Abstract
This paper develops an analytical two-part covariance kernel from velocity correlations across a two-dimensional (vertical and flow directions) Particle Image Velocimetry (PIV) flow field. This will form the basis of a model of wave action in flood water that includes the underlying turbulence velocity field using Karhunen–Loéve (KL) expansion. The PIV data was from the supercritical flow area immediately upstream of an undular hydraulic jump. This paper derives a one-dimensional solution for the associated integral equations. It also discusses a relationship between the two parts of the kernel and the turbulent production and turbulent dissipation.
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