I am reading a paper, and I see someone decompose a divergence operator as follows. Could someone judge and see if it is correct?
$\nabla \cdot {\bf{v}} = \left( {{\bf{n}} \cdot \nabla } \right){v_n} + {\nabla _\parallel } \cdot {{\bf{v}}_t}$
Notation: $\bf{v}$ is velocity vector field, and $n$ means normal, $t$ is tangent component.
I do not understand why ${\bf{v}}_t$ is a vector and $v_n$ is not.