# Homework Help: Rossby Waves

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1. Nov 17, 2014

### geojon

1. The problem statement, all variables and given/known data
Consider a Rossby wave propagating in a homogeneous ocean with a water depth of 4,000m at 35o N latitude. If the wave length of this wave is 500km, is this a long or short Rossby wave?

2. Relevant equations
shortwaves: |kx-1| <<RD
longwaves: |kx-1| >> RD

kx is the x-component of the wave number, k. wavenumber = 2pie/λ
-kx = k

RD = Rossby Radius of Deformation = (gh)1/2 / ƒ
where ƒ is the Coriolis parameter.

3. The attempt at a solution
RD = Rossby Radius of Deformation = (gh)1/2 / ƒ = 2.38 x 106m. ƒ is in seconds-1, RD is in meters.

-kx = k = 2Pie / λ. = 1.26 x 10-5 rad m-1.

I want to compare |kx-1| to RD. How do I change my units for kx?? Because I cannot compare something in rad*m-1 to meters.

I think that I have to change the radians to a distance, using the earth's radius (6,371 km), at a latitude of 35o North. This is where I am stumped??

2. Nov 17, 2014

### Staff: Mentor

One radian on the earth = 1 earth radius in length right?