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Three Coins in a Fountain, and Some Salty Finger Problems

We are, all of us, in a certain sense enjoying a steady flow of research reports about fluids. Here are two of the newest items:

“Three coins in a fountain ,” H. K. Moffatt,  Journal of Fluid Mechanics , Volume 720 , April 2013, pp 1 – 4. [doi: 10.1017/jfm.2013.55] (Thanks to investigator Tom Gill for bringing this to our attention.) The author, at the University of Cambridge, writes:

“If, in a large expanse of fluid such as air or water, an object that is heavier than the fluid displaced is released from rest, it descends in a manner that can depend in a complex way on its geometry and density (relative to that of the fluid), and on the fluid viscosity, which, as in other fluid contexts, remains important no matter how small this viscosity may be. A major numerical attack on this problem for the case in which the object is a thin circular disc is presented by Auguste, Magnaudet Fabre (J. Fluid Mech., vol. 719, 2013, pp. 388–405).”

and

Finger puzzles,” R. W. Schmitt, Journal of Fluid Mechanics, Volume 692, February 2012, pp 1-4. The author, at Woods Hole Oceanographic Institution, reports:

“Salt fingers are a form of double-diffusive convection that can occur in a wide variety of fluid systems, ranging from stellar interiors and oceans to magma chambers. Their amplitude has long been difficult to quantify, and a variety of mechanisms have been proposed. Radko & Smith (J. Fluid Mech., this issue, vol. 692, 2012, pp. 5–27) have developed a new theory that balances the basic growth rate with that of secondary instabilities that act on the finite amplitude fingers. Their approach promises a way forward for computationally challenging systems with vastly different scales of decay for momentum, heat and dissolved substances.”

Improbable Research