Additional Materials


Generation and destruction of the vortex ring

Numerically generated movie downloaded from

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Ship waves

Boat goes across the lake generating ship-wave Kelvin pattern. HD movie.

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Water drop, jet and ripples

Slow motion shot of a single drop of water splashing. Shot with a high speed camera at 1000 frames per second. 

This serves as an illustration to the Exercises 1.15 and 3.3. In particular, one can see that the distance between circles decreases with the radius as it must be for capillary waves. One also ultimately sees a quiescent circle that expans with the minimal group velocity v*.

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Jet shooting up

Slow motion video of jet shooting up after water drop. Illustrate Exercise 1.15. One can also distinguish a second small bump of fluid formed after the last drop falls.

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Yet another cumulative jet

Football free kick using Magnus force

Roberto Carlos free kick using full power of the Magnus force


Magic of water waves

Water surface filmed by the camera mounted about a hundred meters above facing the shore.

Phographer Albert Delamour

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Creating half of a vortex ring in a pool

See cool video at YouTube

Darwin drift

On fluid displacement upon the passage of a body see also the webpage on Darwin drift.

Reversibility of laminar mixing



Modern Fluid Mechanics (lecture notes)

Short course (5 lectures) taught in Lyon and Moscow in October-December 2010

Tidal bore on the River Severn (hydraulic jump)

Kelvin and Mach ship patterns

Kelvin ship pattern, as shown in the picture, can be observed only when the ship speed V is less than the speed of the boat-length wave U(L)=(gL)1/2. Since an object cannot effectively excite waves much longer than its size, then at V>>U the ship pattern looks more like a Mach like cone with the angle being arcsinus of U/L. In other words, U effectively plays the role of  maximal speed of perturbations i.e. sound speed - see

Colour figure 2.6 - three smoke jets

Frame-by-frame images of droplet falling into milk

At this link one finds frame-by-frame images of droplet falling into milk, where one can see subsequently:  propagation of a shock on a surface and creation of a crown, appearance of a crater, refilling the crater and shooting out the first column, the collapse of the column and shooting the secondary column, the secondary splash.

Alternative derivation of the Kelvin ship pattern

Русская версия книги "Современная Гидродинамика"

Современная Гидродинамика Краткий курс

Flow past a wing

As mentioned in Sect 1.5.4, fluid elements, separated by a wing, do not meet at the trailing edge. One can see that this is indeed so in the photograph (taken from here). The explanation can be found in the Q&A Flow past a wing.

Purcell swimmer

Theory pf Purcell swimmer (PDF)

Slow-motion video of droplets colliding with cumulative jets