Equations in Cartesian Coordinates

The velocity components are given by

$$u = {{\partial \phi} \over {\partial x}} = {{\partial \psi} \over {\partial y}}$$

$$v = {{\partial \phi} \over {\partial y}} = -{{\partial \psi} \over {\partial x}}$$ (4.67)

The Laplacian is given by,

$${{\partial^2 \phi} \over {\partial x^2}} + {{\partial^2 \phi} \o... ...rtial^2 \psi} \over {\partial x^2}} + {{\partial^2 \psi} \over {\partial y^2}}$$ (4.68)

(c) Aerospace, Mechanical & Mechatronic Engg. 2005
University of Sydney