Fluid Flow & Aerodynamics
why things fly, and why the usual explanation is wrong
Concept

Streaming — where it appears

A steady mean flow generated by an oscillation that has no mean of its own. It arises because the fluid is not in the same place on the two halves of the cycle, so a correlation between position and velocity survives the average.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

An oscillation with no mean, and the steady flow it drives. The steady second-order velocity through a Stokes layer, in units of U U′/ω. The first-order flow averages to zero at every height; the average of its own nonlinear term does not, and the pale curve is that forcing. Integrating it twice across the layer, with no slip at the wall and no stress at the top, gives a steady velocity that rises through the layer and settles at -0.749998 — Rayleigh's −3/4, which was not put in anywhere. Beyond about five layer thicknesses nothing more happens, which is why the number is a boundary condition for the flow outside.

An oscillation with somewhere to go

Shake a fluid back and forth over a body and it develops a steady circulation that never reverses. The driving flow has no mean at all; the mean of its own nonlinear term does, and integrating that twice across the oscillatory layer gives a slip velocity of exactly three-quarters of U dU/dx over the frequency.

viscous · Streaming Six orbits that do not close. One parcel's path under a linear deep-water wave of steepness 0.05, at a fifth of a wavelength down, released at the phase that centres the orbit on its release depth. Each loop returns almost to where it began and not quite.

A drift made of two things that average to zero

Stokes drift is usually explained as a parcel spending longer in the forward half of its orbit. That is true and it is not a formula. The formula is a correlation between a displacement and a gradient, each of which averages to exactly nothing, and it splits into two halves that are equal to twelve figures.

kinematics · Stokes drift

Named alongside it

The objects these essays reach for when they reach for this one.

AveragingAcousticsBoundary layerCorrelationDispersionEulerian and LagrangianMeasurementMemory kernelMixingModel validityNonlinearityRegime

All concepts