For a kk, the angular wavenumber is k|k|, its Euclidean length. It measures spatial phase variation in radians per unit distance. In one dimension authors may instead use a signed wavenumber; the convention must be stated.

Frequency parameters

For eiκΦe^{i\kappa\Phi}, the local wavenumber is κΦ|\kappa|\,|\nabla\Phi|, not merely κ|\kappa|. If Φ\nabla\Phi changes along a flow, viscous damping changes even when the carrier parameter κ\kappa is fixed.