fieldquasiperpendicular

Fieldquasiperpendicular is a coined term describing a relation between two vector or tensor fields in which the angle between the fields is approximately ninety degrees over a region or domain. It conveys a near-orthogonality that is not exact but bounded by a chosen tolerance.

Definition and criteria. Consider two vector fields F and G defined on a domain D with a metric. At a point x in D, the angle θ(x) between F(x) and G(x) satisfies cos θ(x) = (F(x) · G(x)) / (||F(x)|| ||G(x)||) whenever both norms are nonzero. The fields are said to be fieldquasiperpendicular on D with tolerance ε ∈ [0,1) if |cos θ(x)| ≤ ε for all x in D (uniform condition), or if an averaged or RMS version of |cos θ| remains below ε. In such cases the dot product F · G is small, while the magnitude of the cross product |F × G| tends toward |F||G| sin θ, which is near its maximum when θ is near 90 degrees.

Notes on interpretation. Fieldquasiperpendicular does not require a global alignment; regions of near orthogonality can vary across the domain. It is often used as a simplifying assumption in analytical or numerical treatments where coupling terms involving F · G are small or can be neglected within the chosen tolerance.

Examples and contexts. In electromagnetism, two field components that are nearly orthogonal in a region may justify decoupled or simplified models. In fluid or plasma contexts, alignment between velocity-type and vorticity-type fields may be described as fieldquasiperpendicular under certain flow conditions. The term is not widely standardized and appears primarily as a descriptive or heuristic label rather than a formal quantity in mainstream literature.