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hamilbr · Jun 26, 2013, 11:33 AM

Hello everyone,
I am having some problems with a question about the coriolis acceleration in a particular region. Attached is an image showing velocity measurements going in a circular motion at the surface of the ocean. A to B is 200 km and the fastest velocity is .5 m/s. The center is located at 30 degrees N. I am asked to make vectors of coriolis acceleration at the small circles, which I am assuming would go to the right of each one. I am also asked to sketch the magnitude of the coriolis acceleration as a function of x along the line from A to B. X is the distance from the center of the figure along the line AB. It is also asked to sketch the x (eastward) and y (northward) component of the coriolis acceleration. I am really stumped on these last two things and any info would be greatly appreciated. Thanks

ebaines · Jun 26, 2013, 12:41 PM

The figure is a bit hard to understand, so please clarify something: do the arrows signify that a particle starting near the center slowly spirals outward? Or is this intended to show concentric circles? I assume the former, because coriolis acceleration requires movement in the radial direction.

The amount of coriolis acceleration is:

$<br /> a_c = -2 v_r \omega$

where $v_r$ is velocity in the radial direction and $\omega$ is rotational velocity in radians/second. The direction of the coriolis acceleration as the particles spiral outward is in the direction opposite of rotation. The tricky part here is that the rotational velocity is equal to

$\omega = \frac v r$

So you need to estimate the relative magnitude of $\omega$ based on the ratio of the tangential velocity (as signified by the length of the arrows) to the distance from the center. As for $v_r$ - you can assume that its magnitude is bigger where the current is fast, as that would cause the particle to gain distance from the center quicker.