Visualizing High-Order Symmetric Tensor Field Structure with Differential Operators

Table 3

Lamb tensor components.

	Source	Vortex	Saddle	Helix	Spiral
𝐿𝑥𝑥𝑥	𝑥𝑦^2	3𝑥𝑦^2	−𝑥𝑦^2	3𝑥𝑦^2	—
𝐿𝑥𝑥𝑦	−𝑥^2𝑦	−3𝑥^2𝑦	𝑥^2𝑦	−𝑦−3𝑥^2𝑦	—
𝐿𝑥𝑥𝑧	0	0	0	−2𝑥𝑦	0
𝐿𝑥𝑦𝑥	𝑦^3	−3𝑥^2𝑦	−𝑥^2𝑦	−3𝑥^𝑦	—
𝐿𝑥𝑦𝑦	−𝑥𝑦^2	3𝑥^3	𝑥^3	𝑥+3𝑥^3	—
𝐿𝑥𝑦𝑧	0	0	0	2𝑥^2	0
𝐿𝑥𝑧𝑥	0	0	0	−3𝑥𝑦	0
𝐿𝑥𝑧𝑦	0	0	0	1+3𝑥^2	0
𝐿𝑥𝑧𝑧	0	0	0	2𝑥	0
𝐿𝑦𝑥𝑥	−𝑥^2𝑦	3𝑦^3	𝑦^3	𝑦+3𝑦^3	—
𝐿𝑦𝑥𝑦	𝑥^3	−3𝑥𝑦^2	−𝑥𝑦^2	−3𝑥𝑦^2	—
𝐿𝑦𝑥𝑧	0	0	0	−2𝑦^2	0
𝐿𝑦𝑦𝑥	−𝑥𝑦^2	−3𝑥𝑦^2	𝑥𝑦^2	−𝑥−3𝑥𝑦^2	—
𝐿𝑦𝑦𝑦	𝑥^2𝑦	3𝑥^2𝑦	−𝑥^2𝑦	3𝑥^2𝑦	—
𝐿𝑦𝑦𝑧	0	0	0	2𝑥𝑦	0
𝐿𝑦𝑧𝑥	0	0	0	−1−3𝑦^2	0
𝐿𝑦𝑧𝑦	0	0	0	3𝑥𝑦	0
𝐿𝑦𝑧𝑧	0	0	0	2𝑦	0
𝐿𝑧𝑥𝑥	0	0	0	−𝑥𝑦	0
𝐿𝑧𝑥𝑦	0	0	0	−𝑦^2	0
𝐿𝑧𝑥𝑧	0	0	0	0	0
𝐿𝑧𝑦𝑥	0	0	0	𝑥^2	0
𝐿𝑧𝑦𝑦	0	0	0	𝑥𝑦	0
𝐿𝑧𝑦𝑧	0	0	0	0	0
𝐿𝑧𝑧𝑥	0	0	0	𝑥	0
𝐿𝑧𝑧𝑦	0	0	0	𝑦	0
𝐿𝑧𝑧𝑧	0	0	0	0	0