= Point-forced Sverdrup–drag Green function
{title2=$\psi=-\frac{H}{2\pi r}e^{-\beta x/(2r)}K_0\!\left(\frac{\beta\sqrt{x^2+y^2}}{2r}\right)$}
The unbounded constant-depth steady transport response to a unit point wind-curl source solves $r\nabla_h^2\psi+\beta\psi_x=H\delta(x)\delta(y)$ for $r,\beta>0$. An exponential substitution reduces it to a modified Helmholtz equation, yielding the expression shown in terms of the <Modified Bessel function of the second kind>. Its finite-level <streamfunction> contours are nearly circular near the source and stretched into a western wake far away. The wake width is of order $\sqrt{(r/\beta)|x|}$.
Back to article page
