Uniform Neumann control for strictly outward non-gradient flows

We prove uniform null controllability of an advection--diffusion equation with Neumann boundary conditions as the diffusion coefficient tends to zero. The drift is autonomous, belongs to $W^{2,\infty}$, points strictly outward on the boundary, and its backward flow carries a neighborhood of every point into the interior control region within a bounded time. For every sufficiently large control time, an $L^2$ control drives any $L^2$ initial state to zero with a norm bound independent of the diffusion coefficient. No gradient representation of the drift is required. A scalar function prescribed only through its boundary normal derivative leaves a tangential drift and a positive Robin coefficient in the adjoint equation. Two Carleman weights then cancel the uncontrolled tangential boundary terms. Their fixed-time observation estimate combines with the known flushing dissipation estimate to give the uniform control bound.