The pattern shown in these swirling clouds is known as a von Kármán vortex street, named after Theodore von Kármán. They occur when a more viscous fluid flows through water and encounters a cylindrical object, creating vortices in the flow. These structures were first noticed in the laboratory by fluid dynamicists. Study of these vortices is very important in the understanding of laminar and turbulent fluid flow; these control a wide variety of real-world phenomena, like the lift under an aircraft wing and Earth's weather.
In the photo, the Alejandro Selkirk Island, off the Chilean coast, is acting like the cylinder. A vortex street is shown disrupting a layer of stratocumulus clouds which are low enough to be affected by the island, which is nearly 1.6 km above sea level and 1.5 km in diameter. When the wind-driven clouds run into the obstacle of the island, they flow around it clockwise and anticlockwise to form the beautiful spinning eddies, advecting hundreds of kilometres downwind to make a street 10,000 times longer than those made in the laboratory.
A vortex street can be observed only over a given range of Reynolds numbers (Re), normally above a limiting Re value of about 90. The Reynolds number is a measure of the ratio of inertial to viscous forces in the flow of a fluid and may be defined as:
Re = Vd/v
d = the diameter of the cylinder around which the fluid is flowing.
V = the steady velocity of the flow upstream of the cylinder.
v = the kinematic viscosity of the fluid.
You can view a simple animation of the von Kármán vortex street here.