Bulletin of the American Physical Society
72nd Annual Meeting of the APS Division of Fluid Dynamics
Volume 64, Number 13
Saturday–Tuesday, November 23–26, 2019; Seattle, Washington
Session B02: Waves: Surface Waves II |
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Chair: Graham Benham, LadHyX, Ecole Polytechnique Room: 2B |
Saturday, November 23, 2019 4:40PM - 4:53PM |
B02.00001: Modulation instability and rogue waves for shear flows with a free surface Qing Pan, Roger Grimshaw, Kwok Wing Chow The evolution of weakly nonlinear, narrow-band wave packets for free surface flows is governed by the nonlinear Schr\"{o}dinger equation. Rogue waves, unexpectedly large displacements from equilibrium background can occur if the water depth is sufficiently large. In practice, shear currents nearly always occur in oceans, but modeling studies on wave dynamics are usually restricted to the case of linear current. The dynamics of rogue waves in the presence of a linear shear current has been studied in the literature. Generally rogue waves become narrower and with a short period of existence in terms of time if the background plane wave moves against the current. However, the modulation instability can be enhanced when background plane wave moves with the current. Here the investigation is extended to the case of a current with arbitrary vorticity gradient, by enhancing theoretical formulation established earlier by our group. The transient growth rate and the spatial extent of the rogue waves will be reported for two broad classes of velocity profiles, those convex to the right and those convex to the left. And thus knowledge on such focusing mechanisms of free surface waves will be of importance in both nonlinear science and physical oceanography. [Preview Abstract] |
Saturday, November 23, 2019 4:53PM - 5:06PM |
B02.00002: A new deep water equation for unidirectional surface gravity waves in two dimensions Nail S. Ussembayev Using Hamiltonian theory of weakly nonlinear surface waves we derive a set of nonlinear evolution equations describing propagation of unidirectional gravity waves on the surface of a two-dimensional ideal fluid of infinite depth. The proposed equations admit an exact solution in terms of Lambert’s $W$-function. We compare this solution with the approximate irrotational solution due to Stokes (1847) and the exact rotational solution found by Gerstner (1802). Being irrotational and exact, our solution exhibits a distinctive advantage over the aforementioned classical examples of deep-water gravity waves. [Preview Abstract] |
Saturday, November 23, 2019 5:06PM - 5:19PM |
B02.00003: Wave-current interaction in a laboratory flume: an analogue of the Hawking effect Daniel Robb, Edmund Tedford, Gregory Lawrence The propagation of surface water waves against an adverse current is studied both numerically and experimentally. In particular, we examine a flume experiment where a streamlined obstacle was placed in a steady open-channel flow to create a spatially-varying current (Weinfurtner et al. 2011, Phys. Rev. Lett.). Long waves were generated downstream of the obstacle and propagated upstream against the current. As they travelled over the lee side of the obstacle they were blocked and converted into a pair of outgoing short (deep-water) waves. The first of the pair had a group velocity and phase velocity both pointing downstream, whereas the second had the unusual property of a group velocity and phase velocity pointing in opposite directions. Here we present the correspondence between the Saint-Venant equations for shallow water flows and the wave equation on a general curved spacetime geometry used in general relativity. We then describe the analogy between the pair of outgoing surface water waves and the Hawking effect. Finally, based on our numerical simulations we discuss the conditions which are favorable for detecting the analogue Hawking effect in a hydraulics laboratory with the aim to support future experimental studies. [Preview Abstract] |
Saturday, November 23, 2019 5:19PM - 5:32PM |
