= Solution
{c}
Along $y=0$, differentiating the approximate <streamfunction> gives
$$
v(x)\simeq A\gamma\left[\lambda L e^{-\lambda x}-e^{\gamma(x-L)}\right]
\simeq\frac{F_0}\beta\left[1-\frac L{\delta_W}e^{-x/\delta_W}\right]
$$
in the leading small-friction limit. Hence the <velocity> is strongly southward at the west wall, crosses zero after a few <Stommel boundary layer> widths, and approaches a much weaker northward interior value $F_0/\beta$. The leading zero is $x\simeq\delta_W\ln(L/\delta_W)$ when $L/\delta_W\gg1$.
For plotting or finite-friction evaluation, use the exact derivative
$$
\boxed{v(x)=A\left[\lambda C_W e^{-\lambda x}-\gamma C_E e^{\gamma(x-L)}\right].}
$$
It increases monotonically from its negative western value to its positive eastern value because $v'(x)=-A[\lambda^2C_W e^{-\lambda x}+\gamma^2C_E e^{\gamma(x-L)}]>0$. Moreover $\int_0^L v(x)\,dx=\Psi(L)-\Psi(0)=0$, as required for a closed basin.
\Image[/past-exam-of-the-physics-of-atmospheres-and-oceans-course-of-the-university-of-oxford/2021-pluto-meridional-velocity.png]
{title=Equatorial northward <velocity> profile: exact linear-drag solution and leading <Stommel boundary layer> approximation}
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