The flow field for an atmospheric flow is given by [vec{V}=-frac{K y}{2 pileft(x^{2}+y^{2} ight)} hat{i}+frac{K x}{2 pileft(x^{2}+y^{2}

The flow field for an atmospheric flow is given by

\[\vec{V}=-\frac{K y}{2 \pi\left(x^{2}+y^{2}\right)} \hat{i}+\frac{K x}{2 \pi\left(x^{2}+y^{2}\right)} \hat{j}\]

where \(K=10^{5} \mathrm{~m}^{2} / \mathrm{s}\), and the \(x\) and \(y\) coordinates are parallel to the local latitude and longitude. Plot the velocity magnitude along the \(x\) axis, along the \(y\) axis, and along the line \(y=x\), and discuss the velocity direction with respect to these three axes. For each plot use a range \(x\) or \(y=-1 \mathrm{~km}\) to \(1 \mathrm{~km}\), excluding \(|x|\) or \(|y|<100 \mathrm{~m}\). Find the equation for the streamlines and sketch several of them. What does this flow field model?