Bulletin of the American Physical Society
68th Annual Meeting of the APS Division of Fluid Dynamics
Volume 60, Number 21
Sunday–Tuesday, November 22–24, 2015; Boston, Massachusetts
Session H13: Free Surface Flows V: Jets, Hydraulic Jumps, Impact 
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Chair: Laurent Limat, Université Paris Diderot Room: 201 
Monday, November 23, 2015 10:35AM  10:48AM 
H13.00001: On a nearly constant Froude number observed in circular hydraulic jumps Laurent Limat, Alexis Duchesne, Luc Lebon, Enrique Cerda, Mederic Argentina Circular hydraulic jumps are reminiscent of a shock for surface waves, but the flow is viscous, and analogous to boundary layer detachment. This yields [1] a scaling R$_{\mathrm{J}} \propto $ Q$^{5/8}\nu ^{3/8}$g$^{1/8}$ that links the jump radius R$_{\mathrm{J}}$ to flow rate Q, viscosity $\nu $ and gravity g. In a recent experiment [2], with a jet of radius $\varphi $ impacting a horizontal disk of radius R, we observed that the Froude number Fr at the jump exit was constant, which yields a modified scaling R$_{\mathrm{J}}$(Log(R/R$_{\mathrm{J}})^{3/8} \approx $ (2$^{11/8}$3$^{3/8}\pi^{5/8}$/Fr) Q$^{5/8}\nu^{3/8}$g$^{1/8}$ in good agreement with experiment. We show that this behavior is universal but Fr depends on phi/R. We also investigate the behavior of Fr (and more generally of the structure of the hydraulic jump) in the case of confinement walls. Theoretically, these results cannot be recovered by connecting two domains of negligible interface slope with a localized shock. Instead, a generalized inertial lubrication theory [3] seems able to explain these behaviors, that we relate to finite slope effects at the free surface. [1] T. Bohr et al., JFM 254, 635 (1993). [2] A. Duchesne et al., EPL 107, 54002 (2014). [3] N Rojas et al., PRL 104, 187801 (2010). [Preview Abstract] 
Monday, November 23, 2015 10:48AM  11:01AM 
H13.00002: Diving seabirds: the stability of a diving elastic beam~ Brian Chang, Matthew Croson, Sunghwan Jung In this study, we examine the buckling stability of a beam attached to a cone plunge diving into a bath of water, which is inspired by diving birds. This beamcone system initially experiences an impact force before the cone is completely submerged, followed by a hydrodynamic drag force. Using high speed imaging techniques, it was observed that the soft elastic beam exhibits either buckling (unstable) or nonbuckling (stable) behaviors upon impact and submergence. Large cone angles, long beams, and high impact velocities likely~cause buckling in the beam. By varying geometric factors of the beamcone system and changing the impact velocity, a transition from nonbuckling to buckling is characterized through physical experiments and~is verified by~an analytical model.~This study elucidates under which conditions diving birds may possibly get injured. [Preview Abstract] 
Monday, November 23, 2015 11:01AM  11:14AM 
H13.00003: Hydrodynamic forces during the initial stage of body lifting from water surface Patricia VegaMartínez, Javier RodríguezRodríguez, A Korobkin, Tatyana Khabakhpasheva We consider the flow induced by a rigid flat plate, initially touching a horizontal water surface, when it starts to move upwards with constant acceleration. Negative hydrodynamic pressures on the wetted surface of the plate are allowed, thus the water follows the plate due to the resulting suction force. The acceleration of the plate and the plate length are such that gravity, surface tension and viscous effects can be neglected. Under these assumptions, the potential flow caused by the plate lifting is obtained by using the smalltime expansion of the velocity potential. This smalltime solution fails close to the plate edges, as it predicts there singular velocities and unbounded displacements of the free surface. It is shown that close to the plate edges the flow is nonlinear and selfsimilar in the leading order. This nonlinear flow is computed by the boundary element method combined with a timemarching scheme. We also present the results of an experimental investigation aimed at measuring the hydrodynamic force felt by the plate. This force seems to be very weak, what suggests that cavitation occurs during these initial stages. Supported by the NICOP research grant N62909131N274, and the Spanish Ministry of Economy and Competitiveness, grant DPI201459292C31P. [Preview Abstract] 
Monday, November 23, 2015 11:14AM  11:27AM 
H13.00004: Numerical investigation of the water entry of cylinders with and without spin Areti Kiara, Ruben Paredes, Dick K.P. Yue We perform laminar, weakly compressible, numerical simulations of water impacting cylinders with radius $R$, entry velocity $V$, and spin $\omega$ about their axis. We consider two Froude numbers $F$r=$V/\sqrt{g2R}$=0.5, 1.5 and moderate spin ratios $\Omega$=$\omega R/V \le$3. Our numerical predictions are in agreement with experiments and identify the effects of $F$r and $\Omega$ on the separation points, flow dynamics, and body trajectory. We find that the separation points depend primarily on $F$r and observe two distinct regimes: for $F$r=0.5 quasistatic cavities are obtained, while for $F$r=1.5 the separation points approach a limiting angle of 70$^o\  $80$^o$ with respect to the negative vertical axis. For times $tV/R>$0.1 the total pressure force on the cylinder decreases with $F$r, obtaining significantly larger values for $F$r=0.5. The corresponding drag reduces with $\Omega$, while lift is towards the windward side and increases with both $\Omega$ and time. As a consequence, freefalling spinning cylinders drop slightly faster, while at a given depth their lateral displacement increases with $\Omega$. [Preview Abstract] 
