Question

Given an incompressible 2D flow with x and z velocity given by u= alpha*x and w= beta* z

A) how are alpha and beta related?
B) if the initial positions (t=0) are given by X and Z what are the fluid positions x,z in terms of X,Z,t?
C) sketch the x,z fluid element trajectory D) express the velocity field in lagrangian coordinates.

Answer 1

A) The alpha and beta are related because they both represent the space time of the flow in the two directions
B) In terms of X, Z, t, the fluid positions x,z are alpha*x and beta*z
C) and D) The velocity field can be expressed a <u,w>