TKE

Turbulent kinetic energy, commonly abbreviated as TKE and denoted by k in many models, is a scalar quantity used to characterize the intensity of turbulence in a fluid flow. It represents the mean kinetic energy per unit mass associated with velocity fluctuations around a flow’s mean motion. In Reynolds decomposition, a velocity component is written as u = U + u', where U is the temporal or spatial mean and u' is the fluctuating part. The TKE is defined as k = 1/2 ⟨u'_i u'_i⟩, with summation over the three spatial directions and ⟨·⟩ denoting a time, ensemble, or spatial average.

Physical interpretation and budget: TKE is governed by a balance among production, dissipation, and transport. In a statistically steady flow, its evolution can be written as dk/dt = P − ε + T, where P is the production of TKE from mean shear, ε is the rate at which TKE is converted into heat by viscous effects, and T encompasses turbulent and viscous transport. Production arises from velocity gradients in the mean flow, while dissipation increases with viscosity and the small-scale structure of the turbulence.

Measurement and modeling: In experiments, TKE is inferred from measurements of velocity fluctuations using hot-wire anemometry, laser Doppler velocimetry, or particle image velocimetry. In simulations, DNS resolves all scales of motion to compute k directly; LES resolves large scales while modeling subgrid contributions to k. TKE serves as a fundamental variable in many turbulence models, such as the k-ε and k-ω families, and informs predictions of mixing, transport, and energy cascades in engineering, atmospheric, oceanic, and combustion contexts.

See also: turbulence, Reynolds-averaged Navier–Stokes equations, turbulence models.