The Hammock Papers: Eddies.

01 August 2016

Eddies.

The phenomenon that is shown in the image of Guadalupe Island at the top of this page (acquired on August 20, 1999) features a ubiquitous occurrence in the motion of fluids—a vortex street, which is a linear chain of spiral eddies called von Karman vortices. Von Karman vortices are named after Theodore von Karman, who first described the phenomenon in the atmosphere. Dr. von Karman was a co-founder of NASA's Jet Propulsion Laboratory.

von Karman vortices form nearly everywhere that fluid flow is disturbed by an object. In the cloud images shown on this page, the "object" that is disturbing the fluid flow is an island or group of islands. As a prevailing wind encounters the island, the disturbance in the flow propagates downstream of the island in the form of a double row of vortices which alternate their direction of rotation. The animation below shows how a von Karman vortex street develops behind a cylinder moving through a fluid.

Both the ocean and atmosphere are fluids, in constant motion. On our limited “human”-scale, we are aware of this motion when we feel the wind blow, or when we encounter a current running along the beach while swimming. Yet our eyes alone can rarely observe the larger scale of fluid motion in the ocean and atmosphere.

Technical description: As a fluid particle flows toward the leading edge of a cylinder, the pressure on the particle rises from the free stream pressure to the stagnation pressure. The high fluid pressure near the leading edge impels flow about the cylinder as boundary layers develop about both sides. The high pressure is not sufficient to force the flow about the back of the cylinder at high Reynolds numbers. Near the widest section of the cylinder, the boundary layers separate from each side of the cylinder surface and form two shear layers that trail aft in the flow and bound the wake. Since the innermost portion of the shear layers, which is in contact with the cylinder, moves much more slowly than the outermost portion of the shear layers, which is in contact with the free flow, the shear layers roll into the near wake, where they fold on each other and coalesce into discrete swirling vortices. A regular pattern of vortices, called a vortex street, trails aft in the wake.

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WOLFGANG AMADEUS MOZART

"When I am, as it were, completely myself, entirely alone and of good cheer – say travelling in a carriage or walking after a good meal, or during the night when I cannot sleep – it is on such occasions that my ideas flow best and most abundantly. Whence, and how, they come I know not ; nor can I force them. Those ideas that please me I retain in memory and am accustomed, as I have been told, to hum them to myself. If I continue in this way, it soon occurs to me how I may turn this dainty morsel to account, so as to make a good dish of it. That is to say, agreeable to the rules of counterpoint, to the peculiarities of various instruments etc. All this fires my soul, and, provided I am not disturbed, my subject enlarges itself, becomes methodised, and defined, and the whole, though it be long, stands almost complete and finished in my mind, so that I can survey it like a fine picture or a beautiful statue at a glance. Nor do I hear in my imagination the parts successively, but I hear them, as it were, all at once. What a delight this is, I cannot tell."

MARCUS AURELIUS

"Is your cucumber bitter? Throw it away. Are there briars in your path? Turn aside. That is enough. Do not go on and say, 'Why were things of this sort ever brought into this world?' neither intolerable nor everlasting - if thou bearest in mind that it has its limits, and if thou addest nothing to it in imagination. Pain is either an evil to the body (then let the body say what it thinks of it!)-or to the soul. But it is in the power of the soul to maintain its own serenity and tranquility."

VINCENT van GOGH

"What am I in the eyes of most people? A nonentity or an oddity or a disagreeable person — someone who has and will have no position in society, in short a little lower than the lowest. Very well — assuming that everything is indeed like that, then through my work I’d like to show what there is in the heart of such an oddity, such a nobody. This is my ambition, which is based less on resentment than on love in spite of everything, based more on a feeling of serenity than on passion. Even though I’m often in a mess, inside me there’s still a calm, pure harmony and music. In the poorest little house, in the filthiest corner, I see paintings or drawings. And my mind turns in that direction as if with an irresistible urge. As time passes, other things are increasingly excluded, and the more they are the faster my eyes see the picturesque. Art demands persistent work, work in spite of everything, and unceasing observation."

DAN CAMPBELL