In fluid mechanics, the Okubo–Weiss (OW) parameter, (normally denoted by "W") is a scalar quantity used to partition a two-dimensional flow field into regions dominated by rotation (vorticity) and regions dominated by deformation (strain). It is widely applied in geophysical fluid dynamics, particularly in the analysis of oceanic and atmospheric flows, where it serves as a diagnostic tool for identifying and characterizing coherent structures such as eddies. For a horizontally non-divergent flow in the ocean, the parameter is given by:
W = s n 2 + s s 2 − ω 2 {\displaystyle W=s_{n}^{2}+s_{s}^{2}-\omega ^{2}}
where:
s n {\displaystyle s_{n}} is the normal strain.
s s {\displaystyle s_{s}} is the shear strain.
ω {\displaystyle \omega } is the relative vorticity. OW is widely used in the fields of Meteorology and Oceanography to identify regions of strong vorticity within atmospheric and oceanic flows. It is often employed as a tracer for cyclonic development because it is generally less "noisy" than relative vorticity alone. The Okubo-Weiss parameter quantifies the balance between rotational and deformational components of the flow: positive values indicate that deformation dominated, while negative values indicate that rotation is dominant.
Derivation Let u → ( x → ; t 0 ) = ( u , v ) ( x , y ; t 0 ) {\displaystyle {\vec {u}}({\vec {x}};t_{0})=(u,v)(x,y;t_{0})} be a two-dimensional velocity field at an instant in time, t = t 0 {\displaystyle t=t_{0}} . If x → = x → 0 {\displaystyle {\vec {x}}={\vec {x}}_{0}} is a non-singular point in the flow then it is possible to write down a Taylor series approximation
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