James H. Duncan

The breaking and non-breaking wave resistance of a two-dimensional hydrofoil

Measurements of the surface-height profile and the vertical distributions of velocity and total head were made behind a two-dimensional fully submerged hydrofoil moving horizontally at constant speed and angle of attack. These measurements were used to resolve the drag on the foil into two parts: one associated with the turbulent breaking region that is sometimes present on the forward face of the first wave, and the other associated with the remaining non-breaking wavetrain. It was found that at ‘incipient breaking’ the first wave existed in either a breaking or a non-breaking state depending on the starting procedures. It was possible to induce steady breaking when the wave slope was 17° or higher. The wake survey measurements showed that the drag associated with breaking reached more than three times the maximum drag that could theoretically be obtained with non-breaking waves. The drag associated with breaking was found to be proportional to the downslope component of the weight of the breaking region.

The final stage of the collapse of a cavitation bubble near a rigid wall

During the collapse of an initially spherical cavitation bubble near a rigid wall, a reentrant jet forms from the side of the bubble farthest from the wall. This re-entrant jet impacts and penetrates the bubble surface closest to the wall during the final stage of the collapse. In the present paper, this phenomenon is modelled with potential flow theory, and a numerical approach based on conventional and hypersingular boundary integral equations is presented. The method allows for the continuous simulation of the bubble motion from growth to collapse and the impact and penetration of the reentrant jet. The numerical investigations show that during penetration the bubble surface is transformed to a ring bubble that is smoothly attached to a vortex sheet. The velocity of the tip of the re-entrant jet is always directed toward the wall during penetration with a speed less than its speed before impact. A high-pressure region is created around the penetration interface. Theoretical analysis and numerical results show that the liquid-liquid impact causes a loss in the kinetic energy of the flow field. Variations in the initial distance from the bubble centre to the wall are found to cause large changes in the details of the flow field. No existing experimental data are available to make a direct comparison with the numerical predictions. However, the results obtained in this study agree qualitatively with experimental observations.

On the detection of motion and the computation of optical flow

A method for the detection of motion in image sequences is presented. In this method, the intensity history at each pixel is convolved with the second derivative in time of a temporal Gaussian smoothing function. The zero crossings in a single frame of the resulting function indicate the positions of moving edges. Intensity changes in time due to illumination effects do not produce zero crossings; thus, they are not interpreted as motion by the present method. It is also shown that the spatial and temporal derivatives of this function can be used to compute the component of the optical flow that is normal to the zero-crossing contours. This computation is also insensitive to nonconvective temporal and spatial variations in the image intensity that are caused by illumination effects. >

On the nonspherical collapse and rebound of a cavitation bubble

The behavior of a cavitation bubble adjacent to a rigid wall is studied numerically with the boundary integral method described in Zhang, Duncan, and Chahine [J. Fluid Mech. 257, 147 (1993)]. In the previous work, the pressure inside the bubble was held constant (this is referred to herein as the empty bubble case). In the present calculations, an internal gas pressure, which is a function of the bubble volume, is included in the model. The present results are qualitatively similar to those in the empty bubble case in several ways: a wall‐directed reentrant jet is formed in the later phase of the collapse; this jet impacts with the side of the bubble closest to the wall creating a toroidal‐shaped bubble; and a shear layer develops along the impact interface. However, unlike the empty bubble, whose volume decreases monotonically to zero at the end of the collapse, the present gas‐filled bubble reaches a minimum volume and then, due to its high internal gas pressure, begins to grow again (rebound). In the e...

Temporal Edges: The Detection Of Motion And The Computation Of Optical Flow

A new method for the detection of motion and the computation of optical flow is presented. In the first step of the calculation the intensity history at each pixel is convolved with the second derivative in time of a temporal Gaussian smoothing function. The zero crossings in a single frame of the resulting function indicate the positions of moving edges. Spatial and temporal derivatives of the function at the zero-crossing locations are then used to compute the component of the flow that is normal to the zero-crossing contours. Both the detection of motion and the computation of the normal velocity are insensitive to slow temporal and spatial changes in the image intensity that are caused by illumination effects rather than motion. A framework in which to relate the present work to a number of gradient based flow measurement techniques is also presented.

3-D translational motion and structure from binocular image flows

Image flow fields from parallel stereo cameras are analyzed to determine the relative 3-D translational motion of the camera platform with respect to objects in view and to establish stereo correspondence of features in the left and right images. A two-step procedure is suggested. In the first step, translational motion parameters are determined from linear equations the coefficients of which consist of the sums of measured quantities in the two images. Separate equations are developed for cases when measurements of either the full optical flow or the normal flow are available. This computation does not require feature-to-feature correspondence. In addition, no assumption is made about the surfaces being viewed. In the second step of the calculation, with the knowledge of the estimated translational motion parameters, the binocular flow information is used to find features in one image that correspond to given features in the other image. Experimental results with synthetic and laboratory images indicate that the method provides accurate results even in the presence of noise. >

An experimental investigation of divergent bow waves simulated by a two-dimensional plus temporal wave marker technique

