The Gulf Stream flows northward off the Florida coast, so tends to be deflected eastward. This causes the water level to rise on the eastern side, since the more stationary Atlantic waters cannot easily be moved aside. The higher waters on the eastern side provide the higher pressures needed to counteract the Coriolis force, so the stream is relatively undeflected. Looking northward, the stream looks as shown in Figure 9.23, with a greatly exaggerated eastern rise. Using a thin vertical slice of water and balancing the pressure and Coriolis forces upon it on the left and right, find an expression for the slope \(d y / d x\) of the surface in terms of the earth's angular velocity \(\omega\), the latitude \(\lambda\), the acceleration of gravity \(g\), and the stream velocity \(v\). The westernmost islands of the Bahamas are only about \(80 \mathrm{~km}\) from the east coast of Florida. Between them the Gulf Stream flows somewhat in excess of \(1 \mathrm{~m} / \mathrm{s}\), and the sea level is about \(0.5 \mathrm{~m}\) higher at the Bahamas. Are these measurements consistent with your results?

Data from Figure 9.23

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