Point-forced Sverdrup–drag Green function ($\psi =-\frac{H}{2\pi r}{e}^{-\beta x/(2r)}{K}_0\left(\frac{\beta \sqrt{x^2+y^2}}{2r}\right)$)

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 $\sqrt{(r/\beta )|x|}$.