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Terrestrial laboratory experiments studying various fluid dynamical processes are constrained, by being in an Earth laboratory, to have a gravitational body force which is uniform and unidirectional. Therefore fluid free-surfaces are horizontal and flat. Such free surfaces must have a vertical solid boundary to keep the fluid from spreading horizontally along a gravitational potential surface. In atmospheric, oceanic, or stellar fluid flows that have a horizontal scale of about one-tenth the body radius or larger, sphericity is important in the dynamics. Further, fluids in spherical geometry can cover an entire domain without any sidewall effects, i.e. have truly periodic boundary conditions. We describe spherical body-force laboratory experiments using ferrofluid. Ferrofluids are dilute suspensions of magnetic dipoles, for example magnetite particles of order 10 nm diameter, suspended in a carrier fluid. Ferrofluids are subject to an additional body force in the presence of an applied magnetic field gradient. We use this body force to conduct laboratory experiments in spherical geometry. The present study is a laboratory technique improvement. The apparatus is cylindrically axisymmetric. A cylindrical ceramic magnet is embedded in a smooth, solid, spherical PVC ball. The geopotential field and its gradient, the body force, were made nearly spherical by careful choice of magnet height-to-diameter ratio and magnet size relative to the PVC ball size. Terrestrial gravity is eliminated from the dynamics by immersing the "planet" and its ferrofluid "ocean" in an immiscible silicone oil/freon mixture of the same density. Thus the earth gravity is removed from the dynamics of the ferrofluid/oil interface and the only dynamically active force there is the radial magnetic gravity. The entire apparatus can rotate, and waves are forced on the ferrofluid surface by exterior magnets. The biggest improvement in technique is in the wave visualization. Fluorescing dye is added to the oil/freon mixture and an argon ion laser generates a horizontal light that can be scanned vertically. Viewed from above, the experiment is a black circle with wave deformations surrounded by a light background. A contour of the image intensity at any light sheet position gives the surface of the ferrofluid "ocean" at that "latitude". Radial displacements of the waves as a function of longitude are obtained by subtracting the contour line positions from a no-motion contour at that laser sheet latitude. The experiments are run by traversing the forcing magnet with the laser sheet height fixed and images are frame grabbed to obtain a time-series at one latitude. The experiment is then re-run with another laser-sheet height to generate a full picture of the three-dimensional wave structure in the upper hemisphere of the ball as a function of time. We concentrate here on results of laboratory studies of waves that are important in Earth's atmosphere and especially the ocean. To get oceanic scaling in the laboratory, the experiment must rotate rapidly (4-second rotation period) so that the wave speed is slow compared to the planetary rotation speed as in the ocean. In the Pacific Ocean, eastward propagating Kelvin waves eventually run into the South American coast. Theory predicts that some of the wave energy should scatter into coastal-trapped Kelvin waves that propagate north and south along the coast. Some of this coastal wave energy might then scatter into mid-latitude Rossby waves that propagate back westward. Satellite observations of the Pacific Ocean sea-surface temperature and height seem to show signatures of westward propagating mid-latitude Rossby waves, 5 to 10 years after the 1982-83 El Nino. The observational data is difficult to interpret unambiguously owing to the large range of motions that fill the ocean at shorter timescales. This series of reflections giving eastward, north- ward, and then westward traveling waves is observed cleanly in the laboratory experiments, confirming the theoretical expectations.

The aim of the present investigation is to characterize the motion of dendrite fragments falling under the influence of gravity in a uniform liquid medium at low Reynolds number. In an earlier study, Zakhem, Weidman and de Groh (1992) reported on the settling speed of model equiaxed dendrite grains released along their axis of symmetry. In this follow-up study uniaxial model dendrite grains were released off-axis to observe and document their motion at different orientations. It was hypothesized that the dendrite models might rotate when released off-axis in which case an attempt would be made to document the ensuing unsteady motion. This latter event turned out to be in fact true: at the small but finite Reynolds numbers that existed, each uniaxial dendrite slowly rotated towards its equilibrium orientation while failing under the influence of gravity. In addition to completing the original goal, we have made use of a beads-on-a shell Stokes flow code to numerically determine the drag coefficient for capsules, i.e.. uniaxial dendrites without arms. The drag on horizontally and vertically falling capsules are reported and compared with measurements.

