Derive the following form of the pressure Poisson equation shown in the book by Saffman (1993) on vortex dynamics:

\[abla^{2} p=ho(\tilde{W}: \tilde{W}-\tilde{E}: \tilde{E})\]

where \(\tilde{W}\) is the vorticity tensor and \(\tilde{E}\) is the rate-of-strain tensor. The symbol : indicates a double dot product of a tensor. This is defined, for example, in index notation as \(W_{i j} W_{i j}\). Double summation is implied with respect to both indices, and the resulting quantity is a scalar.