Bulletin of the American Physical Society
76th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 19–21, 2023; Washington, DC
Session G44: Waves: Surface Waves II 
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Chair: James Duncan, University of Maryland, College Park Room: 208AB 
Sunday, November 19, 2023 3:00PM  3:13PM 
G44.00001: Steady radiating gravity waves: an exponential asymptotics approach Triantaphyllos Akylas, Takeshi Kataoka The radiation of steady gravity surface waves by a uniform stream over locally confined smooth topography is analyzed based on potential flow theory. The linear solution to this classical problem is readily found by Fourier transforms, and the nonlinear response has been studied extensively by numerical methods. Here an asymptotic analysis is made for subcritical flow in the low Froude number limit, where the wavelength of the radiating waves is much shorter than the horizontal extent of the topography. In this regime, the radiating wave amplitude, although formally exponentially small with respect to the Froude number, is determined by a fully nonlinear mechanism even for small topography amplitude. Based on comparisons of asymptotic results with direct numerical computations, it is argued that this mechanism controls the wave response for a broad range of flow conditions, beyond those assumed by the asymptotic analysis, in contrast to linear theory which has very limited validity. 
Sunday, November 19, 2023 3:13PM  3:26PM 
G44.00002: Abstract Withdrawn

Sunday, November 19, 2023 3:26PM  3:39PM 
G44.00003: The role of the meniscus in determining the temporal response of parametricallyexcited surface waves Dingqian Ding, Joshua B Bostwick Recent experiments by Shao et al. 2021, JFM, have revealed complex surface wave dynamics in a mechanicallyvibrated fluid bath related to the geometry of the meniscus formed at the container sidewall, including the observation of i) harmonic axisymmetric waves, ii) subharmonic asymmetric waves, and iii) the mixing of harmonic axisymmetric waves and subharmonic asymmetric waves at a fixed driving frequency. We develop a corresponding theoretical model for this system including meniscus effects through detuning the driving acceleration of the container, which results in an inhomogeneous Mathieu equation that governs the wave dynamics whose spatial structure is defined by the mode number pair (n, m), with n and m the radial and azimuthal mode numbers, respectively. A perturbation method (PoincareLindstedt) is used to compute the instability tongues for the axisymmetric m=0 modes, while the asymmetric m≠ 0 modes are unaffected by the meniscus and satisfy a homogeneous Mathieu equation from which we compute the instability tongues using Floquet theory. Our model results explicitly show how the shape of the meniscus and spatial structure of the wave determine the temporal response, as it depends upon the Galilei number (Ga), Bond number (Bo), and meniscus wave amplification factor (f*). Our model predictions are in excellent agreement with prior experimental observations for both pure modes and mixed modes. Notably, the meniscus only affects the shape of the harmonic instability tongues for the axisymmetric m=0 modes, which can have a lower threshold acceleration and larger bandwidth than the subharmonic instability tongues, consistent with the experiment and suggesting our model recovers the essential physics associated with these complex surface wave dynamics. 
Sunday, November 19, 2023 3:39PM  3:52PM 
G44.00004: Abstract Withdrawn

Sunday, November 19, 2023 3:52PM  4:05PM 
G44.00005: The effect of surfactants on droplet generation in a plunging breaker Chang Liu, Martin A Erinin, Xinan Liu, James H Duncan An experimental study is conducted to compare droplet generation in a deepwater plunging breaker in filtered tap water (referred to as case TAP, ambient surface tension σ_{0} = 72 mN/m) and in the presence of two bulk concentrations (C_{TX}) of the soluble surfactant Triton X100: TX1, where C_{TX} = 2.1μmol/L and σ_{0} = 69 mN/m; and TX6, where C_{TX} = 193 μmol/L and σ_{0} = 35 mN/m. In the TX6 case, C_{TX} is close to the critical micelle concentration (CMC). The breakers are generated by a programmable wave maker that is set with a single motion profile that produces a highly repeatable dispersively focused quasi2D wave packet with a central frequency of f_{0 }= 1.15 Hz and a corresponding wavelength of λ_{0} = 1.18 m (by linear theory). The droplets are measured with an inline cinematic holographic system operating with measurement volumes that span the width of the tank. The positions, diameters (d ≥ 100 μm), times and velocities of droplets generated in these three cases are measured as the droplets move up across a prescribed horizontal measurement plane. It is found that the surfactants have strong effects on the droplet production mechanisms and the droplet number, diameter, and velocity distributions. One example is the droplets produced by the closure of the crater generated between the upper surface of the plunging jet and the splash that it produces. This crater closes rapidly in the TAP and TX6 cases but not in the TX1 case, resulting in much fewer droplets produced in TX1 than in TAP and TX6. 
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