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The Balanced Motion experiment develops three kinds of force balance: hydrostatic balance in the vertical, and geostrophic and cyclostrophic balance in the horizontal. It also introduces the Rossby number as a tool to determine whether geostrophic or cyclostrophic balance dominates in a given system.

Hydrostatic balance relates the pressure at a given surface to the weight of fluid above it.

p = \rho g (H - z)

Geostrophic balance is between the Coriolis force and the pressure gradient force, and dominates when centrifugal force is small.

2 \Omega v_\theta = g \frac{\partial h}{\partial r}

Cyclostrophic balance is between centrifugal force and the pressure gradient force, and dominates when the Coriolis force is small.

\frac{v_\theta^2}{r} = g \frac{\partial h}{\partial r}

Whether geostrophic or cyclostrophic balance is a better approximation is determined by the Rossby number, which is simply the ratio of centrifugal to Coriolis forces in a system.

R_O = \frac{|V_\theta|}{2 \Omega r}

Tank Experiment

Two rotating tank experiments were set up. Tank rotation speed was the important parameter varied: one tank rotated at a speed of 1 

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