Question

The sea surface height concentric isolines (L1 and L2 in cm) and the distance between them (dx in km) for three different eddies at the same latitude are given in the figure below. (The figures are not to scale.) 

Which one of the following orders is correct about the magnitudes of the geostrophic currents within the isolines? 
 

• A. \( i>ii>iii \)
• B. \( ii>iii>i \)
• C. \( iii>ii>i \)
• D. \( iii>ii>i \)

Hint:

The geostrophic current strength increases with a greater pressure gradient (\( \Delta h \)) and a smaller distance between isolines (\( \Delta x \)).

Answer 1

The Correct Option is C

The geostrophic current is determined by the pressure gradient force and Coriolis force, which balance each other in the ocean. The equation for the geostrophic current \( V \) is given by: \[ V = \frac{g}{f} \times \frac{\Delta h}{\Delta x} \] where: - \( g \) is the acceleration due to gravity,
- \( f \) is the Coriolis parameter,
- \( \Delta h \) is the sea surface height difference between two isolines, and
- \( \Delta x \) is the distance between them.
Now, let's compare the three eddies:
1. Eddy (i): \( L1 = 20 \, {cm}, \, L2 = 30 \, {cm}, \, dx = 200 \, {km} \) The height difference \( \Delta h = 30 - 20 = 10 \, {cm} \) and \( dx = 200 \, {km} \). 
2. Eddy (ii):* \( L1 = 10 \, {cm}, \, L2 = 20 \, {cm}, \, dx = 300 \, {km} \) The height difference \( \Delta h = 20 - 10 = 10 \, {cm} \) and \( dx = 300 \, {km} \). 
3. Eddy (iii): \( L1 = 5 \, {cm}, \, L2 = 15 \, {cm}, \, dx = 100 \, {km} \) The height difference \( \Delta h = 15 - 5 = 10 \, {cm} \) and \( dx = 100 \, {km} \).
Looking at these, the current is proportional to the ratio \( \frac{\Delta h}{\Delta x} \):
- For eddy (i): \( \frac{10}{200} = 0.05 \, {cm/km} \)
- For eddy (ii): \( \frac{10}{300} = 0.033 \, {cm/km} \)
- For eddy (iii): \( \frac{10}{100} = 0.1 \, {cm/km} \)
Since the geostrophic current increases with \( \frac{\Delta h}{\Delta x} \), the order of the geostrophic currents is: \[ iii>ii>i \] 
Thus, the correct answer is (C) \( iii>ii>i \).