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Single-particle Lagrangian statistics from direct numerical simulations of rotating-stratified turbulence

Abstract:

Geophysical fluid flows are predominantly turbulent and often strongly affected by the Earth's rotation, as well as by stable density stratification. Using direct numerical simulations of forced Boussinesq equations, we study the influence of these effects on the motion of fluid particles. We perform a detailed study of Lagrangian statistics of acceleration, velocity, and related quantities, focusing on cases where the frequencies associated with rotation and stratification (RaS), f and N, respectively, are held at a fixed ratio N/f=5. The simulations are performed in a periodic domain, at Reynolds number Re≈4000, and Froude number Fr in the range 0.03Fr0.2 (with Rossby number Ro=5Fr). As the intensity of RaS increases, a sharp transition is observed between a regime dominated by eddies to a regime dominated by waves, which corresponds to Fr0.07. For the given runs, this transition to a wave-dominated regime can also be seemingly described by simply comparing the timescales 1/N and τη, the latter being the Kolmogorov timescale based on the mean kinetic energy dissipation. Due to the known anisotropy induced by RaS, we consider separately the motion in the horizontal and vertical directions. In the regime Nτη<1, acceleration statistics exhibit well known characteristics of isotropic turbulence in both directions, such as probability density functions with wide tails and acceleration variance approximately scaling as per Kolmogorov's theory. In contrast for Nτη>1, they behave very differently, experiencing the direct influence of the imposed rotation and stratification. On the other hand, the Lagrangian velocity statistics exhibit visible anisotropy for all runs; nevertheless the degree of anisotropy becomes very strong in the regime Nτη>1. We observe that in the regime Nτη<1, rotation enhances the mean-square displacements in horizontal planes in the ballistic regime at short times but suppresses them in the diffusive regime at longer times. This suppression of the horizontal displacements becomes stronger in the regime Nτη>1, with no clear diffusive behavior. In contrast, the displacements in the vertical direction are always reduced. This inhibition is extremely strong in the Nτη>1 regime, leading to a scenario where particles almost appear to be trapped in horizontal planes.