skip to main content

SciTech ConnectSciTech Connect

Title: Stratified spin-up in a sliced, square cylinder

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 E{sup −1/2}Ω{sup −1}/log (α/E{sup 1/2}) (compared to E{sup −1/2}Ω{sup −1} for the uniform-depth cylinder), where Ω is the rotation rate and E the Ekman number. Experiments were performed for Burger numbers, S, between 0.4 and 16, and showed that for S≳O(1), the Rossby modes are severely damped, and it is only at small S, and during the early stages, that the presence of these wave modes was evident. Thesemore » observations are supported by the theory, which shows the damping factors increase with S and are numerically large for S≳O(1)« less
Authors:
 [1] ;  [2]
  1. Faculty of Engineering, University of Nottingham, Nottingham NG7 2RD (United Kingdom)
  2. Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, New York 12180 (United States)
Publication Date:
OSTI Identifier:
22257091
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Fluids (1994); Journal Volume: 26; Journal Issue: 2; Other Information: (c) 2014 Author(s); Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ASYMPTOTIC SOLUTIONS; CYLINDERS; DAMPING; DEPTH; ERUPTION; FLUIDS; ROTATION; SPIN; STEADY-STATE CONDITIONS