Computational and Applied Mathematics seminar

Abstract: Regularisation of turbulent flows is essential for computationally efficient forecasting. In this talk, we highlight a geometric mechanism for regularising two-dimensional turbulence that preserves key conserved quantities. We begin with a high-level introduction to how energy is distributed across scales in turbulent flows, using energy spectra to quantify turbulence intensity and to illustrate energy cascades that govern flow evolution. We then discuss the conserved quantities unique to two-dimensional turbulence and how they give rise to the inverse energy cascade. This sets the stage for recent results on geometric regularisation, which allows for control over the energy distribution to enable reduced-complexity computations while retaining fundamental invariants and the inverse energy cascade.