Derive the vorticity-velocity formulation of the (mathrm{N}-mathrm{S}) equation and discuss the advantages and disadvantages of using this

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Derive the vorticity-velocity formulation of the \(\mathrm{N}-\mathrm{S}\) equation and discuss the advantages and disadvantages of using this formulation. Take the cross product of the NavierStokes equation and simplify the resulting equation using standard vector identities.

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