Mapping the Energy Cascade in the North Atlantic Ocean: The Coarse-graining Approach

This is the final version of the article. Available from AMS via the DOI in this record.A coarse-graining framework is implemented to analyze nonlinear processes, measure energy transfer rates and map out the energy pathways from simulated global ocean data. Traditional tools to measure the energy cascade from turbulence theory, such as spectral flux or spectral transfer rely on the assumption of statistical homogeneity, or at least a large separation between the scales of motion and the scales of statistical inhomogeneity. The coarse-graining framework allows for probing the fully nonlinear dynamics simultaneously in scale and in space, and is not restricted by those assumptions. This paper describes how the framework can be applied to ocean flows. Energy transfer between scales is not unique due to a gauge freedom. Here, it is argued that a Galilean invariant subfilter scale (SFS) flux is a suitable quantity to properly measure energy scale-transfer in the Ocean. It is shown that the SFS definition can yield answers that are qualitatively different from traditional measures that conflate spatial transport with the scale-transfer of energy. The paper presents geographic maps of the energy scale-transfer that are both local in space and allow quasi-spectral, or scale-by-scale, dynamics to be diagnosed. Utilizing a strongly eddying simulation of flow in the North Atlantic Ocean, it is found that an upscale energy transfer does not hold everywhere. Indeed certain regions, near the Gulf Stream and in the Equatorial Counter Current have a marked downscale transfer. Nevertheless, on average an upscale transfer is a reasonable mean description of the extra-tropical energy scale-transfer over regions of O(10^3) kilometers in size.Financial support was provided by IGPPS at Los Alamos National Laboratory (LANL) and NSF grant OCE-1259794. HA was also supported through DOE grants de-sc0014318, de-na0001944, and the LANL LDRD program through project number 20150568ER. MH was also supported through the HiLAT project of the Regional and Global Climate Modeling program of the DOE’s Office of Science, and GKV was also supported by NERC, the Marie Curie Foundation and the Royal Society (Wolfson Foundation). This research used resources of the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231

Localness of energy cascade in hydrodynamic turbulence, II. Sharp spectral filter

We investigate the scale-locality of subgrid-scale (SGS) energy flux and inter-band energy transfers defined by the sharp spectral filter. We show by rigorous bounds, physical arguments and numerical simulations that the spectral SGS flux is dominated by local triadic interactions in an extended turbulent inertial-range. Inter-band energy transfers are also shown to be dominated by local triads if the spectral bands have constant width on a logarithmic scale. We disprove in particular an alternative picture of ``local transfer by nonlocal triads,'' with the advecting wavenumber mode at the energy peak. Although such triads have the largest transfer rates of all {\it individual} wavenumber triads, we show rigorously that, due to their restricted number, they make an asymptotically negligible contribution to energy flux and log-banded energy transfers at high wavenumbers in the inertial-range. We show that it is only the aggregate effect of a geometrically increasing number of local wavenumber triads which can sustain an energy cascade to small scales. Furthermore, non-local triads are argued to contribute even less to the space-average energy flux than is implied by our rigorous bounds, because of additional cancellations from scale-decorrelation effects. We can thus recover the -4/3 scaling of nonlocal contributions to spectral energy flux predicted by Kraichnan's ALHDIA and TFM closures. We support our results with numerical data from a $512^3$ pseudospectral simulation of isotropic turbulence with phase-shift dealiasing. We conclude that the sharp spectral filter has a firm theoretical basis for use in large-eddy simulation (LES) modeling of turbulent flows.Comment: 42 pages, 9 figure

Localness of energy cascade in hydrodynamic turbulence, I. Smooth coarse-graining

We introduce a novel approach to scale-decomposition of the fluid kinetic energy (or other quadratic integrals) into band-pass contributions from a series of length-scales. Our decomposition is based on a multiscale generalization of the ``Germano identity'' for smooth, graded filter kernels. We employ this method to derive a budget equation that describes the transfers of turbulent kinetic energy both in space and in scale. It is shown that the inter-scale energy transfer is dominated by local triadic interactions, assuming only the scaling properties expected in a turbulent inertial-range. We derive rigorous upper bounds on the contributions of non-local triads, extending the work of Eyink (2005) for low-pass filtering. We also propose a physical explanation of the differing exponents for our rigorous upper bounds and for the scaling predictions of Kraichnan (1966,1971). The faster decay predicted by Kraichnan is argued to be the consequence of additional cancellations in the signed contributions to transfer from non-local triads, after averaging over space. This picture is supported by data from a $512^3$ pseudospectral simulation of Navier-Stokes turbulence with phase-shift dealiasing.Comment: 26 pages, 4 figure

Effect of filter type on the statistics of energy transfer between resolved and subfilter scales from a-priori analysis of direct numerical simulations of isotropic turbulence

The effects of different filtering strategies on the statistical properties of the resolved-to-sub-filter scale (SFS) energy transfer are analyzed in forced homogeneous and isotropic turbulence. We carry out a priori analyses of statistical characteristics of SFS energy transfer by filtering data obtained from direct numerical simulations (DNS) with up to $2048^3$ grid points as a function of the filter cutoff scale. In order to quantify the dependence of extreme events and anomalous scaling on the filter, we compare a sharp Fourier Galerkin projector, a Gaussian filter and a novel class of Galerkin projectors with non-sharp spectral filter profiles. Of interest is the importance of Galilean invariance and we confirm that local SFS energy transfer displays intermittency scaling in both skewness and flatness as a function of the cutoff scale. Furthermore, we quantify the robustness of scaling as a function of the filtering type

