Spectral Energy Budget in Wall Turbulence

1964 ◽  
Vol 7 (2) ◽  
pp. 190 ◽  
Author(s):  
J. L. Lumley
Keyword(s):  
Energy Budget ◽  
Wall Turbulence ◽  
Spectral Energy

scholarly journals Frequency-Domain Analysis of the Energy Budget in an Idealized Coupled Ocean–Atmosphere Model

2020 ◽  
Vol 33 (2) ◽  
pp. 707-726 ◽  
Author(s):  
Paige E. Martin ◽  
Brian K. Arbic ◽  
Andrew McC. Hogg ◽  
Andrew E. Kiss ◽  
James R. Munroe ◽  
...  
Keyword(s):  
Frequency Domain ◽  
Time Scales ◽  
Energy Budget ◽  
Western Boundary Current ◽  
Spectral Energy ◽  
Western Boundary ◽  
Intrinsic Variability ◽  
Boundary Current ◽  
Ocean Atmosphere ◽  
Atmosphere Model

AbstractClimate variability is investigated by identifying the energy sources and sinks in an idealized, coupled, ocean–atmosphere model, tuned to mimic the North Atlantic region. The spectral energy budget is calculated in the frequency domain to determine the processes that either deposit energy into or extract energy from each fluid, over time scales from one day up to 100 years. Nonlinear advection of kinetic energy is found to be the dominant source of low-frequency variability in both the ocean and the atmosphere, albeit in differing layers in each fluid. To understand the spatial patterns of the spectral energy budget, spatial maps of certain terms in the spectral energy budget are plotted, averaged over various frequency bands. These maps reveal three dynamically distinct regions: along the western boundary, the western boundary current separation, and the remainder of the domain. The western boundary current separation is found to be a preferred region to energize oceanic variability across a broad range of time scales (from monthly to decadal), while the western boundary itself acts as the dominant sink of energy in the domain at time scales longer than 50 days. This study paves the way for future work, using the same spectral methods, to address the question of forced versus intrinsic variability in a coupled climate system.

scholarly journals Applications of a Moist Nonhydrostatic Formulation of the Spectral Energy Budget to Baroclinic Waves. Part I: The Lower-Stratospheric Energy Spectra

2015 ◽  
Vol 72 (5) ◽  
pp. 2090-2108 ◽  
Author(s):  
Jun Peng ◽  
Lifeng Zhang ◽  
Jiping Guan
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Energy Budget ◽  
Vertical Flux ◽  
Energy Spectra ◽  
Spectral Energy ◽  
Positive Contribution ◽  
Flux Divergence ◽  
Available Potential Energy ◽  
Baroclinic Waves

Abstract The authors investigate the mesoscale dynamics that produce the lower-stratospheric energy spectra in idealized moist baroclinic waves, using the moist nonhydrostatic formulation of spectral energy budget of kinetic energy and available potential energy by J. Peng et al. The inclusion of moist processes energizes the lower-stratospheric mesoscale, helping to close the gap between observed and simulated energy spectra. In dry baroclinic waves, the lower-stratospheric mesoscale is mainly forced by weak downscale cascades of both horizontal kinetic energy (HKE) and available potential energy (APE) and by a weak conversion of APE to HKE. At wavelengths less than 1000 km, the pressure vertical flux divergence also has a significant positive contribution to the HKE; however, this positive contribution is largely counteracted by the negative HKE vertical flux divergence. In moist baroclinic waves, the lower-stratospheric mesoscale HKE is mainly generated by the pressure and HKE vertical flux divergences. This additional HKE is partly converted to APE and partly removed by diffusion. Another negative contribution to the mesoscale HKE is from the forcing of a visible upscale HKE cascade. Besides the conversion of HKE, however, the three-dimensional divergence also has a significant positive contribution to the mesoscale APE. With these two direct APE sources, the lower-stratospheric mesoscale also undergoes a much stronger upscale APE cascade. These results suggest that both downscale and upscale cascades through the mesoscale are permitted in the real atmosphere and the direct forcing of the mesoscale is available to feed the upscale energy cascade.

Submesoscale Eddies in the Upper Ocean of the Kuroshio Extension from High-resolution Simulation: Energy Budget

2021 ◽  
Author(s):  
Haijin Cao ◽  
Baylor Fox-Kemper ◽  
Zhiyou Jing
Keyword(s):  
Energy Budget ◽  
Kuroshio Extension ◽  
Energy Budgets ◽  
Spectral Energy ◽  
Upper Ocean ◽  
Energy Cycle ◽  
Energy Transfers ◽  
Energetic Analysis ◽  
The Kuroshio ◽  
Resolution Simulation

AbstractThe submesoscale energy budget is complex and remains understood only in region-by-region analyses. Based on a series of nested numerical simulations, this study investigated the submesoscale energy budget and flux in the upper ocean of the Kuroshio Extension, including some innovations for examining submesoscale energy budgets in general. The highest-resolution simulation on a ~500 m grid resolves a variety of submesoscale instabilities allowing an energetic analysis in the submesoscale range. The frequency–wavenumber spectra of vertical vorticity variance (i.e., enstrophy) and horizontal divergence variance were used to identify the scales of submesoscale flows as distinct from those of inertia-gravity waves but dominating horizontal divergence variance. Next, the energy transfers between the background scales and the submesoscale were examined. The submesoscale kinetic and potential energy (SMKE and SMPE) were mainly contained in the mixed layer and energized through both barotropic (shear production) and baroclinic (buoyancy production) routes. Averaged over the upper 50 m of ROMS2, the baroclinic transfers amounted to approximately 75% of the sources for the SMKE (3.42 × 10−9 W/kg) versus the remaining 25% (1.12 × 10−9 W/kg) via barotropic downscale KE transfers. The KE field was greatly strengthened by energy sources through the boundary—this flux is larger than the mesoscale-to-submesoscale transfers in this region. Spectral energy production, importantly, reveals upscale KE transfers at larger submesoscales and downscale KE transfers at smaller submesoscales (i.e., a transition from inverse to forward KE cascade). This study seeks to extend our understanding of the energy cycle to the submesoscale and highlight the forward KE cascade induced by upper-ocean submesoscale activities in the research domain.

