Thayer Watkins
Silicon Valley
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The Creation of Discrete Clouds

Sometimes clouds form a continuous layer but other times, as in the picture below, there are discrete clouds.

When there is a layer of lighter air lying under a layer of heavier air the lighter layer cannot just rise en masse because its place must be taken by other heavier air. What has to happen is that cells develop in which there is rising air around the center and falling air around the periphery.

This also happens when water is boiled in a pan. The water at the bottom of the pan gets hot enough to turn into steam. The steam rises from a multitude of cells. This phenomenon of thermal convection was first studied systematically and quantitatively by Henri Bé in France around 1900. Count Rumford had discovered thermal convection much earlier but only noted it on a qualitative level. James Thomson in 1882 noted the cellular structure and pattern of thermal convection between horizontal layers of fluids. He called the pattern a tesselated structure.

The following diagram depicts the crossection of the pattern that could be created. The pink figures represent the warmer, moister rising air and the cyan figures the descending cooler, drier air. This diagram has the cross section area of the rising air decreasing with altitude due to the erosion of the lighter parcel of air as it moves past the surrounding air. The cross section could increase as the rising air expands in volume at the lower pressures of higher altitudes.

The two dimensional picture of the process would look something like this:

In the atmosphere when the moist air rises it cools until it reaches a level where condensation of the water vapor occurs. This is where clouds form and it is notable that the relatively flat lower side of the clouds clearly shows where this process occurs. Here is the previous diagram with the formation of clouds depicted.

If the volume of rising moist air is not sufficient to cause the clouds to coalesce then there are discrete clouds. In the relatively dry areas of the western United States this discreteness of clouds is seen. In relatively moist areas the clouds amalgamate into one cloud layer.

(To be continued.)

Thermal Convection Between Horizontal
Layers of Fluids (The Bénard Problem)

After Henri Bénard introduced the scientific world to the empirical aspects of the cellular convection in fluids Lord Rayleigh in 1916 developed some analytical results. Rayleigh's analysis indicated that a thermally stratified liquid develops an instability leading to cellular convection based upon a nondimensional parameter

R = (g*αβ/(κν))h4

where g is the acceleration due to gravity, α is the coefficient of thermal expansion of the fluid, β is the temperature gradient (ΔT/Δz), κ the thermal conductivity of the fluid, ν the kinematic viscosity of the fluid and h the thickness of the layer. This parameter is now known as the Rayleigh number for the fluid. According to Rayleigh's analysis when R reaches a certain critical level cellular convection will develop. The critical level for R is approximately 1700.

(To be continued.)

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