We consider the nonlinear spin-up of a rotating stratified fluid in a conical container. An analysis of similarity-type solutions to the relevant boundary-layer problem (Duck et al, 1997) has revealed three types of behavior for this geometry. In general, the boundary-layer evolves to either a steady state, a growing boundary-layer, or a finite-time singularity depending on the initial to final rotation rate ratio, and a “modified Burger number.” We emphasize the experimental aspects of our continuing spin-up investigations and make some preliminary comparisons with the boundary-layer theory, showing good agreement. The experimental data presented is obtained through particle tracking velocimetry. We briefly discuss the qualitative features of the spin-down experiments which, in general, are dominated by nonaxisymmetric effects. The experiments are performed using a conical container filled with a linearly stratified fluid, the generation of which is nontrivial. We present a general method for creating a linear density profile in containers with sloping boundaries.

1.
Duck
P. W.
,
Foster
M. R.
, and
Hewitt
R. E.
,
1997
, “
On the Boundary Layer Arising in the Spin-Up of a Stratified Fluid in a Container with Sloping Walls
,”
Journal of Fluid Mechanics
, Vol.
335
, pp.
233
259
.
2.
Greenspan, H. P., 1968, “The Theory of Rotating Fluids,” Cambridge University Press.
3.
Greenspan
H. P.
, and
Howard
L. N.
,
1963
, “
On a Time-Dependent Motion of a Rotating Fluid
,”
Journal of Fluid Mechanics
, Vol.
17
, pp.
385
404
.
4.
Greenspan
H. P.
, and
Weinbaum
S.
,
1965
, “
On Nonlinear Spin-Up of a Rotating Fluid
,”
Journal of Mathematics and Physics
, Vol.
44
, pp.
66
85
.
5.
MacCready
P.
, and
Rhines
P. B.
,
1991
, “
Buoyant Inhibition of Ekman Transport on a Slope and Its Effect on Stratified Spin Up
,”
Journal of Fluid Mechanics
, Vol.
223
, pp.
631
661
.
6.
Oster
G.
,
1965
, “
Density Gradients
,”
Scientific American
, Vol.
213
, pp.
70
76
.
7.
Sakurai
T.
,
1969
, “
Spin Down Problem of a Rotating Stratified Fluid in Thermally Insulated Circular Cylinders
,”
Journal of Fluid Mechanics
, Vol.
37
, pp.
689
699
.
8.
Spence
G. S. M.
,
Foster
M. R.
, and
Davies
P. A.
,
1992
, “
The Transient Response of a Contained Rotating Stratified Fluid to Impulsively Started Surface Forcing
,”
Journal of Fluid Mechanics
, Vol.
243
, pp.
33
50
.
9.
Walin
G.
,
1969
, “
Some Aspects of Time-Dependent Motion of a Stratified Rotating Fluid
,”
Journal of Fluid Mechanics
, Vol.
36
, pp.
289
307
.
10.
Wedemeyer
E. H.
,
1964
, “
The Unsteady Flow Within a Spinning Cylinder
,”
Journal of Fluid Mechanics
, Vol.
20
, pp.
383
399
.
This content is only available via PDF.
You do not currently have access to this content.