Session GP: Waves I

The Effects of Wind and Surfactants on Mechanically Generated Spilling Breakers

The effects of both wind and surfactants on mechanically generated weakly spilling breakers are explored in a wind wave tank that is 11.8 m long, 1.15 m wide and 1.8 m high (1.0 m of water). A wave maker, which resides at the upwind end of the tank, is used to generate the breakers via a dispersive focusing method with a central wave packet frequency of 1.15 Hz. Low wind speeds (less than 3.0 m/s) are used to minimize the effect of short-wavelength wind-generated waves on the breakers. The profiles of the spilling breakers along the center plane of the tank are measured with an LIF technique that utilizes a high-speed digital movie camera. Measurements are performed with clean water and water mixed with various concentrations of Triton X-100, a soluble surfactant. It is found that the capillary waves/bulge patterns found in the initial stages of spilling breakers are dramatically affected by wind and surfactants. The size of bulge increases with the wind speed while the capillary waves are kept nearly the same. In the presence of surfactants and wind, both the amplitude and number of capillary waves are reduced and the slope of the front face of the wave increases.   

On the Shape of the Crest of Short Wavelength Water Waves at Incipient Breaking

Breaking waves with wavelengths ranging from about 0.1 to 1.2 m are studied experimentally in a wind wave tank that is 11.8 m long, 1.15 m wide and 1.8 m high (1.0 m of water). The tank includes a wind tunnel with speeds up to 10 m/s and a programmable wave maker that resides at the upwind end of the tank. The shortest waves are generated by wind with speeds ranging from about 4 to 7 m/s. The longest waves are generated mechanically from focused wave packets with average frequencies ranging from 1.15 to 1.42 Hz. Waves with intermediate lengths are formed either by wind or by a nonlinear wave train with unstable sidebands generated by the wave maker. At incipient breaking, all the waves have a capillary-ripple pattern at the crest rather than a plunging jet. It is found that in spite of the wide range of wavelengths and major differences in the generation methods, the shapes of the capillary-ripple pattern are remarkably similar. Various geometrical parameters including the length of the first capillary wave and the length and thickness of the bulge that forms at the crest are extracted from the data. The variation of these parameters with gravity wavelength and slope of the front face of the wave is examined.   

On the Jet Impact in a Plunging Breaker

Plunging breaking ship bow waves were simulated experimentally using a 2D+T wave maker in a tank that is 14.8 m long, 1.15 m wide and 2.1 m deep (water depth of 1.83 m). In the 2D+T simulation, the sequence of shapes of the flexible surface (wave board) of the wave maker reproduces the time varying intersection of one side of the ship hull with a vertical plane oriented normal to the ship's track as the ship moves in calm water at constant speed. For equivalent full-scale ship speeds greater than about 20 knots, a large plunging breaker is formed. An LIF system that employs a high-speed digital movie camera taking pictures at 256 frames per second was used to measure the temporal history of the profile of the plunging jet. In each image, the top surface of the jet is easily extracted as the intersection of the light sheet with the water surface. The bottom surface of the jet is also seen in the images, but since it is seen by looking through the jet, its profile must be obtained by using an inverse refraction method. The characteristics of the jet including the velocity and acceleration of the jet tip and the distribution of jet thickness are presented. It is interesting to note that the jet tip trajectory is ballistic, but that the vertical acceleration ranges from about 0.6 to 0.8 times the acceleration of gravity.   

Resonant interaction of waves generated by a moving/oscillating body in a two-layer density stratified fluid

The problem of nonlinear interactions among surface and interfacial waves generated by an oscillating-translating body in a two layer density stratified fluid is studied both analytically and numerically. In two dimension, according to linear theory, an oscillating-translating body in a two layer density stratified fluid generates up to eight waves depending on the dimensionless frequency, Froude number, density ratio and the depth ratio. When nonlinear effects are considered, we show that unlike in a homogeneous fluid, the second-order interactions of two of these ship waves may become resonant for a finite number of special values of the dimensionless frequency. Under the resonance, a new free wave is generated, and travels in the same or opposite direction of the original ship waves. The effects of such resonant interactions on the wave pattern and resistance of a ship are investigated. This study may have implications to the detection of vehicles in littoral zones using remote sensing.   

