The Thermal Wind
The expected geostrophic balance in the interior fluid is expressed through the applicability of the thermal wind equations in local Cartesian coordinates $(x, y, z)$ are $$ f \frac{\partial v}{\partial z} = -\frac{g}{\rho_0} \frac{\partial \rho}{\partial x} $$ $$ f \frac{\partial u}{\partial z} = \frac{g}{\rho_0} \frac{\partial \rho}{\partial y} $$
ThermalWindExperiment

1 Wunsch, Carl. “A Time-Average Ocean: Thermal Wind and Flow Spirals.” Progress in Oceanography, vol. 221, 15 Jan. 2024, pp. 103206–103206, https://doi.org/10.1016/j.pocean.2024.103206. Accessed 23 Nov. 2024.

2 Marshall, John, and R. Alan Plumb. Atmosphere, Ocean, and Climate Dynamics: An Introductory Text. Boston, MA: Elsevier Academic Press, 2007. ISBN: 9780125586917.

3 DIYnamics. Affordable materials for geoscience teaching demonstrations. https://diynamics.github.io/pages/tips.html

4Brian Rose. Thermal Wind demo with ice bucket. https://www.youtube.com/watch?v=GFrZarxnMXE

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