Define the Rossby number. Under what conditions will a fluid flow be at (a) high and (b) low values of the Rossby number? Briefly describe both an oceanographic and a meteorological example of each type of flow.

Explain the concept of quasi-geostrophy for a thin layer of homogeneous fluid in a rapidly rotating system. Write down the quasi-geostrophic approximation for the vorticity in terms of the pressure, the fluid density and the rate of rotation. Define the potential vorticity and state the associated conservation law.

A broad current flows directly eastwards ( $+x$ direction) with uniform velocity $U$ across a flat ocean basin of depth $H$. The current encounters a low, two-dimensional ridge of width $L$ and height $H h(x)(0<x<L)$, whose axis is aligned in the north-south $(y)$ direction. Neglecting any effects of stratification and assuming a constant vertical rate of rotation $\frac{1}{2} f$, such that the Rossby number is small, determine the effect of the ridge on the current. Show that the direction of the current after it leaves the ridge is dependent on the cross-sectional area of the ridge, but not on the explicit form of $h(x)$.