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

Production — where it appears

The rate at which mean-flow energy is fed into turbulence, which is the Reynolds stress working against the mean strain. It is the source term in the turbulent kinetic energy budget, and it is balanced by dissipation only when the flow has had time to settle.

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

A normal stress the closure makes negative. The Boussinesq closure's first normal stress in a plane strain, against the strain measured in units of the turbulence's own time scale. It crosses zero at S k/eps = 1/(3 C_mu) = 3.704 — eleven per cent above the value the constant was calibrated at — and goes on falling. A variance below zero is not a small error; it is a statement that cannot be true.

The constant that makes a variance negative

Every engineering turbulence calculation in the world rests on one number, C-mu equals 0.09. It is not a property of turbulence. It is the assertion that a particular ratio is ten thirds, which is true in one flow — and eleven per cent above that flow the same closure reports a mean square below zero.

turbulence · Closure The production jumps and the dissipation does not. Production and dissipation against time, through a step change in the strain rate. The production follows the strain immediately — it is the strain squared times an eddy viscosity — and the dissipation moves by less than one per cent at the instant of the step, because it is set by a cascade that has not been told yet.

A dissipation that lags its production

Change the strain rate on a patch of turbulence and the production of energy follows instantly — it is the strain squared. The dissipation moves by less than one per cent, because it is the far end of a cascade that has not been told yet, and the two are out of balance by a factor of six for the next turnover.

turbulence · Dissipation

Named alongside it

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

ClosureDissipationEddy viscosityBoussinesqCalibrationCascadeEquilibriumMeasurementMemory kernelModel limitModel validityRealizability

All concepts