Divergent ship bow waves were simulated experimentally with a two-dimensional wavemaker that employs a flexible wave board. The wavemaker was programmed so that the wave board created a time sequence of shapes that simulated the line of intersection between one side of the hull of a slender ship model moving at constant speed and an imaginary vertical plane oriented normal to the ship model track. The time history of the water surface shape was measured with a cinematic laser-induced fluorescence technique for eight Froude numbers ( F D = U / , where U is the forward speed of the equivalent three-dimensional ship model, g the acceleration of gravity and D the ship model draft). The waves produced ranged from small-amplitude non-breaking waves at the lowest Froude numbers to plunging breakers at the highest Froude numbers. These waves are strongly forced and at the higher Froude numbers begin breaking before leaving the wave board. The time histories of various geometric characteristics of the water surface shape including the hull contact line, the wave crest, the plunging jet and the splash zone, which is here defined as both the turbulent zone on the front face of the wave in the spilling breakers and the turbulent zone generated ahead of the jet impact point in the plunging breakers, were measured. The phase speed of the primary wave generated during each run ranged from 2.56 U wl (where U wl is the maximum speed of the wave board at the undisturbed water level in the tank) at the lowest Froude number to about 1.7 U wl at the three highest Froude numbers. The maximum heights of the primary wave, the contact point on the wavemaker and the splash zone increased in a nearly linear fashion with increasing F D . In the cases with plunging jets, the jet tip trajectory was parabolic with a vertical acceleration ranging from 0.6 g at F D = 1.467 to 0.8 g at F D = 1.817 (the highest Froude number).

Recovering the Three-Dimensional Motion and Structure of Multiple Moving Objects from Binocular Image Flows

A new method is presented for recovering the three-dimensional motion and structure of multiple, independently moving, rigid objects through the analysis of binocular image flow fields. The input to the algorithm is the image location and image velocity of a sparse set of feature points in the stereo image pair. The algorithm analyzes one rigid object at a time by simultaneously segmenting the associated feature points from the input data set, establishing the stereo correspondence of these feature points and determining the three-dimensional motion of the object. The solution method is iterative and is based on the stereo-motion algorithm presented in J. H. Duncan, L. Li, and W. Wang, “Recovering Three-Dimensional Velocity and Established Stereo Correspondence from Binocular Image Flows” (Opt. Eng.34(7), July 1995, 2157?2167.) for the analysis of scenes with only one set of three-dimensional motion components. No restrictions on the three-dimensional structure of the scene are required by the theory. Experimental results with numerically generated and laboratory image sequences are given to verify the method.

An experimental study of surfactant effects on spilling breakers

The dynamics of spilling breakers in the presence of surfactants were studied experimentally. The spilling breakers were produced from Froude-scaled mechanically generated dispersively focused wave packets with average frequencies of 1.15, 1.26 and 1.42 Hz. Separate experiments were performed with the same wave-maker motions in clean water and in water with various bulk concentrations of the soluble surfactants sodium dodecyl sulfate (SDS) and Triton X-100 (TX). For nearly all surfactant conditions, the surface-pressure isotherm, equilibrium surface elasticity and surface viscosity were measured in situ in order to characterize the dynamic properties of the free surface. In clean water, all the waves considered herein break without overturning of the free surface. This breaking process begins with the formation of a bulge on the forward face of the wave crest and capillary waves upstream of the leading edge of the bulge (called the toe). After a short time, the flow separates under the toe and a turbulent flow is developed while the toe moves rapidly down the wave face. During the toe motion, a train of ripples appears between the toe and the crest and this train of ripples is swept downstream. In the presence of surfactants, the bulge shape is modified and its size generally decreases with increasing surfactant concentration. The capillary waves found upstream of the toe in the clean-water case are dramatically reduced at even the lowest concentrations of surfactants. With surfactants, the start of the breaking process is still initiated when the toe begins to move down the forward face of the wave. The pattern of ripples generated between the toe and the crest of the wave during this phase of the breaking process varies with the concentration of surfactant. It was found that the temporal history of the vertical distance between the toe and the wave crest scales with the nominal length (σ 0 /ρg) 1/2 while the bulge length from toe to crest scales with the nominal length (μ s /ρ √g) 2/5 , where σ 0 and μ s are the ambient surface tension and the surface viscosity, respectively.

The implosion of cylindrical shell structures in a high-pressure water environment.

The implosion of cylindrical shell structures in a high-pressure water environment is studied experimentally. The shell structures are made from thin-walled aluminium and brass tubes with circular cross sections and internal clearance-fit aluminium end caps. The structures are filled with air at atmospheric pressure. The implosions are created in a high-pressure tank with a nominal internal diameter of 1.77 m by raising the ambient water pressure slowly to a value, Pc, just above the elastic stability limit of each shell structure. The implosion events are photographed with a high-speed digital movie camera, and the pressure waves are measured simultaneously with an array of underwater blast sensors. For the models with larger values of length-to-diameter ratio, L/D0, the tubes flatten during implosion with a two-lobe (mode 2) cross-sectional shape. In these cases, it is found that the pressure wave records scale primarily with Pc and the time scale (where Ri is the internal radius of the tube and ρ is the density of water), whereas the details of the structural design produce only secondary effects. In cases with smaller values of L/D0, the models implode with higher-mode cross-sectional shapes. Pressure signals are compared for various mode-number implosions of models with the same available energy, PcV , where V is the internal air-filled volume of the model. It is found that the pressure records scale well temporally with the time scale , but that the shape and amplitudes of the pressure records are strongly affected by the mode number.