where ∇ ∇ 4 is the 2D biharmonic operator and ν ν is the kinematic viscosity, ν ν = μ μ p . We can also express this compactly using the Jacobian determinant : ∂ ∂ ∂ ∂ t ( ∇ ∇ 2 ψ ψ ) + ∂ ∂ ( ψ ψ , ∇ ∇ 2 ψ ψ ) ∂ ∂ ( y , x ) = ν ν ∇ ∇ 4 ψ ψ .