Energy transfer due to nonlinear wave-wave interactions in deep ocean

It was believed that the Garrett-Munk spectrum was the ``universal'' energy spectrum of oceanic internal waves. However, it has become apparent from recent categorization of oceanic observations that the Garrett-Munk spectrum can not be as universal as been previously thought. One may use the weak turbulence theory to attempt to explain the formation of the spectral energy density of internal waves. It turns out that the large wavenumbers (small scales) interact in triads via small wavenumbers (large scales). This hypothesis provides possible explanation for the variability of the energy spectra. Namely, several families of statistically steady solutions are found in consideration of the nonlocality in wavenumber spaces of resonant interactions. The new families of power-law exponents of the energy spectra are in good agreement with the observations. To check these theory we perform direct numerical simulations based on Hamiltonian formalism. It is shown also by the numerical simulations that the nonlocal interactions in the wavenumber space are dominant in the inertial wavenumbers. The validity of the weak turbulence theory is also discussed.   

Direct Numerical Simulation of Turbulence over Wavy Surfaces

In order to study the mechanism of wind-wave growth, we perform direct numerical simulation for turbulent flows over surface waves. The simulation is realized through a hybrid pseudo-spectral and finite-difference method on boundary fitted grid. We consider wavy surfaces with various conditions of wave age, wave slope, wave nonlinearity, and wind drift. Instantaneous and statistical flow features have been investigated. It is found that the distributions of wave-correlated pressure, momentum flux, and TKE budget are sensitive to surface orbital velocity and wave age. Near the wavy surface, semi-streamwise vortices are found to be prominent, the generation of which is associated with the Gortler instability. Evolution and transport of coherent vortex structures can be strongly affected by the value of wave age. Based on the extensive simulation data obtained, we quantify statistics of wave-coherent pressure, which is useful for modeling wind input for water waves.   

Oscillation of Multiple-Bodies in a Free Surface.

The present problem is of relevance in sea-keeping assessment of multi-hull ships (eg., catamaran or trimaran). Using boundary-integral and finite-difference algorithms, inviscid and viscous hydrodynamics of multiple bodies (hulls) under rigid-body oscillatory motions are studied. The findings of the research include: (i) The separation distance between the multi-hulls is a crucial parameter governing the hydrodynamic coefficients and, therefore, hull response in a given sea; (ii) At frequencies close to natural frequency of standing waves between the hulls, negative added mass and a large spike in wave damping due to outward radiating waves are observed; (iii) Trapped waves of various modes, including that on oscillating column of fluid between the hulls, are observed; (iv) Viscous effects on the hydrodynamic forces are significant at large Keulegan-Carpenter (KC) number and at natural frequencies of waves between the hulls with the significance being associated with vortices shed off the bilges of multi-hull ships due to body motion as well as set up of large-amplitude oscillating column of fluid between the hulls; and (v) In design, one can effectively adjust the dimensions of the main and side hulls to ensure small amplitude hull response to sea loads.   

Flow field near the corner of a partially submerged flat plate perpendicular to a uniform stream.

The flow field downstream the corner of a partially submerged vertical flat plate perpendicular to a uniform stream has been experimentally studied. The main feature of this flow is the formation of a steady wave originating at the vertex and whose front is bent towards the centerline of the resulting wake. The amplitude of the wave front grows with the downstream distance to the plate, eventually creating either a spilling or a plunging breaker depending on the flow parameters. The internal structure of these waves is investigated and a criterion to determine the transition between both regimes is proposed. Furthermore, the similarities of these laboratory breakers with breaking waves in the ocean and other flows of interest in oceanography and ship hydrodynamics are explored. This work has been sponsored by the ONR through grant N00014-05-1-0121.