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Register a new userSelf-consistent theory of capillary-wave generation by small moving objects
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We investigate theoretically the onset of capillary-gravity waves created by a small object moving at the water-air interface. It is well established that, for straight uniform motion, no steady waves appear at velocities below the minimum phase velocity $c_text{min} = 23 {rm cm/s}$. At higher velocities the emission of capillary-gravity waves creates an additional drag force. The behavior of this force near the critical velocity is still poorly understood. A linear response theory where the object is replaced by an effective pressure source predicts a singular behavior for the wave drag. However, experimental data tends to indicate a more continuous transition. In this article, we show that a proper treatment of the flow equations around the obstacle can regularize wave emission, even in the linear wave approximation, thereby ensuring a continuous behavior of the drag force.
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In this paper, we present an experimental study of weakly non-linear interaction of axisymmetric internal gravity waves in a resonant cavity, supported by theoretical considerations. Contrary to plane waves in Cartesian coordinates, for which self-interacting terms are null in a linear stratifiation, the non-linear self-interaction of an internal wave mode in axisymmetric geometry is found to be efficient at producing super-harmonics, i.e. waves whose frequencies are integer multiples of the excitation frequency. Due to the range of frequencies tested in our experiments, the first harmonic frequency is below the cut-off imposed by the stratification so the lowest harmonic created can always propagate. The study shows that the super-harmonic wave field is a sum of standing waves satisfying both the dispersion relation for internal waves and the boundary conditions imposed by the cavity walls, while conserving the axisymmetry.
Wave resistance is the drag force associated to the emission of waves by a moving disturbance at a fluid free surface. In the case of capillary-gravity waves it undergoes a transition from zero to a finite value as the speed of the disturbance is increased. For the first time an experiment is designed in order to obtain the wave resistance as a function of speed. The effect of viscosity is explored, and a magnetic fluid is used to extend the available range of critical speeds. The threshold values are in good agreement with the proposed theory. Contrary to the theoretical model, however, the measured wave resistance reveals a non monotonic speed dependence after the threshold.
Recently, the Whitham and capillary-Whitham equations were shown to accurately model the evolution of surface waves on shallow water. In order to gain a deeper understanding of these equations, we compute periodic, traveling-wave solutions to both and study their stability. We present plots of a representative sampling of solutions for a range of wavelengths, wave speeds, wave heights, and surface tension values. Finally, we discuss the role these parameters play in the stability of the solutions.
We present a method to estimate depth of a dynamic scene, containing arbitrary moving objects, from an ordinary video captured with a moving camera. We seek a geometrically and temporally consistent solution to this underconstrained problem: the depth predictions of corresponding points across frames should induce plausible, smooth motion in 3D. We formulate this objective in a new test-time training framework where a depth-prediction CNN is trained in tandem with an auxiliary scene-flow prediction MLP over the entire input video. By recursively unrolling the scene-flow prediction MLP over varying time steps, we compute both short-range scene flow to impose local smooth motion priors directly in 3D, and long-range scene flow to impose multi-view consistency constraints with wide baselines. We demonstrate accurate and temporally coherent results on a variety of challenging videos containing diverse moving objects (pets, people, cars), as well as camera motion. Our depth maps give rise to a number of depth-and-motion aware video editing effects such as object and lighting insertion.
High frequency thickness mode ultrasound is an energy-efficient way to atomize high-viscosity fluid at high flow rate into fine aerosol mists of micron-sized droplet distributions. However the complex physics of the atomization process is not well understood. It is found that with low power the droplet vibrates at low frequency (O[100 Hz]) when driven by high-frequency ultrasound (O[1 MHz] and above). To study the mechanism of the energy transfer that spans these vastly different timescales, we measure the droplets interfacial response to 6.6~MHz ultrasound excitation using high-speed digital holography. We show that the onset of low-frequency capillary waves is driven by feedback interplay between the acoustic radiation pressure distribution and the droplet surface. These dynamics are mediated by the Young-Laplace boundary between the droplet interior and ambient environment. Numerical simulations are performed via global optimization against the rigorously defined interfacial physics. The proposed pressure-interface feedback model is explicitly based on the pressure distribution hypothesis. For low power acoustic excitation, the simulations reveal a stable oscillatory feedback that induces capillary wave formation. The simulation results are confirmed with direct observations of the microscale droplet interface dynamics as provided by the high resolution holographic measurements. The pressure-interface feedback model accurately predicts the on-source vibration amplitude required to initiate capillary waves, and interfacial oscillation amplitude and frequency. The radiation pressure distribution is likewise confirmed with particle migration observations. Viscous effects on wave attenuation are also studied by comparing experimental and simulated results for a pure water droplet and 90% wt.- 10% wt. glycerol-water solution droplet.
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