1887
banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
The full text of this article is not currently available.
oa
Stratified spin-up in a sliced, square cylinder
Rent:
Rent this article for
Access full text Article
/content/aip/journal/pof2/26/2/10.1063/1.4864266
1.
1. H. P. Greenspan and L. N. Howard, “On a time-dependent motion of a rotating fluid,” J. Fluid Mech. 17, 385404 (1963).
http://dx.doi.org/10.1017/S0022112063001415
2.
2. E. R. Benton and A. Clark, “Spin-up,” Annu. Rev. Fluid Mech. 6, 257280 (1974).
http://dx.doi.org/10.1146/annurev.fl.06.010174.001353
3.
3. P. W. Duck and M. R. Foster, “Spin-up of homogeneous and stratified fluids,” Annu. Rev. Fluid Mech. 33, 231263 (2001).
http://dx.doi.org/10.1146/annurev.fluid.33.1.231
4.
4. K. Stewartson, “On almost rigid rotations,” J. Fluid Mech. 3, 1726 (1957).
http://dx.doi.org/10.1017/S0022112057000452
5.
5. G. Walin, “Some aspects of time-dependent motion of a stratified rotating fluid,” J. Fluid Mech. 36(2), 289307 (1969).
http://dx.doi.org/10.1017/S0022112069001662
6.
6. T. Sakurai, “Spin down problem of rotating stratified fluid in thermally insulated circular cylinders,” J. Fluid Mech. 37(4), 689699 (1969).
http://dx.doi.org/10.1017/S0022112069000814
7.
7. R. E. Hewitt, M. R. Foster, and P. A. Davies, “Spin-up of a two-layer rotating stratified fluid in a variable-depth container,” J. Fluid Mech. 438, 379407 (2001).
http://dx.doi.org/10.1017/S0022112001004645
8.
8. R. E. Hewitt, P. W. Duck, and M. R. Foster, “Steady boundary-layer solutions for a swirling stratified fluid in a rotating cone,” J. Fluid Mech. 384, 339374 (1999).
http://dx.doi.org/10.1017/S0022112099004255
9.
9. R. E. Hewitt, P. A. Davies, P. W. Duck, and M. R. Foster, “Spin-up of stratified rotating flows at large Schmidt number: experiment and theory,” J. Fluid Mech. 389, 169207 (1999).
http://dx.doi.org/10.1017/S0022112099004905
10.
10. J. Pedlosky and H. P. Greenspan, “A simple laboratory model for the oceanic circulation,” J. Fluid Mech. 27, 291304 (1967).
http://dx.doi.org/10.1017/S0022112067000321
11.
11. G. J. F. van Heijst, “Spin-up phenomena in non-axisymmetric containers,” J. Fluid Mech. 206, 171191 (1989).
http://dx.doi.org/10.1017/S0022112089002272
12.
12. G. J. F. van Heijst, P. A. Davies, and R. G. Davis, “Spin-up in a rectangular container,” Phys. Fluids A 2, 150159 (1990).
http://dx.doi.org/10.1063/1.857764
13.
13. G. J. F. van Heijst, L. R. M. Maas, and C. W. M. Williams, “The spin-up of fluid in a rectangular container with a sloping bottom,” J. Fluid Mech. 265, 125159 (1994).
http://dx.doi.org/10.1017/S0022112094000789
14.
14. M. R. Foster and R. J. Munro, “The linear spin-up of a stratified, rotating fluid in a square cylinder,” J. Fluid Mech. 712, 740 (2012).
http://dx.doi.org/10.1017/jfm.2012.402
15.
15. G. S. M. Spence, M. R. Foster, and P. A. Davies, “The transient response of a contained rotating stratified fluid to impulsive surface forcing,” J. Fluid Mech. 243, 3350 (1992).
http://dx.doi.org/10.1017/S0022112092002623
16.
16. R. J. Munro, M. R. Foster, and P. A. Davies, “Instabilities in the spin-up of a rotating, stratified fluid,” Phys. Fluids 22, 054108 (2010).
http://dx.doi.org/10.1063/1.3422554
17.
17. G. F. Carnevale, R. C. Kloosterziel, and G. J. F. van Heijst, “Propagation of barotropic vortices over topography in a rotating tank,” J. Fluid Mech. 233, 119139 (1991).
http://dx.doi.org/10.1017/S0022112091000411
18.
18. J. Pedlosky, Geophysical Fluid Dynamics (Springer, New York, 1982).
19.
19. P. Rhines, “Edge-, bottom-, and Rossby waves in a rotating stratified fluid,” Geophys. Fluid Dyn. 1, 273302 (1970).
http://dx.doi.org/10.1080/03091927009365776
20.
20. J. A. van de Konijnenberg and G. J. F. van Heijst, “Free-surface effects on spin-up in a rectangular tank,” J. Fluid Mech. 334, 189210 (1997).
http://dx.doi.org/10.1017/S0022112096004296
21.
21. J. A. van de Konijnenberg, J. B. Flor, and G. J. F. van Heijst, “Decaying quasi-two-dimensional viscous flow on a square domain,” Phys. Fluids 10(2), 595606 (1998).
http://dx.doi.org/10.1063/1.869586
22.
22. P. J. Davis, “Gamma function and related functions,” in Handbook of Mathematical Functions, edited by M. Abramowitz and I. Stegun (National Bureau of Standards, Washington, DC, 1954), pp. 258259.
http://aip.metastore.ingenta.com/content/aip/journal/pof2/26/2/10.1063/1.4864266
Loading
/content/aip/journal/pof2/26/2/10.1063/1.4864266
Loading

Data & Media loading...

Loading

Article metrics loading...

/content/aip/journal/pof2/26/2/10.1063/1.4864266
2014-02-18
2014-11-23

Abstract

We previously reported experimental and theoretical results on the linear spin-up of a linearly stratified, rotating fluid in a uniform-depth square cylinder [M. R. Foster and R. J. Munro, “The linear spin-up of a stratified, rotating fluid in a square cylinder,” J. Fluid Mech.712, 7–40 (2012)]. Here we extend that analysis to a “sliced” square cylinder, which has a base-plane inclined at a shallow angle α. Asymptotic results are derived that show the spin-up phase is achieved by a combination of the Ekman-layer eruptions (from the perimeter region of the cylinder's lid and base) and cross-slope-propagating stratified Rossby waves. The final, steady state limit for this spin-up phase is identical to that found previously for the uniform depth cylinder, but is reached somewhat more rapidly on a time scale of order −1/2Ω−1/log (α/ 1/2) (compared to −1/2Ω−1 for the uniform-depth cylinder), where Ω is the rotation rate and the Ekman number. Experiments were performed for Burger numbers, , between 0.4 and 16, and showed that for , the Rossby modes are severely damped, and it is only at small , and during the early stages, that the presence of these wave modes was evident. These observations are supported by the theory, which shows the damping factors increase with and are numerically large for .

Loading

Full text loading...

/deliver/fulltext/aip/journal/pof2/26/2/1.4864266.html;jsessionid=20krtd5doarb.x-aip-live-03?itemId=/content/aip/journal/pof2/26/2/10.1063/1.4864266&mimeType=html&fmt=ahah&containerItemId=content/aip/journal/pof2
true
true
This is a required field
Please enter a valid email address
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Stratified spin-up in a sliced, square cylinder
http://aip.metastore.ingenta.com/content/aip/journal/pof2/26/2/10.1063/1.4864266
10.1063/1.4864266
SEARCH_EXPAND_ITEM