Coriolis acceleration at the surface of a region in the ocean

[hamilbr]

Homework Statement

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

 

[tiny-tim]

welcome to pf!

hello hamilbr! welcome to pf!

i don't understand how far you've got, and where you're stuck

what equation are you using for the definition of Coriolis force?

what result does it give you for a typical point (x,y) in the diagram?

 

[hamilbr]

coriolis acceleration at the ocean surface

Hi Tiny-tim,

I am assuming I use (2 omega V sin latitude) for coriolis acceleration. I am just confused about sketching the magnitude of the acceleration as a function of x along the line from A to B where y=0. Would that mean that I start at the center and go out to 100 Km since that would be the radius? I am sure I am thinking too much and it is probably a fairly simple sketch. All the info I was given is in that first post so I feel like I am missing something.

 

[tiny-tim]

hi hamilbr!

I am assuming I use (2 omega V sin latitude) for coriolis acceleration. I am just confused about sketching the magnitude of the acceleration as a function of x along the line from A to B where y=0. Would that mean that I start at the center and go out to 100 Km since that would be the radius?

let's see …

the velocity, V, from A to B is either due north or due south

so to get the graph of the magnitude of the coriolis acceleration from A to B, plot the value of 2ΩV|sinθ|, where θ is the angle between the Earth's axis and due north, along the y-axis, against distance from -100 to 100 along the x-axis

 

[Nickie]

I would like to provide some clarification and explanation on the concept of Coriolis acceleration in this scenario.

Firstly, Coriolis acceleration is a result of the Coriolis effect, which is a phenomenon caused by the Earth's rotation. This effect causes objects moving over the Earth's surface to experience a deflection in their path due to the difference in rotational speeds at different latitudes.

In this case, the velocity measurements going in a circular motion at the surface of the ocean suggest that the region is experiencing a circular motion, which is likely caused by a combination of factors such as wind patterns, ocean currents, and the Earth's rotation.

To calculate the Coriolis acceleration at the small circles, you would need to use the formula a = 2Ωv, where a is the Coriolis acceleration, Ω is the Earth's angular velocity (7.29 x 10^-5 rad/s), and v is the velocity of the water. The direction of the Coriolis acceleration will be perpendicular to the direction of the water's velocity, to the right in this case.

As for the sketching of the magnitude and components of the Coriolis acceleration, it is important to understand that the magnitude of the Coriolis acceleration is dependent on the velocity of the water, which varies along the line AB. Therefore, the magnitude of the Coriolis acceleration will also vary along this line.

To sketch the x and y components of the Coriolis acceleration, you can use trigonometric functions to determine the eastward and northward components at different points along the line AB. The x component will be maximum at point A and decrease as you move towards point B, while the y component will be zero at point A and increase as you move towards point B.

I hope this information helps you in your understanding of Coriolis acceleration in this scenario. If you need further assistance, please do not hesitate to ask. Keep up the good work!