlinear Faraday (gravity-capillary) waves. Assuming a finite-depth, infinite-breadth, low-viscosity fluid, we derive an analytic expression for the onset acceleration up to second order in $\epsilon = \sqrt{1/Re}$. This expression allows us to include fluid depth and driving frequency as parameters, in addition to the Marangoni and Boussinesq numbers. For millimetric fluid depths and driving frequencies of 30 to 120 Hz, our analysis recovers prior numerical results and agrees with our measurements of NBD-PC surfactant on DI water. In both case, the onset acceleration increases non-monotonically as a function of Marangoni and Boussinesq numbers. For shallower systems, our model predicts that surfactants could decrease the onset acceleration. [Preview Abstract] |
Sunday, November 19, 2017 9:05AM - 9:18AM |
A19.00006: Effect of liquid surface tension on circular and linear hydraulic jumps; theory and experiments Rajesh Kumar Bhagat, Narsing Kumar Jha, Paul F. Linden, David Ian Wilson The hydraulic jump has attracted considerable attention since Rayleigh published his account in 1914. Watson (1964) proposed the first satisfactory explanation of the circular hydraulic jump by balancing the momentum and hydrostatic pressure across the jump, but this solution did not explain what actually causes the jump to form. Bohr et al. (1992) showed that the hydraulic jump happens close to the point where the local Froude number equals to one, suggesting a balance between inertial and hydrostatic contributions. Bush {\&} Aristoff (2003) subsequently incorporated the effect of surface tension and showed that this is important when the jump radius is small. In this study, we propose a new account to explain the formation and evolution of hydraulic jumps under conditions where the jump radius is strongly influenced by the liquid surface tension. The theory is compared with experiments employing liquids of different surface tension and different viscosity, in circular and linear configurations. The model predictions and the experimental results show excellent agreement. [Preview Abstract] |
Sunday, November 19, 2017 9:18AM - 9:31AM |
A19.00007: Birth of a hydraulic jump Alexis Duchesne, Tomas Bohr, Anders Andersen The hydraulic jump, i.e., the sharp transition between a supercritical and a subcritical free-surface flow, has been extensively studied in the past centuries. However, ever since Leonardo da Vinci asked it for the first time, an important question has been left unanswered: How does a hydraulic jump form? We present an experimental and theoretical study of the formation of stationary hydraulic jumps in centimeter wide channels. Two starting situations are considered: The channel is, respectively, empty or filled with liquid, the liquid level being fixed by the wetting properties and the boundary conditions. We then change the flow-rate abruptly from zero to a constant value. In an empty channel, we observe the formation of a stationary hydraulic jump in a two-stage process: First, the channel fills by the advancing liquid front, which undergoes a transition from supercritical to subcritical at some position in the channel. Later the influence of the downstream boundary conditions makes the jump move slowly upstream to its final position. In the pre-filled channel, the hydraulic jump forms at the injector edge and then moves downstream to its final position. [Preview Abstract] |
Sunday, November 19, 2017 9:31AM - 9:44AM |
A19.00008: Scaling the viscous circular hydraulic jump Mederic Argentina, Enrique Cerda, Alexis Duchesne, Laurent Limat The formation mechanism of hydraulic jumps has been proposed by Belanger in 1828 and rationalised by Lord Rayleigh in 1914. As the Froude number becomes higher than one, the flow super criticality induces an instability which yields the emergence of a steep structure at the fluid surface. Strongly deformed liquid-air interface can be observed as a jet of viscous fluid impinges a flat boundary at high enough velocity. In this experimental setup, the location of the jump depends on the viscosity of the liquid, as shown by T. Bohr et al in 1997. In 2014, A. Duchesne et al have established the constancy of the Froude number at jump. Hence, it remains a contradiction, in which the radial hydraulic jump location might be explained through inviscid theory, but is also viscosity dependent. We present a model based on the 2011 Rojas et al PRL, which solves this paradox. The agreement with experimental measurements is excellent not only for the prediction of the position of the hydraulic jump, but also for the determination of the fluid thickness profile. We predict theoretically the critical value of the Froude number, which matches perfectly to that measured by Duchesne et al. [Preview Abstract] |
Sunday, November 19, 2017 9:44AM - 9:57AM |
A19.00009: Hydraulic jumps in the liquid foam microchannels Christophe Raufaste, Alexandre Cohen, Nathalie Fraysse, Jean Rajchenbach, Yann Bouret, Mederic Argentina Plateau borders (PBs) are the liquid microchannels found at the intersection between three bubbles in liquid foams. They form an interconnected network that plays a major role in foam drainage and stability properties. Each channel has an unbounded geometry but is not subject to the Rayleigh-Plateau instability. This stability is accounted for by an effective negative surface tension (GĂ©minard et al., 2004). We show that their relaxation dynamics can trigger inertial flows characterized by strongly nonlinear features. An experimental setup was designed to study the response of a PB to a liquid perturbation. Extra liquid is injected into the PB by drop coalescence. Depending on the parameters, either a viscous flow or an inertial one is observed. For the latter, the relaxation takes the form of a hydraulic jump, which propagates at a velocity around 0.1-1 m/s. Solitons are also observed for another type of perturbation. The PB dynamics is modeled and its equation presents an analogy with the differential equation of mechanical nonlinear oscillators. [Preview Abstract] |
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