Wednesday, 26 June 2019

fluid dynamics - What does $(mathbf{u}cdotnabla)mathbf{u}$ mean in the Navier-Stokes equation?


I am studying the Navier-Stokes equations and I have the equation in the form: $$\rho \dfrac{\partial{\mathbf{u}}}{\partial{t}} + \rho (\mathbf{u}\cdot\nabla)\mathbf{u} - \mu\nabla^2\mathbf{u} + \nabla p = \rho f$$



Can someone explain me what does $ (\mathbf{u}\cdot\nabla)\mathbf{u}$ mathematically (generally) mean here?




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