Talk:Rossby parameter

From Wikipedia, the free encyclopedia

WikiProject Meteorology
 This article related to meteorology and/or specific weather events is part of WikiProject Meteorology and Weather Events, an attempt to standardize and improve all articles related to weather or meteorology. You can help! Visit the project page or discuss an article at its talk page.
Stub This article has been rated as Stub-Class on the assessment scale.
Low This article has been rated as Low-importance within WikiProject Meteorology.

[edit] Equation Change

Per the following discussion posted at WP:RD/S (May 24, 2007):

More atmospheric physics for you! Our article on Rossby waves says that the wave speed is given by

c = u - \frac{\beta}{k^2+l^2}

where c is the wave speed, u is the mean westerly flow, β is the Rossby parameter, and k and l are the longitudinal and latitudinal wavenumbers. The Rossby parameter is given as

\beta = \frac{2\omega cos\phi}{a}

where φ is the latitude, ω is the angular speed of the Earth's rotation, and a is the mean radius of the Earth.

Given the above, I cannot see how c is anything other than tiny. Yet it is not.

For example, if I put in u = 3, k = 5, l = 3 and calculate ω for a latitude of 60 degrees, I get an answer of order 10 − 13, which is far too small.

I am surely misunderstanding something. Can someone check through this and see where I am going wrong? Many thanks, →Ollie (talk • contribs) 01:22, 24 May 2007 (UTC)


I agree with your assessment. Something must be awry! My understanding of the units in the problem suggest that β must be in units of velocity (meters/sec). However, because it is defined as ω / a = sec − 1 / meters, this does not work out. So, perhaps it ought to be defined as:
β = 2aωcosφ
This would make beta quite a bit larger (~1012x, which solves our issue quite nicely). I will try to find an alternative source for this equation which may verify my belief. Nimur 15:08, 24 May 2007 (UTC)
This lecture note seems to corroborate my belief that earth-radius should be multiplied, not divided. I will edit the articles in question. Nimur 15:16, 24 May 2007 (UTC)

End of copied discussion

Please discuss any issues below this line. Nimur 15:21, 24 May 2007 (UTC)

Yes, the radius a should be in the denominator, as traditionally defined. You can verify here:

http://amsglossary.allenpress.com/glossary/search?id=rossby-parameter1

Or any GFD texts would tell you the same thing.

Pkamostai (talk) 13:23, 20 December 2007 (UTC)

[edit] Equation

Is the current expression of the Rossby parameter really correct? The above equation

c = u - \frac{\beta}{k^2+l^2}

suggests β has a dimension [m − 1s − 1], since dimension of k is [m − 1] and c's is [ms − 1]. So the previous equation

\beta = \frac{2\omega cos\phi}{a}

seems correct to me.

Am I missing something? 210.174.33.192 19:12, 13 November 2007 (UTC)

Yes, the radius a should be in the denominator, as traditionally defined. You can verify here: http://amsglossary.allenpress.com/glossary/search?id=rossby-parameter1 Or any GFD texts would tell you the same thing. —Preceding unsigned comment added by Pkamostai (talk • contribs) 13:21, 20 December 2007 (UTC)

This was the source of confusion some time ago (see the above discussion). I will defer to your more recent edits since I'm not an expert in the field... Nimur (talk) 06:36, 22 December 2007 (UTC)