Strouhal number — where it appears
Named by 6 essays across 4 fields — each of them below, with the objects they name alongside it.
The street a steady calculation cannot draw
The alternating wake behind a cylinder is the most photographed structure in fluid mechanics, and a steady solution does not produce one. What can honestly be drawn instead is a model of it — and the model settles one thing exactly, which is the spacing.
A shock that will not stand still
A converged transonic solution puts the shock in a definite place. Over a band of conditions the real one sweeps back and forth across a fifth of the chord at a fixed frequency, and the period is set almost entirely by how nearly sonic the flow just behind it is — a quantity that is small, hard to compute, and multiplies everything.
A drop rings like a bell
Disturb a drop and it swings between a lemon and a lentil at a pitch set by its surface tension and its size, and it keeps swinging for dozens of cycles because water is nearly frictionless at that scale. The usual story has a falling raindrop's wake ringing it. The wake strikes several times too fast for the note the drop plays.
The follower beats in time with the wake, not the bird
A gliding bird can sit in its neighbour's upwash and stay there. A flapping bird's wake is a wave left in the air — the path its wingtip traced, rising and falling with every beat — and a bird behind gains only if its own wing is where that wave is when it arrives. The best timing is a rule with no aerodynamics in it: lag the bird ahead by the time the wake took to come, so that each wingtip retraces the path of the one before. Directly behind, the rule flips by half a beat, and it buys a smaller loss rather than a gain.
A street's spacing and speed state the drag of the body that shed it
Kármán's stability argument for the vortex street is the part everyone remembers. His momentum argument, written with Rubach a year later, is the part that matters: a control volume round a street needs nothing but the street's spacing and speed to give the drag of the body upstream, without a pressure on the body or a word about its shape. For a cylinder it gives 0.86 at the street's measured speed, against about 1.2 from a balance. And the arithmetic behind it says something else. Only about half the vorticity the separating layers feed in survives into the street, and the famous instability is far too slow to be what ends one.
A flapping plate has no best Strouhal number until it pays for drag
Fish, birds and bats of very different sizes all cruise with a tail or wing beat at a Strouhal number between 0.2 and 0.4, and the usual story credits the wake: a reverse vortex street that has one most-amplified frequency. Garrick's exact inviscid theory of 1936 gives something else. A plunging plate's efficiency has no peak: it falls from one at no flapping at all to a half at frantic flapping, for every amplitude. A best Strouhal number exists only once the plate has a body's drag to pay for, and it then lands in the right band with no wake instability in the argument.
Named alongside it
The objects these essays reach for when they reach for this one.
Model limitCirculationDrag coefficientPoint vortexSeparationVortex streetWakeBuffetControl volumeDampingDropFeedback