Net Energy Transfer Research Articles

Internal Tide Energy Transfers Induced by Mesoscale Circulation and Topography Across the North Atlantic

AbstractThe interactions between the internal tide and the mesoscale circulation are studied from the internal tide energy budget perspective. To that end, the modal energy budget of the internal tide is diagnosed using a high resolution numerical simulation covering the North Atlantic. Compared to the topographic contribution, the advection of the internal tide by the low‐frequency flow component and the horizontal and vertical shear are found to be significant at global scale, while the buoyancy contribution is important locally. The advection of the internal tide by the low‐frequency currents is responsible for a net energy transfer from the large scale to smaller scale internal tide, without exchanges with the low‐frequency flow. On the opposite, the shear of the mesoscale circulation and the buoyancy field are responsible for exchanges between the internal tide and the low‐frequency flow. The importance of the shear increases in the northernmost part of the domain, and a partial compensation between the buoyancy and the shear contributions is found in some areas of the North Atlantic, such as in the Gulf Stream region. In addition, the temporal variability of these energy transfers is investigated. In contrast to topographic scattering, for which the spring‐neap cycle is the dominant frequency, the energy transfer terms driven by low‐frequency motions in areas of strong mesoscale activity are also modulated by variations of the low‐frequency current spatial distribution.

Investigation of cold tube structure on flow characteristics and energy separation in vortex tube based on numerical and thermodynamic analyses

A combined approach of computational fluid dynamics modelling, experimental validation and thermodynamic analysis is used to investigate the effect of cold end tube geometry (namely, straight tube, divergent tube, convergent tube, and convergent-divergent tube) on flow characteristics and energy separation, which to improve the energy efficiency and sustainability of the vortex tube in industrial applications. The analyses indicate that the highest axial velocity (212 m/s) and swirl velocity (193 m/s) at different axial locations in the cold tube are demonstrated in the divergent and convergent-divergent structures, respectively. The divergent tube shows better energy separation at lower cold mass fraction, while the convergent-divergent tube is dominant at higher cold mass fraction. The highest coefficient of performance is found at μc = 0.6, with maximum cooling and heating energy transfer efficiencies of 0.112 and 0.103, respectively. By innovatively incorporating the work-heat transfer theory into structural investigation of cold tubes, it is found that tangential viscous shear effect is the dominant factor in energy separation process. It is noteworthy that the highest net energy transfer of 973 W is achieved by convergent-divergent tube at a cold mass fraction of 0.7.

Fluctuation-dissipation relation in cosmic microwave background

We study the fluctuation-dissipation relation for sound waves in the cosmic microwave background (CMB), employing effective field theory (EFT) for fluctuating hydrodynamics.Treating sound waves as the linear response to thermal radiation, we establish the fluctuation-dissipation relation within a cosmological framework.While dissipation is elucidated in established linear cosmological perturbation theory, the standard Boltzmann theory overlooks the associated noise, possibly contributing to inconsistencies in Lambda Cold Dark Matter (ΛCDM) cosmology. This paper employs EFT for fluctuating hydrodynamics in cosmological perturbation theory, deriving sound wave noise.Notably, the long-time limit of the noise spectrum is independent of viscosity details, resembling a Brownian motion bounded in a harmonic potential.The net energy transfer between the sound wave system and the radiation environment reaches a balance within Hubble time, suggesting the thermal equilibrium of the sound waves themselves.The induced density power spectrum is characterized as white noise dependent on the inverse of the entropy density, which is negligibly small on the CMB scale. The energy density of the entire sound wave system scales as a -4, akin to radiation. While the numerical factor is not determined in the present calculation, the back reaction of the sound wave system to the background radiation may not be negligible, serving as a potential source for various fitting issues in ΛCDM cosmology.

