Jerome H. Milgram

Mean flow in round bubble plumes

Previous experimental studies are reviewed and those whose data are deemed reliable are identified. New experiments at larger scale are described and the results are reported. These are combined with the reliable previous studies to form a data set covering heights from 3.66 to 50 m and gasflow rates from 0.0002 to 0.59 normal m 3 /s. These wide-ranging data are combined with an integral theory for bubble plumes to determine functional relationships between local plume properties and the entrainment coefficient and the fraction of the momentum flux that is carried in the turbulent velocity fluctuations. These relationships together with the integral theory provide a set of equations that are suitable for numerical solution for the mean flow properties of any round bubble plume. Examples of the numerical solutions are presented and a comparison of one of these with existing experimental data is given. The relationships between the local plume properties and the entrainment coefficient and the momentum flux carried by the turbulence are interpreted to provide a qualitative understanding of the parameters involved and their influences on the plume.

Computational reconstruction of images from holograms.

The equations to reconstruct an image plane from a hologram are developed. This development is carried out for planes parallel to the hologram, which allows fast computation through the use of fast Fourier transforms. Algorithms for a digital computer are developed so images can be reconstructed, both with and without the Fresnel approximation, from a digitized hologram without the need for three-dimensional optical reconstruction equipment. Examples of holographically recorded images of marine micro-organisms are shown. A computational method for counting the number of micro-organisms in the holographically recorded volume is developed, and an example is provided.

ACTIVE WATER-WAVE ABSORBERS

The problem considered is that of absorbing two-dimensional water waves in a channel by means of a moving termination at the end of the channel. The problem is formulated for a semi-infinite channel and solutions are determined according to a linearized theory. The motion of the termination that is needed for absorption is determined in the form of a linear operation on the measured surface elevation at a fixed point in the channel so a self-actuating wave-absorbing system can be devised. A theoretical method of studying the stability of such a system is presented. A system of this type was built and experiments with it are described. Wave absorption is demonstrated both for monochromatic waves and for wave pulses. The absorption of a wave pulse is compared with the absorption of the same pulse by a fixed beach making a 10 degrees angle with the horizontal direction.

An experimental study of attenuation of short water waves by turbulence

Measurements of the dissipation of short water waves in a wave tank are analysed and described. Monochromatic waves with lengths between 6 and 10 cm generated by an axisymmetric wavemaker propagated through a turbulent flow field generated by a submerged vertically oscillating grid below the wavemaker. The horizontal turbulence velocity was measured with a hot-film anemometer with the grid oscillating, but the wavemaker off. With the wavemaker operating, wave amplitude vs. distance from the wavemaker was measured with and without operation of the turbulence generator. Wave dissipation due to turbulence was measured and quantified. Much of the wave energy transfer to turbulence may not occur in the normal energy-containing depth of the waves. Rather, most of it may first be convected downward and out of the wave zone by the vertical turbulent velocities. The experimental data are consistent with this possibility.

The motion of a fluid in a cylindrical container with a free surface following vertical impact

The effect of a sudden change in vertical velocity of a vessel partially filled with fluid is considered. It is shown that very small free surface disturbances can be amplified so strongly by a velocity change that instability can occur. This instability frequently causes a jet to emanate from the free surface. Conditions causing free surface disturbances in a vessel in free fall are considered and it is shown that a contact angle between the fluid and the wall of the vessel different from ½π radians can distort the surface in such a way that the amplification and instability upon vertical impact results in a central jet. The results of experiments of this effect are shown. The generation of waves due to transient side wall motions, such as those that might result from fluid pressure at impact, are considered in the appendix. It is shown that such waves would have a different form than those observed in the experiments.

Short wave damping in the simultaneous presence of a surface film and turbulence

Spatial decay rates of short gravity waves and gravity-capillary waves in the frequency range of 3 to 8 Hz were measured in a laboratory wave tank equipped with a submerged oscillating grid to generate turbulence. Experiments were conducted with: clean fresh water, fresh water with an oleyl alcohol insoluble surfactant surface film, fresh water with a Triton X-100 soluble surfactant surface film, and with sea water having a surface film of its own natural surfactants. With each material, decay rate tests were conducted with and without turbulence. The principal purpose of the study was to determine the extent to which turbulence modified the wave decay due to the presence of surface films. This is of importance for modeling the energy balance of short sea waves which influence microwave backscattering used for remote sensing of the ocean. The results show that the wave decay rate is equal to the sum of the rates due to surfactant alone and with turbulence alone. It is concluded that the statistically stationary component of the turbulence that exists near the free surface does not significantly modify the decay mechanism associated with the presence of the surfactant.

Dynamic behavior of natural sea surfactant films

The dynamic behavior of sea surfactants is studied at timescales from 0.04 to 2 seconds by generating waves on the water containing its natural surfactants in the laboratory and comparing dynamical measurements with theoretical predictions for prescribed surfactant properties. The properties considered are film pressure, elasticity and surface viscosity. For longitudinal Marangoni waves in the frequency range of 0.5 to 4.0 Hz, time-varying film pressures are measured. For transverse waves in the frequency range of 3 to 25 Hz, spatial decay rates are measured. Prior to conducting experiments with sea water containing soluble natural surfactants, the procedures and methods of analysis are validated by experiments with clean fresh water and with an insoluble oleyl alcohol film. A notable finding is that the static film elasticity accurately predicts the dynamic behavior of both the insoluble oleyl alcohol film and the soluble natural sea surfactant films. To better understand the reasons for this finding, sea surfactant adsorption and desorption time histories were measured. The adsorption/desorption time scales ranged from 46 to 196 min. One reason for the accurate prediction of surfactant dynamic behavior by the static elasticity is that the timescales of the waves are much shorter than the adsorption/desorption timescales. The conclusion is that the static elasticity controls the interactions of surfactants with most hydrodynamic disturbances having timescales up to several min.

Measurements of the surface flow above round bubble plumes

Abstract When a bubble plume exists beneath a free surface, such as after a subsea gas well blowout, a generally horizontal flow occurs in the vicinity of the surface and this flow is influenced by the fact that the surface is free. Two very different theories for such surface flows have been developed in the past and the bases of these theories are reviewed here. The results of measurements of surface flows above plumes of relatively large scale are given. These are compared with both of the existing theories. One theory is found to be accurate at small radii from the plume centre and the other theory is found to be accurate at large radii. The needed boundary condition for the theory that is accurate at large radii is supplied by the results of the theory that is accurate at small radii.

FORCES AND MOTIONS OF A FLEXIBLE FLOATING BARRIER

The problem of determining the motions, the structural and the hydrodynamic forces on a flexible, floating barrier are considered. Such barriers are frequently used as containment devices for floating liquid pollutants such as oil. Local hydrodynamic forces on a barrier are approximated by those for a straight barrier at angles to the waves and current equal to those of the local section. This affords a simplification in the theory that allows a solution in closed form to the nonlinear problem of a barrier in a current and a numerical solutions for the linearized problem of a barrier in waves. These problems are treated additively inasmuch as the interaction effects between waves and currents on a barrier are not yet known. The degree to which the barrier follows the fluid particle motion in waves is known to be particularly important. Poor following not only leads to degradation of the barrier as a containment device, but also results in enormous forces on the barrier. Application of the method of solutions for barriers to the case of a towed cable in waves is discussed. Previously unpublished force coefficients for a two-dimensional flat plate are given.

Advances in Plankton Imaging Using Digital Holography

An in situ plankton imaging system using a high space-bandwidth product camera and fiber coupled diode laser for digital holography was developed. High quality imaging results and solutions for associated computational challenges are discussed.