You have just completed your registration at OpenAire.
Before you can login to the site, you will need to activate your account.
An e-mail will be sent to you with the proper instructions.
Important!
Please note that this site is currently undergoing Beta testing.
Any new content you create is not guaranteed to be present to the final version
of the site upon release.
A linearly stratified fluid contained in a circular cylinder with a linearly-sloped base, whose axis is aligned with the rotation axis, is spun up from a rotation rate Ώ to Ώ + ΔΏ (with ΔΏ << Ώ ) by Rossby waves propagating across the container. Experimental results presented here, however, show that if the Burger number S is not small, then that spinup looks quite different from that reported by Pedlosky & Greenspan [J. Fluid Mech., vol. 27, 1967, pp. 291–304] for S = 0. That is particularly so if the Burger number is large, since the Rossby waves are then confined to a region of height S−1/2 above the sloped base. Axial vortices, ubiquitous features even at tiny Rossby numbers of spin-up in containers with vertical corners (see van Heijst et al. [Phys. Fluids A, vol. 2, 1990, pp. 150–159] and Munro & Foster [Phys. Fluids, vol. 26, 2014, article no. 026603], for example), are less prominent here, forming at locations that are not obvious a priori, but in the ‘western half’ of the container only, and confined to the bottom S−1/2 region. Both decay rates from friction at top and bottom walls and the propagation speed of the waves are found to increase with S as well. An asymptotic theory for Rossby numbers that are not too large shows good agreement with many features seen in the experiments. The full frequency spectrum and decay rates for these waves are discussed, again for large S, and vertical vortices are found to occur only for Rossby numbers comparable to E1/2, where E is the Ekman number. Symmetry anomalies in the observations are determined by analysis to be due to second-order corrections to the lower-wall boundary condition.
Rhines, P. 1970 Edge-, bottom-, and Rossby waves in a rotating stratified fluid. Geophys. Fluid Dyn. 1, 273-302.
Sneddon, I. N. 1960 On summing infinite series involving the zeros of Bessel functions of the first kind. Proc. Glasgow Math. Assoc. 4, 144-156.
Stewartson, K. 1957 On almost rigid rotations. J. Fluid Mech. 3, 17-26.
van de Konijnenberg, J. A., Naulin, V., Rasmussen, J. Juul, Stenum, B. & van Heijst, G. J. F. 2000 Linear spin-up in a sliced cylinder. Geophys. Astrophys. Fluid Dynamics 92, 85-114.
van Heijst, G. J. F. 1989 Spin-up phenomena in non-axisymmetric containers. J. Fluid Mech. 206, 171-191.
van Heijst, G. J. F., Davies, P. A. & Davis, R. G. 1990 Spin-up in a rectangular container. Phys. Fluids A 2, 150-159.
van Heijst, G. J. F., Maas, L. R. M. & Williams, C. W. M. 1994 The spin-up of fluid in a rectangular container with a sloping bottom. J. Fluid Mech. 265, 125-159.
Walin, G. 1969 Some aspects of time-dependent motion of a stratified rotating fluid. J. Fluid Mech. 36(2), 289-307.
Wedemeyer, E. H. 1964 The unsteady flow within a spinning cylinder. J. Fluid Mech. 20, 383-399.