tangentialflow

Tangentialflow is a term used in the study of motion constrained to a surface or manifold. It refers to the tangential component of a velocity or flow field—that is, the part that lies in the tangent plane of the reference surface—as distinct from any normal component that points away from the surface. In practical modeling, tangentialflow describes how features move along the surface without penetrating it.

Mathematically, let S be a smooth surface in R^3 with unit normal n. Any velocity field v can be decomposed into tangential and normal parts: v_t = v - (v·n)n. The tangential flow is described by the vector field v_t, and its integral curves remain on S if v is tangent to S. On a curved surface, tangentialflow can be analyzed using surface differential operators such as the surface gradient and the tangential divergence.

Applications include modeling particle transport on biological membranes, protein diffusion along cellular surfaces, liposome or droplet surface dynamics, and graphics processes that simulate motion constrained to a surface. It is also used in the study of constrained mechanical systems and in the discretization of surface-based fluids.

Terminology varies by field; some authors treat tangentialflow as synonymous with motion purely within a surface, while others use it as a descriptive term for the tangential component of a broader flow. The concept helps separate surface-bound dynamics from normal interactions, facilitating analysis of constrained systems.

Related topics:

- Tangential velocity

- Normal component

- Surface flow

- Boundary layer

- Vector field on manifolds