Stably stratified turbulence in the presence of large-scale forcing

Abstract

We perform two high-resolution direct numerical simulations of stratified turbulence for Reynolds number equal to Re ≈ 25 000 and Froude number, respectively, of Fr ≈ 0.1 and Fr ≈ 0.03. The flows are forced at large scale and discretized on an isotropic grid of 20483 points. Stratification makes the flow anisotropic and introduces two extra characteristic scales with respect to homogeneous isotropic turbulence: the buoyancy scale, LB, and the Ozmidov scale, oz. The former is related to the number of layers that the flow develops in the direction of gravity, and the latter is regarded as the scale at which isotropy is recovered. The values of LB and oz depend on the Froude number, and their absolute and relative amplitudes affect the repartition of energy among Fourier modes in ways that are not easy to predict. By contrasting the behavior of the two simulated flows we identify some surprising similarities: After an initial transient the two flows evolve towards comparable values of the kinetic and potential enstrophy and energy dissipation rate. This is the result of the Reynolds number being large enough in both flows for the Ozmidov scale to be resolved. When properly dimensionalized, the energy dissipation rate is compatible with atmospheric observations. Further similarities emerge at large scales: The same ratio between potential and total energy (≈0.1) is spontaneously selected by the flows, and slow modes grow monotonically in both regimes, causing a slow increase of the total energy in time. The axisymmetric total energy spectrum shows a wide variety of spectral slopes as a function of the angle between the imposed stratification and the wave vector. One-dimensional energy spectra computed in the direction parallel to gravity are flat from the forcing up to buoyancy scale. At intermediate scales a ∼k−3 parallel spectrum develops for the Fr ≈ 0.03 run, whereas for weaker stratification, the saturation spectrum does not have enough scales to develop and instead one observes a power law compatible with Kolmogorov scaling. Finally, the spectrum of helicity is flat until LB, as observed in the nocturnal planetary boundary layer.