Energy Transfer and Spectra in Simulations of Two-dimensional Compressible Turbulence

We present results of high-resolution numerical simulations of compressible 2D turbulence forced at intermediate spatial scales with a solenoidal white-in-time external acceleration. A case with an isothermal equation of state, low energy injection rate, and turbulent Mach number $M\approx0.34$ without energy condensate is studied in detail. Analysis of energy spectra and fluxes shows that the classical dual-cascade picture familiar from the incompressible case is substantially modified by compressibility effects. While the small-scale direct enstrophy cascade remains largely intact, a large-scale energy flux loop forms with the direct acoustic energy cascade compensating for the inverse transfer of solenoidal kinetic energy. At small scales, the direct enstrophy and acoustic energy cascades are fully decoupled at small Mach numbers and hence the corresponding spectral energy slopes comply with theoretical predictions, as expected. At large scales, dispersion of acoustic waves on vortices softens the dilatational velocity spectrum, while the pseudo-sound component of the potential energy associated with coherent vortices steepens the potential energy spectrum.Comment: 10 pages, 6 figures. To appear in: Turbulence in Complex Conditions, Proc. Euromech/Ercoftac Colloquium 589, ed. M. Gorokhovski, Springer, 201

Physical Processes in Star Formation

© 2020 Springer-Verlag. The final publication is available at Springer via https://doi.org/10.1007/s11214-020-00693-8.Star formation is a complex multi-scale phenomenon that is of significant importance for astrophysics in general. Stars and star formation are key pillars in observational astronomy from local star forming regions in the Milky Way up to high-redshift galaxies. From a theoretical perspective, star formation and feedback processes (radiation, winds, and supernovae) play a pivotal role in advancing our understanding of the physical processes at work, both individually and of their interactions. In this review we will give an overview of the main processes that are important for the understanding of star formation. We start with an observationally motivated view on star formation from a global perspective and outline the general paradigm of the life-cycle of molecular clouds, in which star formation is the key process to close the cycle. After that we focus on the thermal and chemical aspects in star forming regions, discuss turbulence and magnetic fields as well as gravitational forces. Finally, we review the most important stellar feedback mechanisms.Peer reviewedFinal Accepted Versio

Joint downscale fluxes of energy and potential enstrophy in rotating stratified Boussinesq flows

We employ a coarse-graining approach to analyze non-linear cascades in Boussinesq flows using high-resolution simulation data. We derive budgets which resolve the evolution of energy and potential enstrophy simultaneously in space and in scale. We then use numerical simulations of Boussinesq flows, with forcing in the large scales, and fixed rotation and stable stratification along the vertical axis, to study the inter-scale flux of energy and potential enstrophy in three different regimes of stratification and rotation: i) strong rotation and moderate stratification, ii) moderate rotation and strong stratification, and iii) equally strong stratification and rotation. In all three cases, we observe constant fluxes of both global invariants, the mean energy and mean potential enstrophy, from large to small scales. The existence of constant potential enstrophy flux ranges provides the first direct empirical evidence in support of the notion of a cascade of potential enstrophy. The persistent forward cascade of the two invariants reflects a marked departure of these flows from two-dimensional turbulence

Spatio-Temporal Coarse-Graining Decomposition of the Global Ocean Geostrophic Kinetic Energy

AbstractWe expand on a recent determination of the first global energy spectrum of the ocean's surface geostrophic circulation (Storer et al., 2022, https://doi.org/10.1038/s41467-022-33031-3) using a coarse‐graining (CG) method. We compare spectra from CG to those from spherical harmonics by treating land in a manner consistent with the boundary conditions. While the two methods yield qualitatively consistent domain‐averaged results, spherical harmonics spectra are too noisy at gyre‐scales (&gt;1,000 km). More importantly, spherical harmonics are inherently global and cannot provide local information connecting scales with currents geographically. CG shows that the extra‐tropics mesoscales (100–500 km) have a root‐mean‐square (rms) velocity of ∼15 cm/s, which increases to ∼30–40 cm/s locally in the Gulf Stream and Kuroshio and to ∼16–28 cm/s in the ACC. There is notable hemispheric asymmetry in mesoscale energy‐per‐area, which is higher in the north due to continental boundaries. We estimate that ≈25%–50% of total geostrophic energy is at scales smaller than 100 km, and is un(der)‐resolved by pre‐SWOT satellite products. Spectra of the time‐mean circulation show that most of its energy (up to 70%) resides in stationary eddies with characteristic scales smaller than (&lt;500 km). This highlights the preponderance of “standing” small‐scale structures in the global ocean due to the temporally coherent forcing by boundaries. By coarse‐graining in space and time, we compute the first spatio‐temporal global spectrum of geostrophic circulation from AVISO and NEMO. These spectra show that every length‐scale evolves over a wide range of time‐scales with a consistent peak at ≈200 km and ≈2–3 weeks.</jats:p