Concept

Wall law — where it appears

The statement that mean velocity near a wall depends only on distance from it, the wall stress and the fluid. That makes the profile universal in those units, gives the logarithmic layer, and is the assumption every wall model in a computation is built on.

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

And they are one piece of arithmetic. All three corrections against one over the logarithm of their own large parameter. Each is a straight line through the origin, with its own slope: one third exactly for the enstrophy range, near one for the wall layer, and near ln 10 for Oseen's per-decade measure. Three disappointments in three different fields, written up separately, are the same function.

The three that never converge

Oseen's drag coefficient, the overlap layer's power-law exponent and the enstrophy range's slope are three separate disappointments in three different fields. They are one piece of arithmetic, and the arithmetic says why none of them will ever be reached.

regimes · Crossover

The layer that grows from a change of surface. The internal boundary layer's height against distance downwind of a change in roughness, with the sublayer inside it that is genuinely in equilibrium with the new surface. The layer grows as the fetch to the four-fifths power and the equilibrium sublayer is a tenth of it.

How far downwind a surface is remembered

Walk from a field into a wood and the wind ten metres above your head is still the field's wind. It takes about a kilometre of trees before a ten-metre measurement is measuring the trees — a hundred times the height it is made at, and a great deal more than most masts are given.

turbulence · Roughness

Named alongside it

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

Measurement Regime Asymptotics Atmospheric Boundary layer Convergence Creeping flow Dimensionless Equilibrium Fetch Instrument Logarithm

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