scholarly journals A New Formulation of the Spectral Energy Budget of the Atmosphere, with Application to Two High-Resolution General Circulation Models

2013 ◽  
Vol 70 (7) ◽  
pp. 2293-2308 ◽  
Author(s):  
Pierre Augier ◽  
Erik Lindborg
Keyword(s):  
High Resolution ◽  
Spherical Harmonics ◽  
Energy Budget ◽  
General Circulation ◽  
Three Dimensional ◽  
General Circulation Models ◽  
Energy Cascade ◽  
Spectral Energy ◽  
Base Functions ◽  
New Formulation

Abstract A new formulation of the spectral energy budget of kinetic and available potential energies of the atmosphere is derived, with spherical harmonics as base functions. Compared to previous formulations, there are three main improvements: (i) the topography is taken into account, (ii) the exact three-dimensional advection terms are considered, and (iii) the vertical flux is separated from the energy transfer between different spherical harmonics. Using this formulation, results from two different high-resolution GCMs are analyzed: the Atmospheric GCM for the Earth Simulator (AFES) T639L24 and the European Centre for Medium-Range Weather Forecasts (ECMWF) Integrated Forecast System (IFS) T1279L91. The spectral fluxes show that the AFES, which reproduces quite realistic horizontal spectra with a k−5/3 inertial range at the mesoscales, simulates a strong downscale energy cascade. In contrast, neither the k−5/3 vertically integrated spectra nor the downscale energy cascade are produced by the ECMWF IFS.

scholarly journals Applications of a Moist Nonhydrostatic Formulation of the Spectral Energy Budget to Baroclinic Waves. Part II: The Upper-Tropospheric Energy Spectra

2015 ◽  
Vol 72 (10) ◽  
pp. 3923-3939 ◽  
Author(s):  
Jun Peng ◽  
Lifeng Zhang ◽  
Jiping Guan
Keyword(s):  
Energy Budget ◽  
Large Scale ◽  
Lower Troposphere ◽  
Gravitational Energy ◽  
Energy Spectra ◽  
Spectral Energy ◽  
Positive Contribution ◽  
Latent Heating ◽  
Baroclinic Waves ◽  
Moist Processes

Abstract In this second part of a two-part study, a newly developed moist nonhydrostatic formulation of the spectral energy budget of both kinetic energy (KE) and available potential energy (APE) is employed to investigate the dynamics underlying the mesoscale upper-tropospheric energy spectra in idealized moist baroclinic waves. By calculating the conservative nonlinear spectral fluxes, it is shown that the inclusion of moist processes significantly enhances downscale cascades of both horizontal KE and APE. Moist processes act not only as a source of latent heat but also as an “atmospheric dehumidifier.” The latent heating, mainly because of the depositional growth of cloud ice, has a significant positive contribution to mesoscale APE. However, the dehumidifying reduces the diabatic contribution of the latent heating by 15% at all scales. Including moist processes also changes the direction of the mesoscale conversion between APE and horizontal KE and adds a secondary conversion of APE to gravitational energy of moist species. With or without moisture, the vertically propagating inertia–gravity waves (IGWs) produced in the lower troposphere result in a significant positive contribution to the upper-tropospheric horizontal KE spectra at the large-scale end of the mesoscale. However, including moist processes generates additional sources of IGWs located in the upper troposphere; the upward propagation of the convectively generated IGWs removes much of the horizontal KE there. Because of the restriction of the anelastic approximation, the three-dimensional divergence has no significant contribution. In view of conflicting contributions of various direct forcings, finally, an explicit comparison between the net direct forcing and energy cascade is made.

Towards a Global Spectral Energy Budget for Internal Gravity Waves in the Ocean

2020 ◽  
Vol 50 (4) ◽  
pp. 935-944 ◽  
Author(s):  
Carsten Eden ◽  
Friederike Pollmann ◽  
Dirk Olbers
Keyword(s):  
Kinetic Equation ◽  
Gravity Waves ◽  
Energy Budget ◽  
Wave Energy ◽  
Internal Gravity Waves ◽  
Rate Of Change ◽  
Spectral Energy ◽  
Spectral Space ◽  
Wave Interactions ◽  
Energy Transfers

AbstractEnergy transfers by internal gravity wave–wave interactions in spectral space are diagnosed from numerical model simulations initialized with realizations of the Garrett–Munk spectrum in physical space and compared with the predictions of the so-called scattering integral or kinetic equation. Averaging the random phase of the initialization, the energy transfers by wave–wave interactions in the model agree well with the predictions of the kinetic equation for certain ranges of frequency and wavenumbers. This validation allows now, in principle, the use of the energy transfers predicted by the kinetic equation to design a global spectral energy budget for internal gravity waves in the ocean where divergences of energy transports in physical and spectral space balance forcing, dissipation, the energy transfers by the wave–wave interactions, or the rate of change of the spectral wave energy. First global estimates show indeed accumulation of the wave energy in a range of latitude ϕ consistent with tidal waves at frequency ωT propagating toward the latitudinal window where 2 < ωT/f(ϕ) < 3, as predicted by the kinetic equation.

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