Calculating Geostrophic Flow and Pressure Gradient | Station J and K Example

[geojon]

Homework Statement

Station J is 100 km West of station K at 30^o N. The sea level difference between the two stations is +0.10m. What is the geostrophic flow between J and K, and what is it's direction? Specify and justify any assumptions you make.

Homework Equations

What is the pressure gradient between station J and K? Will this be needed to solve the problem.
When determining which direction it will flow (and we are in the northern hemisphere), do I need to consider that Coriolis acts perpendicular to the direction the parcel travels, along isobars? Or is it sort of intuitive that it will flow to the West?

The Attempt at a Solution

I am assuming a number of things: the horizontal velocities are much greater than the vertical, w<<u, v; the only external force is gravity; friction is very small.
Thus, there is a balance between Coriolis forces and horizontal pressure gradient.
Surface geostrophic currents are proportional to the slope of the topography.

Equation of Motion simplified for geostrophic flow is then: -fv = -(1/ro) * (dp/dx) ; fu = -(1/ro) * (dp/dy)

Geostrophic flow for W-E is then: u = -(g/f) * (dz/dx) ; f = 2(angularspeed)sin(30^o latitude)

u = -](9.81/7.27*10^-5)] * [(0.10m)/(100000m)] = -0.135

The direction of the flow, I think, is to the West. Working in a non-inertial reference frame sort of throws me off though. Do i need to consider Coriolis acting perpendicular to parcel travel direction?

 

[Chestermiller]

I haven't worked in this area for a long time, so my memory may not serve me well. But, since no one else has ventured an answer, here goes.

If I remember correctly, the effects of Coriolis forces are included in the geostrophic equations. And, also, if I remember correctly, the isobars of the pressure field coincide with the streamlines of the flow. So, in this case, shouldn't the flow velocity be in the NS direction? What are the units of your velocity?

Chet