Lambda2

Lambda2, often written as λ2, is a vortex identification criterion used in fluid dynamics to detect coherent vortex structures in three-dimensional flows. It was introduced by Jeong and Hussain in 1995 as an objective method to extract vortical regions from velocity fields.

Definition and method: For a velocity field u, compute the velocity gradient ∇u and decompose it into the symmetric part S = (∇u + ∇u^T)/2 and the antisymmetric part Ω = (∇u − ∇u^T)/2. Form the tensor M = S^2 + Ω^2. The eigenvalues of M can be ordered λ1 ≤ λ2 ≤ λ3. A vortex core is identified where λ2 < 0. In practice, iso-surfaces of λ2 are plotted to visualize swirling structures, with negative values indicating a region where rotation dominates over shear.

Applications and interpretation: The λ2 criterion is widely used with data from experiments (such as PIV) and simulations to visualize and quantify vortices. It is valued for being relatively frame-invariant and for often yielding clear separation of vortical regions from shear-dominated areas. It is commonly used alongside or as an alternative to other criteria, such as the Q-criterion (Q = 0), to characterize complex flows.

Limitations and considerations: Reliable λ2 analysis requires accurate velocity gradients and sufficient spatial resolution. Noise, discretization errors, and insufficient data can affect the computed eigenvalues. Thresholding or smoothing may be employed, and results should be interpreted in light of data quality and the specific flow features of interest.

See also: Q-criterion, vorticity-based vortex identification methods.