Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.

An Oscillatory Disturbance of Rigidly Rotating Fluid

W. W. Wood
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Vol. 293, No. 1433 (Jul. 26, 1966), pp. 181-212
Published by: Royal Society
Stable URL: http://www.jstor.org/stable/2415650
Page Count: 32
  • Read Online (Free)
  • Cite this Item
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
An Oscillatory Disturbance of Rigidly Rotating Fluid
Preview not available

Abstract

Periodic disturbances of rigidly rotating inviscid flow of suitable frequency are controlled by a hyperbolic equation (Görtler 1944). In a completely enclosed container, discontinuities of velocity or velocity gradient can result whose location is physically random. The effect of viscosity is here examined for a particular configuration. The inviscid solutions are confirmed as true approximations to the flow at high Reynolds number R, for cases in which the internal inviscid velocity (but not velocity gradient) is continuous. The internal discontinuities become layers of thickness O(R$^{-\frac{1}{3}}$) in which the shears are O(R$^\frac{1}{6}$). The extreme sensitivity of the pattern of internal shear layers to the container's dimensions remains. Provided R$^\frac{1}{6} \ll$ ln R, the rough location of the strongest shears is insensitive to cell dimensions. A minute height change causes the original layers to split into a large number of parallel layers, with the strongest shears on layers near the original, and with a decay as n$^{-\frac{2}{3}}$ on the nth singular surface numbered from the original.

Page Thumbnails

  • Thumbnail: Page 
181
    181
  • Thumbnail: Page 
182
    182
  • Thumbnail: Page 
183
    183
  • Thumbnail: Page 
184
    184
  • Thumbnail: Page 
185
    185
  • Thumbnail: Page 
186
    186
  • Thumbnail: Page 
187
    187
  • Thumbnail: Page 
188
    188
  • Thumbnail: Page 
189
    189
  • Thumbnail: Page 
190
    190
  • Thumbnail: Page 
191
    191
  • Thumbnail: Page 
192
    192
  • Thumbnail: Page 
193
    193
  • Thumbnail: Page 
194
    194
  • Thumbnail: Page 
195
    195
  • Thumbnail: Page 
196
    196
  • Thumbnail: Page 
197
    197
  • Thumbnail: Page 
198
    198
  • Thumbnail: Page 
199
    199
  • Thumbnail: Page 
200
    200
  • Thumbnail: Page 
201
    201
  • Thumbnail: Page 
202
    202
  • Thumbnail: Page 
203
    203
  • Thumbnail: Page 
204
    204
  • Thumbnail: Page 
205
    205
  • Thumbnail: Page 
206
    206
  • Thumbnail: Page 
207
    207
  • Thumbnail: Page 
208
    208
  • Thumbnail: Page 
209
    209
  • Thumbnail: Page 
210
    210
  • Thumbnail: Page 
211
    211
  • Thumbnail: Page 
212
    212