Monday, November 23, 2015 11:27AM  11:40AM 
H13.00005: Spray Formation during the Impact of a Flat Plate on Water Surface An Wang, James H. Duncan Spray formation during the impact of a flat plate on a water surface is studied experimentally. The plate is mounted on a twoaxis carriage that can slam the plate vertically into the water surface as the carriage moves horizontally along a towing tank. The plate is 122~cm by 38~cm and oriented with adjustable pitch and roll angle. The port (lower) edge of the plate is positioned with a 3mm gap from one of the tank walls. A laser sheet is created in a plane oriented perpendicular to the axis of the horizontal motion of the carriage. The temporal evolution of the spray within the light sheet is measured with a cinematic laser induced fluorescence technique at a frame rate of 800~Hz. Experiments are performed with a fixed plate trajectory in a vertical plane, undertaken at various speeds. Two types of spray are found when the plate has nonzero pitch and roll angles. The first type is composed of a cloud of highspeed droplets and ligaments generated as the port edge of the plate hits the water surface during the initial impact. The second type is a thin sheet of water that grows from the starboard edge of the plate as it moves below the local water level. The geometrical features of the spray are found to be dramatically affected by the impact velocity. [Preview Abstract] 
Monday, November 23, 2015 11:40AM  11:53AM 
H13.00006: Ringin' the water bell: dynamic modes of curved fluid sheets John Kolinski, Hillel Aharoni, Jay Fineberg, Eran Sharon A water bell is formed by fluid flowing in a thin, coherent sheet in the shape of a bell. Experimentally, a water bell is created via the impact of a cylindrical jet on a flat surface. Its shape is set by the splash angle (the separation angle) of the resulting cylindrically symmetric water sheet. The separation angle is altered by adjusting the height of a lip surrounding the impact point, as in a water sprinkler. We drive the lip's height sinusoidally, altering the separation angle, and ringin' the water bell. This forcing generates disturbances on the steadystate water bell that propagate forward and backward in the fluid's reference frame at welldefined velocities, and interact, resulting in the emergence of an interference pattern unique to each steadystate geometry. We analytically model these dynamics by linearizing the amplitude of the bell's response about the underlying curved geometry. This simple model predicts the nodal structure over a wide range of steadystate water bell configurations and driving frequencies. Due to the curved water bell geometry, the nodal structure is quite complex; nevertheless, the predicted nodal structure agrees extremely well with the experimental data. When we drive the bell beyond perturbative separation angles, the nodal locations surprisingly persist, despite the strikingly altered underlying water bell shape. At extreme driving amplitudes the water sheet assumes a rich variety of tortuous, nonconvex shapes; nevertheless, the fluid sheet remains intact. [Preview Abstract] 
Monday, November 23, 2015 11:53AM  12:06PM 
H13.00007: Polygonal instabilities Matthieu Labousse The interaction of a vortex with a free surface is encountered in a series of experiments, the hydraulic jump [1], the hydraulic bump [2], the toroidal Leidenfrost experiment [3]. All these experiments share in common an unstable configuration in which azimuthal perturbations give rise to polygonal patterns. We propose a unified theoretical framework to model the emergence of this instability by investigating the stability of a liquid torus with a poloidal motion [4]. As simple as it is, we show that the model retains the necessary ingredients to account for the experimental observations. In this talk, I will first describe the model and compare it to the existing data. However this model is purely inviscid and reaches its limits when being applied to relatively moderate Reynolds flows. So in a second part, I will present a recent experimental and theoretical investigation in which polygonal patterns are now driven by Marangoni flows [5]. To our great surprise, it extends the range of validity of the initial proposed framework, much more than initially expected. \\[4pt] [1] C. Ellegaard, A. E. Hansen, A. Haaning, K. Hansen, A. Marcussen, T. Bohr, J. L. Hansen, S. Watanabe, \textit{Nature} (1998)\\[0pt] [2] M. Labousse, J. W.M. Bush, \textit{Phys. Fluids} (2013)\\[0pt] [3] S. Perrard, Y. Couder, E. Fort, L. Limat, \textit{EPL} (2012)\\[0pt] [4] M. Labousse, J.W.M Bush (under review)\\[0pt] [5] M. Roch\'{e}, Z. Li, I.M. Griffiths, S. Le Roux, I. Cantat, A. SaintJalmes, H. A. Stone, \textit{Phys. Rev. Lett}. (2014) [Preview Abstract] 

H13.00008: ABSTRACT WITHDRAWN 

H13.00009: ABSTRACT WITHDRAWN 
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