  We investigate a reaction-diffusion-advection equation of the form
$u_t-u_{xx}+\beta u_x=f(u)$ $(t>0,\,0<x<h(t))$ with mixed boundary condition at
$x=0$ and a free boundary condition at $x=h(t)$. Such a model may be applied to
describe the dynamical process of a new or invasive species adopting a
combination of random movement and advection upward or downward along the
resource gradient, with the free boundary representing the expanding front. The
goal of this paper is to understand the effect of advection environment and no
flux across the left boundary on the dynamics of this species. When
$|\beta|<c_0$, we first derive the spreading-vanishing dichotomy and sharp
threshold for spreading and vanishing. Then provide a much sharper estimate for
the spreading speed of $h(t)$ and the uniform convergence of $u(t,x)$ when
spreading happens. For the case $|\beta|\geq c_0$, some results concerning
spreading, virtual spreading, vanishing and virtual vanishing are obtained.
Where $c_0$ is the minimal speed of traveling waves of the differential
equation.
