Relative Dispersion on the Inner Shelf: Evidence of a Batchelor Regime

Oceanographic relative dispersion (based on drifter separations r) has been extensively studied mostly finding either Richardson-Obukhov ( ~ t3) or enstrophy cascade ( ~ exp(t)) scaling. Relative perturbation dispersion (, based on perturbation separation r − r0 where r0 is the initial separation) has a Batchelor scaling ( ~ t2) for times less than the r0-dependent Batchelor time. Batchelor scaling has received little oceanographic attention. GPS-equipped surface drifters were repeatedly deployed on the Inner Shelf off of Pt. Sal, CA in water depths ≤ 40 m. From 12 releases of ≈ 18 drifters per release, perturbuation and regular relative dispersion over ≈ 4 h are calculated for 250 ≤ r0 ≤ 1500 m for each release and the entire experiment. The perturbation dispersion is consistent with Batchelor scaling for the first 1000-3000 s with larger r0 yielding stronger dispersion and larger Batchelor times. At longer times, and scale-dependent diffusivities begin to suggest Richardson-Obukhov scaling. This applies to both experiment averaged and individual releases. For individual releases, nonlinear internal waves can modulate dispersion. Batchelor scaling is not evident in as the correlations between initial and later separations are significant at short time scaling as ~ t Thus, previous studies investigating are potentially aliased by initial separation effects not present in the perturbation dispersion . As the underlying turbulent velocity wavenumber spectra is inferred from the dispersion power law time dependence, analysis of both and is critical.

Enstrophy non-conservation and the forward cascade of energy in two-dimensional electrostatic magnetized plasma turbulence

A fluid system is derived to describe electrostatic magnetized plasma turbulence at scales somewhat larger than the Larmor radius of a given species. It is related to the Hasegawa–Mima equation, but does not conserve enstrophy, and, as a result, exhibits a forward cascade of energy, to small scales. The inertial-range energy spectrum is argued to be shallower than a $-11/3$ power law, as compared to the $-5$ law of the Hasegawa–Mima enstrophy cascade. This property, confirmed here by direct numerical simulations of the fluid system, may help explain the fluctuation spectrum observed in gyrokinetic simulations of streamer-dominated electron-temperature-gradient driven turbulence (Plunk et al., Phys. Rev. Lett., vol. 122, 2019, 035002), and also possibly some cases of ion-temperature-gradient driven turbulence where zonal flows are suppressed (Plunk et al., Phys. Rev. Lett., vol. 118, 2017, 105002).

A scale invariance criterion for geophysical fluids

<p>Scale invariance of geophysical fluids is investigated in terms of a scale invariance criterion. It was developed by Schaefer-Rolffs et al. (2015) based on the implication that each scale invariant subrange shall have its own criterion. Two particular cases are considered, namely the synoptic scales with a significant Coriolis term and a case at smaller scales where the anelastic approximation is valid. The first case is characterized by a constant enstrophy cascade, while in the second case small-scale fluctuations of density, pressure, and temperature are taken into account. In both cases, the respective scale invariance criteria are applied to simple parameterizations of turbulent diffusion. It is demonstrated that only dynamic approaches are scale invariant.</p>

Direct Numerical Simulations to Investigate Energy Transfer between Meso- and Synoptic Scales

Understanding the development of the atmospheric energy spectrum across scales is necessary to elucidate atmospheric predictability. In this manuscript, the authors investigate energy transfer between the synoptic scale and the mesoscale using direct numerical simulations (DNSs) of two-dimensional (2D) turbulence transfer under forcing applied at different scales. First, DNS results forced by a single kinetic energy source at large scales show that the energy spectra slopes of the direct enstrophy cascade are steeper than the theoretically predicted −3 slope. Second, the presence of two inertial ranges in 2D turbulence at intermediate scales is investigated by introducing a second energy source in the meso-α-scale range. The energy spectra for the DNS with two kinetic energy sources exhibit flatter slopes that are closer to −3, consistent with the observed kinetic energy spectra of horizontal winds in the atmosphere at synoptic scales. Further, the results are independent of model resolution and scale separation between the two energy sources, with a robust transition region between the lower synoptic and the upper meso-α scales in agreement with classical observations in the upper troposphere. These results suggest the existence of a mesoscale feedback on synoptic-scale predictability that emerges from the concurrence of the direct (downscale) enstrophy transfer in the synoptic scales and the inverse (upscale) kinetic energy transfer from the mesoscale to the synoptic scale in the troposphere.

SIMULTANEOUS OBSERVATION OF ENERGY AND ENSTROPHY CASCADES IN THIN-LAYER TURBULENCE

We report the simultaneous observation of the inverse energy and direct enstrophy cascade in thin-layer turbulence. The experiments are conducted in an electromagnetically driven flow with layers of stratified fluid. Recent questions regarding the two-dimensionality of electromagnetically driven turbulence in such experiments are addressed.