Scalar transport
= Scalar transport
<Scalar transport> follows a material quantity through <advection> and <diffusion equation> terms, for example $\Theta_t+\mathbf U\cdot\nabla\Theta=\kappa\Delta\Theta$. A <passive scalar> does not affect the <velocity field>; an <active scalar> feeds back through forces such as <buoyancy>. With <incompressible flow> bounded by impermeable walls and homogeneous <Neumann boundary conditions>, the spatial mean is conserved.