A physical decomposition of the stress tensor for complex flows

Traditionally, the components of the stress with respect to a relevant coordinate system are used for the purpose of stress visualisation and interpretation. A case for using a flow dependent measure to interpret and visualise stress is made for two dimensional flow, together with a suggestion for extending the idea to three dimensions. The method is illustrated for Newtonian and Oldroyd B fluids in both the eccentrically rotating cylinder and flow past a cylinder benchmark problems. In the context of a generalised Newtonian fluid, the relation between the flow-dependent stress measure to other field variables under certain flow conditions, is examined and is indicative of its importance in complex flow.