flowját

Flowját is a theoretical construct used in fluid dynamics and systems analysis to describe the directional alignment between a velocity field and a specified gradient field, capturing how readily advective transport follows a scalar-gradient direction. In this framing, the local flowját at a point is defined as the cosine of the angle between the velocity vector v(x) and the gradient ∇φ(x) of a scalar field φ(x).

Mathematically, flowját(x) = (v · ∇φ) / (|v| |∇φ|) when both v and ∇φ are nonzero; its value lies in the interval [-1, 1], with +1 indicating perfect alignment, -1 indicating antiparallel orientation, and 0 indicating orthogonality. Global or domain-averaged flowját is obtained by taking a weighted mean of the local values over the region of interest, which yields a scalar measure of transport coherence for the system.

Flowját is used conceptually to assess how effectively a flow carries a scalar along a gradient, and it can be applied in microfluidic device design, environmental transport studies, and porous-media modeling. It is related to, but distinct from, related measures such as advection efficiency, gradient-following, and directional coherence indices.

Practical considerations include handling zero-gradient or zero-velocity zones, where flowját is undefined, and choosing an appropriate weighting for averaging. Computation typically relies on discretized field data from simulations or experiments, with noise mitigation via local smoothing.

Related concepts include gradient, flux, advection, diffusion, and vorticity.