Multiparticle dispersion in rotating-stratified turbulent flows

The transport of matter by turbulent flows plays an important role, in particular in a geophysical context. Here, we study the relative movement of groups of two (pairs) and four (tetrahedra) Lagrangian particles using direct numerical simulations of the stably stratified Boussinsesq equations, with Brunt-Väisälä frequency <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>N</a:mi></a:math> and Coriolis parameter <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mi>f</b:mi></b:math>. We cover regimes close to homogeneous isotropic turbulence, to flows dominated by stratification and rotation, keeping fixed the ratio <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:mi>N</c:mi><c:mo>/</c:mo><c:mi>f</c:mi><c:mo>=</c:mo><c:mn>5</c:mn></c:mrow></c:math>. The flows studied are anisotropic, so the relative motion between two particles depends not only on the initial separation between the particles, but also on their orientation with respect to the vertical axis. In all cases considered, we demonstrate that the relative particle motion differs depending on whether dispersion is considered forward or backward in time, although the asymmetry becomes less pronounced when stratification and rotation increase. On the other hand, the strong fluctuations in the dispersion between two particles become more extreme when <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mi>N</d:mi></d:math> and <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mi>f</e:mi></e:math> increase. We also find evidence for the formation of shear layers, which become more pronounced as <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:mi>N</f:mi></f:math> and <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mi>f</g:mi></g:math> become larger. Finally, we show that the irreversibility on the dispersion of a set of particles initially forming a regular tetrahedron becomes weaker when the influence of stratification and rotation increases, a property that we relate to that of the perceived rate-of-strain tensor.