Looking for billow clouds

First I wondered where that solitary cloud was going.

Then I noticed a longer ‘tail’ of similar clouds following it, looking vaguely like billow clouds.

Are they billow clouds?

Billow clouds are the product of a Kelvin-Helmholtz instability. If two fluids are flowing in parallel layers at different velocities, and have different densities, then the interface between them will always be unstable at short wavelengths.

More specifically, the interface develops small-scale motion that leads to a vortex street. At each point, a vortex is formed and moves away from the surface ā€“ a vortex street is this happening on a line of points. Here’s a simulation of a vortex street produced as a result of a fluid encountering, and then moving past, a stationary blunt object. The vortices begin to show from the 50-second mark. Notice how the instabilities build slowly but, after a point, quickly lead to a turbulent proliferation of vortices.

In smaller systems, like two different liquids moving through a pipe, the liquids’ surface tension will keep the instabilities from erupting into tiny waves. However, surface tension can’t help if the liquids’ relative velocity increases beyond a point ā€“ or when the fluids are two layers of air, or air and water vapour, and the system is as large as our atmosphere.

The Kelvin-Helmholtz instability describes the instability in two dimensions. In three dimensions, the underlying mathematics is more complicated, and the resulting phenomenon is called turbulence ā€“ like when wind blows over the surface of the sea, producing waves that break at the shore.

When air of different density and velocity moves over a cloud layer, it can destabilise the cloud-top to produce Kelvin-Helmholtz waves, like in the simulation below.

These clouds are called fluctus clouds. The World Meteorological Organisation website has a great photo. The clouds in the pictures I took aren’t as well-defined, although their tops do show signs of the sort of shear that induces the wavy shape.

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