Question

give the expression for instantaneous velocity in terms of its rectangular components.

Answer 1

A four component decomposition of the local instantaneous velocity is proposed. It
brings out more readily the terms in the Navier-Stokes equations associated with
different events and fluid structures of turbulent flows than the classic two component
decomposition of Reynolds. In particular the new composition highlights the
existence of two types of Reynolds stresses: fast and slow. The fast Reynolds stresses
can be linked to a streaming process that describes the ejection of wall fluid in the
bursting process. It also provides a simple method for modelling the wall layer. The
four components are a long time average, a slow fluctuating component based on the
difference between the long term average and the smoothed phase velocity developed
by passing coherent structures, a fast fluctuating component which is periodic in
nature and a streaming component created by the interaction between the fast
fluctuations and the fluid viscous effects.
Key words: Velocity components, bursting, streaming flow, smoothed phase velocity,
fast and slow Reynolds stresses, wall layer