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Vector-fields are vector valued functions which define a vector at each point in space. Examples of the vector field include the electric field and the velocity of a fluid.

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Derivation of vorticity equation (incompressible flow)

In the following derivation of the vorticity equation, I do not understand how $\nabla \cdot v=0$ implies $\frac{1}{\rho^2}\nabla \rho \times \nabla p=0$. We start with the Euler equation $$\frac{\par …