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. Which one of the following orders is correct about the magnitudes of the geostrophic currents within the isolines?
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For geostrophic current strength, always compare \(\Delta h / \Delta x\). Larger sea surface slope → stronger geostrophic flow.
The problem involves determining the relative magnitudes of geostrophic currents between concentric isolines of sea surface height (SSH). Geostrophic currents arise due to the balance between the pressure gradient force and the Coriolis effect. The speed of a geostrophic current can be approximated using the formula: Geostrophic Velocity (V) = \( \frac{g}{f} \frac{\Delta h}{\Delta x} \) where:
\(g\) is the acceleration due to gravity.
\(f\) is the Coriolis parameter, which is dependent on latitude and the rotation of the Earth.
\(\Delta h\) is the change in sea surface height between isolines.
\(\Delta x\) is the distance between the isolines.
Given that all eddies are at the same latitude, \(f\) is constant for all, and we can focus on the ratio \(\frac{\Delta h}{\Delta x}\) to compare velocities:
1. **Eddy (i):** \(\frac{\Delta h_1}{dx_1}\)
2. **Eddy (ii):** \(\frac{\Delta h_2}{dx_2}\)
3. **Eddy (iii):** \(\frac{\Delta h_3}{dx_3}\) The order of magnitude of currents is determined by the steepness of the isolines (i.e., the larger the ratio, the stronger the current). Thus, we’re examining who has the largest ratio from \(\frac{\Delta h}{\Delta x}\). Given the choices and the correct answer (iii)>(ii)>(i), Eddy (iii) has the steepest gradient, followed by Eddy (ii), then Eddy (i). This logically arises from visually analyzing the figure or calculating based on given distances and SSH differences, showing the relative strengths of geostrophic currents.
