Stropholysis: Spectral Insights and Transport Theory

The third-rank, fully symmetric tensor Q^*, termed stropholysis, was introduced by Kassinos as a descriptor of turbulence anisotropy for use in turbulence modeling, along with other structure tensors (Reynolds stress and dimensionality). Q^* measures symmetry breaking in turbulence statistics. It was found to be critical to predicting the rapid pressure--strain term in Reynolds transport models, as well as other quantities.

Despite its theoretical and modeling relevance, little is known about the behavior or transport of Q^* in general turbulent flows. A deeper understanding of Q^* will be useful for improving turbulence models.

To investigate its role, we analyze data from direct numerical simulations (DNS) and compute Q^* spectra under various flow conditions. Surprisingly, we observe that Q^* exhibits significant energy at low to intermediate wavenumbers even in flows with pure mean strain, where theory predicts it should vanish. This anomaly motivated us to derive the transport equation for Q^* under arbitrary mean velocity gradients, extending previous results limited to pure rotation.

The resulting equation reveals new production terms that explain the observed DNS behavior and establish the conditions under which Q^* becomes dynamically active. This formulation provides both physical insight and a foundation for incorporating stropholysis dynamics into one-point turbulence closures.