B02.00004: Surface Gravity Wave Mechanics and Analogy with Black Hole Horizon Akanksha Gupta, Anirban Guha, Eyal Heifetz Surface gravity waves in the presence of a mean current flowing over a bottom topography have analogies with the Black hole horizon. Refraction of surface waves at the white hole (time reversal of a black hole) horizon occurs when (i) the imposed mean current is counter to the direction of the surface waves and furthermore, (ii) the flow speed exceeds the wave speed. At the horizon, the incident shallow water wave splits into two distinct deep water waves: one oscillating with a positive frequency and the other with a negative frequency. Such a situation is known as the "pair-wave creation", analogous to the celebrated Hawking radiation in Black holes (S.W. Hawking, Nature 1974). Theoretical and numerical investigations on total internal reflection and tunneling have been performed using an in-house Higher-order spectral code in order to find deeper analogies between Hawking radiation and surface wave-current interactions. Conserved wave activities like pseudomentum and pseudoenergy have been utilized to understand the pair wave creation. [Preview Abstract] |
Saturday, November 23, 2019 5:32PM - 5:45PM |
B02.00005: The Effect of Wind on Wave Shape: Shallow Water Thomas Zdyrski, Falk Feddersen Wave shape (e.g., wave skewness and asymmetry) impacts sediment transport, beach morphology, and ship safety. Previous work by the authors showed that wind (via changes in surface pressure) affects wave shape in intermediate and deep water. This effect was most pronounced as the depth ($kh$) decreased. Here, this work investigates the interaction of wind and wave shape in shallow water. A multiple-scales analysis is applied to waves propagating over a shallow ($kh \ll 1$), flat bottom with a variety of wind-induced surface-pressure profiles, such as Jeffreys-type and generalized Miles-type. The shallow depth enhances the influence of wind on wave shape and intensifies the waves' second-harmonic modes. The results are compared to previous wave-tank experimental data and numerical simulation results. [Preview Abstract] |
Saturday, November 23, 2019 5:45PM - 5:58PM |
B02.00006: Wave drag on asymmetric bodies Graham Benham, Jean-Philippe Boucher, Romain Labbé, Michael Benzaquen, Christophe Clanet More than a century ago, Michell derived an integral formula for the wave resistance on a body, using the approximation of a slender body in an irrotational, inviscid fluid (Michell 1898). The major shortcoming of this formula is that, due to the reversibility of the steady potential flow formulation, it does not distinguish the difference in wave drag when an object with front-back asymmetry moves forwards or backwards. However, it is well known that an asymmetric body with a sharp leading edge and a rounded trailing edge produces a smaller wave disturbance moving forwards than backwards, and this is reflected in the wave drag coefficient. In this talk, we discuss recent experimental observations investigating the effects of body asymmetry on wave drag, and show that these effects can be replicated by modifying Michell’s theory to include the growth of a symmetry-breaking boundary layer. We demonstrate that asymmetry can have either a positive or a negative effect on drag, depending on the depth of motion and the Froude number. We discuss the implications and scope of this work in the context of sports physics, including the design of rowing, kayak and canoe boats. [Preview Abstract] |
Saturday, November 23, 2019 5:58PM - 6:11PM |
B02.00007: Jetting in large amplitude axisymmetric capillary gravity waves Ratul Dasgupta, Saswata Basak, Palas Kumar Farsoiya The phenomenon of jetting and accompanying droplet ejection is known to occur in many fluid dynamical situations involving collapse of a gaseous cavity at a liquid-gas interface. In a recent study of free, capillary-gravity oscillations on a quiescent cylindrical pool of liquid [Farsoiya et.al J. Fluid Mech., 857, pp. 80-110 (2017)], it has been shown using DNS that jetting may be obtained with an initial interfacial perturbation in the form of a single Bessel mode. Sufficiently large values of wave steepness lead to the formation of a jet at the axis of symmetry that can eject droplets from its tip. In this study, we formulate the solution to the weakly nonlinear, inviscid-irrotational, initial-value problem in axisymmetric cylindrical coordinates using wave steepness as a small parameter and obtain a third order solution for the free surface profile. It is seen that the weakly nonlinear solution is able to describe the onset of jet formation. A detailed discussion of capillary effects along with comparisions with Direct Numerical Simulations, will be presented. [Preview Abstract] |
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