scholarly journals Spectral energy cascade in nonlinear acoustic and thermoacoustic waves

2018 ◽  
Author(s):  
Prateek Gupta ◽  
Carlo Scalo
Keyword(s):  
Energy Cascade ◽  
Spectral Energy ◽  
Nonlinear Acoustic

Knudsen number effects on the nonlinear acoustic spectral energy cascade

2020 ◽  
Vol 101 (2) ◽  
Author(s):  
Shubham Thirani ◽  
Prateek Gupta ◽  
Carlo Scalo
Keyword(s):  
Knudsen Number ◽  
Energy Cascade ◽  
Spectral Energy ◽  
Nonlinear Acoustic

Spectral energy cascade of body rotations and oscillations under turbulence

2016 ◽  
Vol 94 (6) ◽  
Author(s):  
Yaqing Jin ◽  
Sheng Ji ◽  
Leonardo P. Chamorro
Keyword(s):  
Energy Cascade ◽  
Spectral Energy

scholarly journals Analyzing the spectral energy cascade in turbulent channel flow

2018 ◽  
Vol 30 (6) ◽  
pp. 065110 ◽  
Author(s):  
João Rodrigo Andrade ◽  
Ramon Silva Martins ◽  
Gilmar Mompean ◽  
Laurent Thais ◽  
Thomas B. Gatski
Keyword(s):  
Channel Flow ◽  
Turbulent Channel Flow ◽  
Energy Cascade ◽  
Spectral Energy

scholarly journals Spectral energy cascade in thermoacoustic shock waves

2017 ◽  
Vol 831 ◽  
pp. 358-393 ◽  
Author(s):  
Prateek Gupta ◽  
Guido Lodato ◽  
Carlo Scalo
Keyword(s):  
Shock Wave ◽  
Growth Rate ◽  
Energy Production ◽  
Second Harmonic ◽  
Travelling Wave ◽  
Acoustic Energy ◽  
Energy Cascade ◽  
Spectral Energy ◽  
Production Cycle ◽  
Shock Thickness

We have investigated thermoacoustically amplified quasi-planar nonlinear waves driven to the limit of shock-wave formation in a variable-area looped resonator geometrically optimized to maximize the growth rate of the quasi-travelling-wave second harmonic. Optimal conditions result in velocity leading pressure by approximately $40^{\circ }$ in the thermoacoustic core and not in pure travelling-wave phasing. High-order unstructured fully compressible Navier–Stokes simulations reveal three regimes: (i) modal growth, governed by linear thermoacoustics; (ii) hierarchical spectral broadening, resulting in a nonlinear inertial energy cascade, (iii) shock-wave-dominated limit cycle, where energy production is balanced by dissipation occurring at the captured shock-thickness scale. The acoustic energy budgets in regime (i) have been analytically derived, yielding an expression of the Rayleigh index in closed form and elucidating the effect of geometry and hot-to-cold temperature ratio on growth rates. A time-domain nonlinear dynamical model is formulated for regime (ii), highlighting the role of second-order interactions between pressure and heat-release fluctuations, causing asymmetry in the thermoacoustic energy production cycle and growth rate saturation. Moreover, energy cascade is inviscid due to steepening in regime (ii), with the $k$th harmonic growing at $k/2$-times the modal growth rate of the thermoacoustically sustained second harmonic. The frequency energy spectrum in regime (iii) is shown to scale with a $-5/2$ power law in the inertial range, rolling off at the captured shock-thickness scale in the dissipation range. We have thus shown the existence of equilibrium thermoacoustic energy cascade analogous to hydrodynamic turbulence.

