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Explain from a physical perspective and a mathematical one, how the material derivative defines to convective and transient acceleration in a velocity field. The material derivative is given by: \frac{D U}{D t}=\frac{\partial U}{\partial t}+u \frac{\partial U}{\partial x}+v \frac{\partial U}{\partial y} where U is the velocity vector, u the x-component of velocity, and v the y-component of velocity.

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