The CSU Spin Tank




Introduction

Rotating tables have been in use for many years because of their ability to demonstrate fluid dynamical phenomena, shedding insight on the sometimes complicated or esoteric mathematics used to describe such processes. A small team of students at the CSU Department of Atmospheric Science constructed a rotating table, or "spin tank", apparatus that is simple and affordable, yet instructive.
The device is designed to be easy to maintain and operate. The number of moving parts is kept at a minimum, and the electrical components chosen are of high quality. With the aid of a brief instruction manual or tutorial, students and faculty can operate the rotating table and easily perform many demonstrations, with the freedom to vary fluid depth, rotation rate, and acceleration. The entire design and construction process was conducted on a limited budget of $3,000.
A spin tank such as this has practical applications for the qualitative study of fluid dynamics. Fundamental concepts in rotating flow dynamics can be demonstrated to supplement the more rigorous mathematical treatment typically given in oceanography or atmospheric physics graduate-level courses. Topics that have been explored thus far are Ekman pumping, Taylor columns, and barotropic instability, but could be broadened to include subjects such as Rossby waves, baroclinic instability, vortex merger, and rotating convection.



Construction Details

Timeline

October 2000: practicum proposed to design and build spin tank
January 2001: begin work on ideas, theory, desired demonstrations
February 2001: get donated base and platter from CU
March 2001 - September 2001: work on tank, mechanics, electronics
September 2001: present spin tank to department at seminar
October 2001 - present: use spin tank in classrooms
May 2002: submit paper to BAMS on design and construction of spin tank
August 2002 - December 2002: practicum on rotating convection
April 2003: submit revised final manuscript to BAMS
December 2003: paper published in BAMS (DOWNLOAD PDF)
January 2004 - May 2004: practicum on Hadley/Rossby waves

Spin Tank Specifications

Power demand through slip rings: 115W [40W (x2) for lights, 35W for camcorder]
Current demand through slip rings: 0.95A [.33A (x2) for lights, .29A for camcorder]
Tank material: 1.3 cm thick acrylic from Regal Plastics
Tank adhesive: IPS Weld-On #16
Tank dimensions: 50.8 cm internal diameter, 53.4 cm external diameter, 61.0 cm height
Base dimensions: 92.0 cm long, 61.0 cm wide, 40 cm tall (55 cm with platter, 177 cm with superstructure)
Maximum tank capacity: 124 kg water
Motor type: Oriental Motor model FBL5120AW-50
Maximum motor horsepower/power: 0.17hp / 120W
Maximum motor angular velocity: 3.0 rad/s
Maximum motor torque: 34.0 N m
Motor drive cord: Polycord UPRB2 (1/8" diam)
Digital Camcorder: Canon ZR-20

Approximate Costs

Acrylic (tube and sheets): $960
Motor (controller, dial, wheel, drive cord): $740
Hardware, Tools, Misc. supplies: $400
Superstructure (rods, clamps, lights): $215
Shop labor: $200
Wooden platform (with wheels, handle): $175
TOTAL: ~$2690




Demonstrations

All experiments thus far utilize a constant volume of a rotating incompressible, homogeneous fluid (water) with a free upper surface.

Ekman boundary layers, Ekman pumping/suction, and spin-up/spin-down

Ekman pumping works on the principle of frictional geostrophic motion. If the fluid is at solid body rotation and the rotation rate is then increased, the bulk of the fluid (except near the walls) is now in relative motion to the new rotation rate of the inertial reference frame. A frictional, viscous layer is created along the floor (Ekman layer) and the walls (Stewartson layer) of the tank. At this point, the geostrophic balance between Coriolis force and pressure gradient force is destroyed, and the Coriolis force dominates, forcing mass transport to the right of the surface stress, or outward along the floor of the tank and upward along the walls. A secondary circulation is then induced.


MPEG-1 MOVIE (~5Mb)

Taylor-Proudman Theorem

The Taylor-Proudman Theorem states that the motion of a homogeneous fluid will be the same in all planes perpendicular to the axis of rotation, assuming friction is negligible and the Rossby number is small. The water is brought up to solid body rotation and an obstacle (can of cat food) is placed on the bottom of the tank approximately 2/3 out from the center. If the rotation rate is then increased slightly, a relative flow around the obstacle will be introduced, and the flow pattern at low levels will be mirrored at all depths in the fluid, creating a Taylor column.


MPEG-1 MOVIE (~7Mb)

Barotropic Instability

While experimenting with spin-up and spin-down, it is easy to produce flow instabilities. For example, near the end of the spin-up process shown in the previous Ekman pumping section, water containing red and green dye has moved radially outward along the bottom, up the side wall, and then radially inward a small distance, stopping its inward radial displacement when spin-up is complete. We end up with a banded pattern near the outer edge of the tank. Now suppose the rotation rate of the tank is abruptly (but within reason) and significantly decreased. The relative flow is now counterclockwise, with a large radial shear of the azimuthal velocity near the edge of the tank (see below). In this region of large shear, barotropic instability begins to set in, as shown by the waviness in the upper right figure below. As this instability extracts increasing amounts of kinetic energy from the primary circulation, the waves continue to amplify, resembling the cresting and breaking of ocean waves, as shown in the bottom row of figures. These eddies can rapidly mix the dye, leaving a featureless colored haze. This process can be repeated over and over until the water is too murky with dye to see these features. If the change in rotation rate is not large enough, the spin-up time will actually be shorter than the time required to set up the barotropic instability, and the aforementioned features will never be seen.


MPEG-1 MOVIE (~6Mb)




Uses

The spin tank was first demonstrated in a lecture hall during one of the weekly department seminars. It generated a lot of interest withinin the department, and since then, has been requested for several other classes, including AT351 (an introductory course in Atmospheric Science for undergraduates), AT601 and AT602 (introductory courses in Atmospheric Dynamics for graduate students).
The tank can be used with or without the superstructure attached, with or without the video camera and lights, or basically in any configuration desired. The ability to show live video from the rotating frame to small and large audiences alike is usually taken advantage of. The freedom of taking the superstructure (and lights and camera) off is beneficial for small groups who want to get right in on the action and not worry about the rotating metal posts hitting them.
The spin tank will continually be maintained and upgraded as its uses and demands increase. It is a new and valuable asset to the department.



This page created and maintained by Brian McNoldy.
Last modified 14 Jan 2004.