Spectral Energy Fluxes in Geostrophic Turbulence: Implications for Ocean Energetics

2007 ◽  
Vol 37 (3) ◽  
pp. 673-688 ◽  
Author(s):  
Robert B. Scott ◽  
Brian K. Arbic
Keyword(s):  
Kinetic Energy ◽  
Energy Cascade ◽  
Altimeter Data ◽  
Spectral Energy ◽  
Model Parameters ◽  
Baroclinic Mode ◽  
Mean Flow ◽  
Energy Fluxes ◽  
Inverse Cascade ◽  
Geostrophic Turbulence

Abstract The energy pathways in geostrophic turbulence are explored using a two-layer, flat-bottom, f-plane, quasigeostrophic model forced by an imposed, horizontally homogenous, baroclinically unstable mean flow and damped by bottom Ekman friction. A systematic presentation of the spectral energy fluxes, the mean flow forcing, and dissipation terms allows for a comprehensive understanding of the sources and sinks for baroclinic and barotropic energy as a function of length scale. The key new result is a robust inverse cascade of kinetic energy for both the baroclinic mode and the upper layer. This is consistent with recent observations of satellite altimeter data over the South Pacific Ocean. The well-known forward cascade of baroclinic potential and total energy was found to be very robust. Decomposing the spectral fluxes into contributions from different terms provided further insight. The inverse baroclinic kinetic energy cascade is driven mostly by an efficient interaction between the baroclinic velocity and the barotropic vorticity, the latter playing a crucial catalytic role. This cascade can be further enhanced by the baroclinic mode self-interaction, which is only present with nonuniform stratification (unequal layer depths). When model parameters are set such that modeled eddies compare favorably with observations, the inverse baroclinic kinetic energy cascade is actually much stronger than the well-known inverse cascade in the barotropic mode. The upper-layer kinetic energy cascade was found to dominate the lower-layer cascade over a wide range of parameters, suggesting that the surface cascade and time mean density stratification may be sufficient for estimating the depth-integrated cascade from ocean observations. This may find useful application in inferring the kinetic to gravitational potential energy conversion rate from satellite measurements.

Scale interactions and spectral energy transfer in turbulent channel flow

2018 ◽  
Vol 854 ◽  
pp. 474-504 ◽  
Author(s):  
Minjeong Cho ◽  
Yongyun Hwang ◽  
Haecheon Choi
Keyword(s):  
Energy Transfer ◽  
Channel Flow ◽  
Turbulent Transport ◽  
Turbulent Channel Flow ◽  
Energy Cascade ◽  
Large Energy ◽  
Spectral Energy ◽  
Length Scale ◽  
Scale Interaction ◽  
Near Wall

Spectral energy transfer in a turbulent channel flow is investigated at Reynolds number $Re_{\unicode[STIX]{x1D70F}}\simeq 1700$, based on the wall shear velocity and channel half-height, with a particular emphasis on full visualization of triadic wave interactions involved in turbulent transport. As in previous studies, turbulent production is found to be almost uniform, especially over the logarithmic region, and the related spanwise integral length scale is approximately proportional to the distance from the wall. In the logarithmic and outer regions, the energy balance at the integral length scales is mainly formed between production and nonlinear turbulent transport, the latter of which plays the central role in the energy cascade down to the Kolmogorov microscale. While confirming the classical role of the turbulent transport, the triadic wave interaction analysis unveils two new types of scale interaction processes, highly active in the near-wall and the lower logarithmic regions. First, for relatively small energy-containing motions, part of the energy transfer mechanisms from the integral to the adjacent small length scale in the energy cascade is found to be provided by the interactions between larger energy-containing motions. It is subsequently shown that this is related to involvement of large energy-containing motions in skin-friction generation. Second, there exists a non-negligible amount of energy transfer from small to large integral scales in the process of downward energy transfer to the near-wall region. This type of scale interaction is predominant only for the streamwise and spanwise velocity components, and it plays a central role in the formation of the wall-reaching inactive part of large energy-containing motions. A further analysis reveals that this type of scale interaction leads the wall-reaching inactive part to scale in the inner units, consistent with the recent observation. Finally, it is proposed that turbulence production and pressure–strain spectra support the existence of the self-sustaining process as the main turnover dynamics of all the energy-containing motions.

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.

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