Einstein's summation notation

A special notation for writing vector equations using the scalar components of vectors rather than the vectors themselves.

This notation has found widespread use in the study of atmospheric turbulence, where the many vector and tensor components of a governing equation can be concisely represented by a much smaller number of terms. The key to this notation is the use of indices (subscripts) i, j, and k, which can each take on the values of 1, 2, or 3 to represent the three Cartesian directions (x, y, z).
See also alternating unit tensor.
Stull, R. B. 1988. An Introduction to Boundary Layer Meteorology. 57–63.

1. The study of the physics, chemistry, and dynamics of the earth's atmosphere, including the related effects at the air–earth boundary over both land and the oceans. Fundamental topics include the composition, structure, and motion of the atmosphere. The goals ascribed to meteorology are the complete understanding and accurate prediction of atmospheric phenomena.