Waves in Radial Gravity Using Magnetic Fluid
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.