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Category: Fluid Dynamics

Geopotential Height

Geopotential Height

In practice, most measurements of the atmosphere are made of pressure not elevation due to the variation in gravity at different elevations and  latitudes. The pressure contours of the atmosphere are defined by a geopotential height (i.e. a “gravity-corrected elevation”). To understand this mathematically, consider the equation for hydrostatic equilibrium: We can replace by invoking the Ideal Gas Law which can rearranged as This is a solvable ordinary differential equation, which has the measured height as a function of pressure. Here, defines the…

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Parabolic Free Surface

Parabolic Free Surface

Imagine a still pond at the edge of a forest. Make it a beautiful autumn day because that’s a nice thought. The surface is like smooth glass despite the rugged shape of the ground beneath it. This is because the surface of a fluid defines a zero potential height. Essentially the only forces acting on it are gravity and gravity is acting perpendicular to the surface. But what if you could include another force on the pond? How would the…

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Adventures in Your Kitchen Sink: Stream Thinning

Adventures in Your Kitchen Sink: Stream Thinning

Turn on your faucet. Go on, I’ll wait. Make sure you keep the speed of the water low enough that the water still appears clear (i.e. laminar). Now consider the diameter of the stream near the faucet and then closer to the basin. You should notice that the stream thins as it flows down into the sink. How strange! Stream thinning is not just a quirk of your sink! It is, in fact, a consequence of the very fundamental law…

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Ice Pump

Ice Pump

An Ice Pump is a thermohaline mechanism of varying the thickness of an ice shelf. Salt is rejected as water crystallizes so the remaining liquid is saltier. The saltier water is more dense (i.e. has negative buoyancy) and sinks The salty water will melt the ice sheet through contact with it at deeper depths because it has a lower melting point The freshwater melt from the ice shell will be less dense and rise to shallower regions where it will refreeze…

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Rossby Number

Rossby Number

The Rossby Number describes the importance of the rotation of the frame on the flow. It is the ratio of the inertial force (e.g. buoyancy) of the fluid to the Coriolis force imposed by rotation. A larger Rossby number will mean the flow’s behavior is less dependent on the rotation.   where describes the typical magnitude of the horizontal flow components, is the rotation rate, is the latitude of the fluid parcel on a sphere (e.g. Earth), f is the…

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