I'm looking @ convective accerlation term in http://en.wikipedia.org/wiki/Navier_stokes_equation#Convective_acceleration. I don't understand the terminology. If v is a vector, it says that [tex](\mathbf{v}\cdot\nabla)\mathbf{v}[/tex] can be written as [tex]\mathbf{v}\cdot\nabla \mathbf{v}[/tex]. I thought that [tex]\nabla \mathbf{v}[/tex] is the transpose of the Jacobian matrix for [tex]\mathbf{v}[/tex]. As I'm not familiar with the terminology it almost looks like ([tex]\mathbf{v} \cdot \nabla \mathbf{v}[/tex] = vector . matrix), which can't be right. However, it appears [tex](v\cdot\nabla)v[/tex] is a vector. Can somebody shed some light on how [tex]v\cdot\nabla v[/tex] is a vector? If [tex](\mathbf{v}\cdot\nabla)\mathbf{v}=\mathbf{v}\cdot\nabla \mathbf{v}[/tex] & [tex]\nabla \mathbf{v} = (\mathbf{J}\mathbf{v})^T[/tex]. I'm sure I'm mutilating the terminology, if anybody could shed light on this, much appreciated.(adsbygoogle = window.adsbygoogle || []).push({});

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# How to interpret advection (v.del) v->v.(del v)

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