Advection transports a quantity with a velocity field. For a scalar field , its local advective rate is , the spatial contribution to the material derivative. The same term transports the components of a vector field.
Chaotic advection is complicated, sensitive material motion generated by a smooth velocity field, often even when the Eulerian flow is periodic and simple. Transverse intersections of stable manifolds and unstable manifolds create stretching, folding and lobe transport across former separatrices. Incompressible flow preserves parcel area and advected scalar values in the absence of diffusion, so chaotic motion can create fine filaments without independently producing molecular homogenization.
A trajectory with a persistent random velocity has . An ensemble with finite velocity variance therefore has displacement variance , contrasting with the linear-in-time variance of diffusion. In an impulsively kicked sinusoidal shear dispersion model with zero transverse diffusivity, the shear phase never changes and repeated identical kicks have this ballistic scaling. Transverse diffusion instead decorrelates the velocity and permits a long-time diffusive limit.
Articles by others on the same topic
Advection is the transport of a substance or property by the bulk motion of a fluid. It primarily refers to the transfer of heat, moisture, or pollutants within a moving fluid, such as air or water. In meteorology, for example, advection plays a significant role in weather patterns as warm, moist air can be advected into a region, potentially leading to changes in temperature and humidity.