How do I determine the wavenumber of a Rossby wave with longitudinal width?

[kirovman]

Hi, I was wondering how to find the wavenumber of a Rossby wave?

The information I have so far is speed of the wave is c = &\overline{u} - \frac{\beta}{k^2 + l^2}}

where l and k are longitudinal/latitudinal wavenumbers, beta is df/dy and u is basic westward flow. I have determined the value of beta already.

What I want to know is, how can I determine the Rossby wavenumbers if I have a wave with longitudinal width. I believe I can discard one of the wavenumbers since the wave only propagates longitudinally.
But I am stuck trying to determine it. I think it is something like k = \frac{n \pi}{L} but it does not give me exactly the right answer. - it is about 2 - 5 times bigger than required for various questions.

 

[selfAdjoint]

Hi, I was wondering how to find the wavenumber of a Rossby wave?

The information I have so far is speed of the wave is c = &\overline{u} - \frac{\beta}{k^2 + l^2}}

where l and k are longitudinal/latitudinal wavenumbers, beta is df/dy and u is basic westward flow. I have determined the value of beta already.

What I want to know is, how can I determine the Rossby wavenumbers if I have a wave with longitudinal width. I believe I can discard one of the wavenumbers since the wave only propagates longitudinally.
But I am stuck trying to determine it. I think it is something like k = \frac{n \pi}{L} but it does not give me exactly the right answer. - it is about 2 - 5 times bigger than required for various questions.

As I understand it, the wave number varies due to meteorological causes. As your second formula states, there has always to be an integral number of waves circling the earth, but that number can change, and when it does, the velocity changes. Normally the waves advance, but for some wave numbers they can halt or even reverse.

 

[kirovman]

So for a wave at latitude 45 degrees, with 5 maxima around a circle of longitude, and latitudinal width 5000km, superimposed on u= 5 m/s, I have tried to determine the speed of the wave relative to the ground.

I used n= 5 (for 5 maxima), and L = 5000km. My value for beta is 1.6 x 10^-11.
This give me value for k = pi x 10^-6 and I set the other wavenumber (l) to zero.

This gives me 3.37 m/s, but apparently I am supposed to get -0.75 m/s.
Any advice? This is one of the few points driving me crazy before my next exam. Thanks.