While I've read "[Variational Inference with Normalizing Flows](https://arxiv.org/pdf/1505.05770.pdf)" ([abstract](https://arxiv.org/abs/1505.05770.pdf)), I don't understand about an intuition of Planar Flow.
The author defined Planar Flow as below

> 
> Let $\boldsymbol{w} \in \mathbb{R}^D, \boldsymbol{u} \in \mathbb{R}^D,
> > b \in \mathbb{R}$ and $h(\cdot)$ be a smooth element-wise
>  non-linearity.   
>  Then the following formula is Planar Flow
> 
> 
> $$\begin{array}{c} f(\mathbf{z}) = \mathbf{z} + \mathbf{u}h(\mathbf{w}^T\mathbf{z}+b) \\
> \psi(\mathbf{z})=h^{\prime}\left(\mathbf{w}^{\top} \mathbf{z}+b\right) \mathbf{w} \\ |\operatorname{det} \frac{\partial f}{\partial \mathbf{z}}|=| \operatorname{det}\left(\mathbf{I}+\mathbf{u} \psi(\mathbf{z})^{\top}\right)|=| 1+\mathbf{u}^{\top} \psi(\mathbf{z}) | \quad (1)\end{array}$$
> 
> 
> 

The author said that 

> 
> The flow defined by the transformation (1) modified the initial density $q\_0$ by applying a series of contractions and expansions in the direction perpendicular to the hyperplane $\mathbf{w}^T\mathbf{z}+b=0$.
> 
> 
> 

I couldn't understand that why the transformation (1) move the vector $\mathbf{z}$ along the direction perpendicular to the hyperplane $\mathbf{w}^T\mathbf{z}+b=0$.

 Would anybody elaborate this?