Computational modelling of turbulent velocity structures for an open channel flow using Karhunen-Loeve expansion

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–Lo´eve (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.