An experimental study of low Reynolds number drag on laboratory models of dendrite fragments has been conducted. The terminal velocities of the dendrites undergoing free fall along their axis of symmetry were measured in a large Stokes flow facility. Corrections for wall interference give nearly linear drag vs Reynolds number curves. Corrections for both wall interference and inertia effects show that the dendrite Stokes settling velocities are always less than that of a sphere of equal mass and volume. In the Stokes limit, the settling speed ratio is found to correlate well with primary dendrite arm aspect ratio and a second dimensionless shape paremeter which serves as a measure of the fractal-like nature of the dendrite models. These results can be used to estimate equiaxed grain velocities and distance of travel in metal castings. The drag measurements may be used in numerical codes to calculate the movement of grains in a convecting melt in an effort to determine macrosegregation patterns caused by the sink/float mechanism.

An experimental study of low Reynolds number drag on laboratory models of dendrite fragments has been conducted. The terminal velocities of the dendrites undergoing free fall along their axis of symmetry were measured in a large Stokes flow facility. Corrections for wall interference give nearly linear drag vs Reynolds number curves. Corrections for both wall interference and inertia effects show that the dendrite Stokes settling velocities are always less than that of a sphere of equal mass and volume. In the Stokes limit, the settling speed ratio is found to correlate well with the primary dendrite arm aspect ratio and a second dimensionless shape parameter which serves as a measure of the fractal-like nature of the dendrite models. These results can be used to estimate equiaxed grain velocities and distance of travel in metal castings. The drag measurements may be used in numerical codes to calculate the movement of grains in a convecting melt in an effort to determine macrosegregation patterns caused by the sink/float mechanism.

The effects of rectangular initial data on the evolution of solitons governed by the Korteweg-de Vries equation is studied. Both isolated and separated disturbances are considered, providing some general insight into how the nature of the initial condition influences the appearance of solitons in the asymptotic state. The analytic approach is based on the inverse scattering transform which relates the initial condition to Schroedinger's equation. The results are used to model the initial shallow-water disturbances, and the results can be summarized by stating that the number of evolved solitons depends on the strength of each rectangular disturbance, the relative amplitudes of the rectangular disturbances, and the relative proximity of the disturbances.

The effects of vertical shear on regular neutral mode Rossby solitons driven by a horizontal shear are investigated in light of the proposition that certain features in the Jupiter atmosphere may be explained by solitary Rossby waves. Consideration is given to a two-layer quasi-geostrophic model in which the motion in each layer consists of a different zonal shear flow, with vertical shear concentrated at the interface between the layers. In the case of a strong vertical shear, it is found that only a very restricted set of flows will admit Rossby neutral model solitons. For the more realistic case of a weak vertical shear, results indicate similar, but latitudinally shifted, wave patterns in each layer. It is noted that no such slant has yet been detected in the Great Red Spot.

An experiment was designed to measure the fluid oscillations in planar isochronous containers. Measurements of the resonant fluid response to forced oscillations provide direct experimental confirmation of the existence of these special containers.

Interactions of long-wave solitons propagating in shear flows are described by a coupled pair of Korteweg-de Vries equations. The basic equation of motion for the analysis is the quasi-geostrophic forecast equation, and the interaction of two wave modes is studied. The solution for mode 1-mode 2 interaction of solitary waves in an asymmetric shear flow of a barotropic atmosphere with divergence is constructed. Streamline patterns for certain flows are obtained. An unsteady solitary wave solution for a modified Korteweg-de Vries equation is derived.

The mode shapes for internal solitary waves propagating in a linearly stratified fluid of finite depth are determined in the limit of weak stratification. The solutions obtained for both a fixed upper boundary and a free surface are compared with known results for exponential stratification. The profound changes which occur depending on whether the upper surface is fixed or free are derived from the strong influence of the free surface when the stratification is weak. Evidence is presented supporting the conjecture that the free surface can no longer effect qualitative differences in the modal structure when the fluid is heavily stratified.

Experiments on the interaction between solitary shallow-water waves propagating in the same direction have been performed in a rectangular channel. Two methods were devised to compensate for the dissipation of the waves in order to compare results with Hirota's (1971) solution for the collision of solitons described by the Korteweg-de Vries equation. Both qualitative and quantitative agreement with theory is obtained using the proposed corrections for wave damping.

Further evidence is presented that strengthens the case for the interpretation of many features in the Jovian atmosphere as solitary Rossby waves (solitons). These include: a mechanism whereby such waves can evolve from the instability of the basic shear flows; further interpretation of the interaction between observed features, and comparison with calculations of the interaction between planetary solitons of a restricted class; and calculations of soliton morphology for a type of shear flow other than the type considered originally by Maxworthy and Redekopp (1976).