momentumtransport

Momentum transport is the transfer of momentum within a fluid, gas, or plasma due to a combination of molecular diffusion, advection, and, in turbulent flows, fluctuating motions. It governs how momentum is redistributed by velocity gradients, external forces, and internal stresses, and it is central to the dynamics described by the Navier–Stokes equations.

In Newtonian fluids, momentum transport is described by the viscous stress tensor. The viscous part of the stress is τ = μ(∇u + ∇u^T) − (2/3)μ(∇·u)I, where μ is the dynamic viscosity and u is the velocity field. The momentum equation can be written as ∂(ρu)/∂t + ∇·(ρu u) = −∇p + ∇·τ + f, with density ρ, pressure p, and body forces f. This formulation shows how viscosity damps velocity gradients and transfers momentum between fluid layers.

In turbulent flows, momentum transport is enhanced by Reynolds stresses arising from velocity fluctuations. Averaging the equations introduces a term −∇·(ρ u' u'), which acts as an effective diffusivity of momentum. Turbulent transport is often modeled with eddy viscosity concepts, using models such as k-ε or k-ω to close the equations and estimate enhanced momentum diffusion.

In plasmas, momentum transport can be significantly anisotropic due to magnetic fields. Viscosity becomes direction dependent (Braginskii viscosity), and cross-field transport is strongly influenced by magnetic geometry and turbulence. Collisions, magnetic drifts, and instabilities together determine the net transport of momentum.

Applications span engineering (pipes, turbines, aerodynamics), geophysical flows (oceanic and atmospheric dynamics), astrophysics (accretion disks), and controlled fusion (tokamaks), where momentum transport shapes flow profiles, rotation, and confinement.