A universal total anomalous dissipator

For all $\alpha \in (0,1)$, we construct an explicit divergence-free vector field $V\in L_t^{\mathrm{\infty }}{C}_x^{\alpha }\cap C_t^{\frac{\alpha }{1-\alpha }}{L}_x^{\mathrm{\infty }}$ so that the solutions to the drift-diffusion equations $${\mathrm{\partial }}_t{\theta }^{\kappa }-\kappa \mathrm{\Delta }{\theta }^{\kappa }+V\cdot \mathrm{\nabla }{\theta }^{\kappa }=0$$ exhibit asymptotic total dissipation for all mean-zero initial data: ${\lim }_{\kappa \to 0}\mathrm{\parallel }{\theta }^{\kappa }(1,\cdot ){\mathrm{\parallel }}_{L^2}=0$. Additionally, we give explicit rates in $\kappa$ and uniform dependence on initial data.