Visualisation of the λ₂ criterion for the turbulent wake of a square cylinder at Re = 4000

Описание: This visualisation captures the λ₂ criterion for the turbulent wake of a square cylinder at Re = 4000, revealing vortex cores defined by local pressure minima (λ₂ less than 0). Compared to the λ₂ flow around a circular cylinder at Re = 4000, the sharp corners of the square geometry lock the separation points, generating a much wider and more energetic recirculation region with stronger trailing-edge vortices. The wake shows intensified vortex shedding from both leading and side edges, resulting in a complex interaction of multiple shear layers, earlier three-dimensional breakdown, and a more disordered turbulent state than the coherent, rhythmic shedding characteristic of a circular cylinder.

Compared to the corresponding Q-criterion visualisation, λ₂ provides a more focused view by filtering out shear-dominated artefacts from the sharp, separated shear layers at the corners. This results in a clearer distinction between the primary, coherent trailing vortices and the chaotic background turbulence, whereas Q tends to show a thicker, more diffuse vortical region. This sharper definition from λ₂ is especially critical around a square geometry, as it more accurately isolates the true rotational cores from the intense strain generated at the fixed separation points, offering a physically more meaningful map of the vortex dynamics driving the unsteady loads on the body.