Observations of Parametric Subharmonic Instability of Diurnal Internal Tides in the Northwest Pacific

Abstract Based on yearlong observations from three moorings at 12°, 14°, and 16°N in the northwest Pacific, this study presents observational evidence for the occurrence and behavior of parametric subharmonic instability (PSI) of diurnal internal tides (ITs) both in the upper and abyssal ocean around the critical latitudes (O1 IT: 13.44°N; K1 IT: 14.52°N), which is relatively less explored in comparison with PSI of M2 ITs. At 14°N, near-inertial waves (NIWs) feature a “checkerboard” pattern with comparable upward- and downward-propagating components, while the diurnal ITs mainly feature a low-mode structure. The near-inertial kinetic energy at 14°N, correlated fairly well with the diurnal KE, is the largest among three moorings. The bicoherence analysis, and a causality analysis method newly introduced here, both show statistically significant phase locking between PSI triads at 14°N, while no significant signals emerge at 12° and 16°N. The estimated PSI energy transfer rate shows a net energy transfer from diurnal ITs to NIWs with an annual-mean value of 1.5 × 10−10 W kg−1. The highly sheared NIWs generated by PSI result in a 2–6 times larger probability of shear instability events at 14°N than 12° and 16°N. Through swinging the local effective inertial frequency close to either O1 or K1 subharmonic frequencies, the passages of anticyclonic and cyclonic eddies both result in elevated NIWs and shear instability events by enhancing PSI efficiency. Particularly, different from the general understanding that cyclonic eddies usually expel NIWs, enhanced NIWs and instability are observed within cyclonic eddies whose relative vorticity can modify PSI efficiency. Significance Statement Parametric subharmonic instability (PSI) effectively transfers energy from low-mode internal tides (ITs) to high-mode near-inertial waves (NIWs), triggering elevated mixing around critical latitudes. This study provides observational evidence for the occurrence of PSI of diurnal ITs in the northwest Pacific and its role in enhancing shear instability. Generally, anticyclonic eddies act to trap NIWs while cyclonic eddies tend to expel NIWs. Here we document elevated NIWs and shear instability within both anticyclonic and cyclonic eddies, which shift the local effective inertial frequency close to either O1 or K1 subharmonic frequencies, thereby enhancing PSI efficiency. Processes associated with PSI and the modulation of PSI efficiency by mesoscale eddies have significant implications for improving mixing parameterizations in ocean circulation and climate models.

Three-dimensional shear-flow instability saturation via stable modes

Turbulence in three dimensions (3D) supports vortex stretching that has long been known to accomplish energy transfer to small scales. Moreover, net energy transfer from large-scale, forced, unstable flow-gradients to smaller scales is achieved by gradient-flattening instability. Despite such enforcement of energy transfer to small scales, it is shown here that the shear-flow-instability-supplied 3D-fluctuation energy is largely inverse-transferred from the fluctuation to the mean-flow gradient, and such inverse transfer is more efficient for turbulent fluctuations in 3D than in two dimensions (2D). The transfer is due to linearly stable eigenmodes that are excited nonlinearly. The stable modes, thus, reduce both the nonlinear energy cascade to small scales and the viscous dissipation rate. The vortex-tube stretching is also suppressed. Up-gradient momentum transport by the stable modes counters the instability-driven down-gradient transport, which also is more effective in 3D than in 2D (≈70% vs ≈50%). From unstable modes, these stable modes nonlinearly receive energy via zero-frequency fluctuations that vary only in the direction orthogonal to the plane of 2D shear flow. The more widely occurring 3D turbulence is thus inherently different from the commonly studied 2D turbulence, despite both saturating via stable modes.

Downward Propagation and Trapping of Near-Inertial Waves by a Westward-Moving Anticyclonic Eddy in the Subtropical Northwestern Pacific Ocean

Abstract Mesoscale eddies can alter the propagation of wind-generated near-inertial waves (NIWs). Different from previous studies, the subsurface mooring observed NIWs are generated outside an anticyclonic eddy (ACE) and then interact with the arriving ACE. It is found that with the arrival of the ACE, the NIWs accelerate to propagate downward and the maximum vertical wavelength and group velocity of NIWs reach ∼500 m and ∼35 m day−1, respectively. When entering the core of the ACE, the near-inertial energy is trapped and finally stalls at a critical depth, which basically corresponds to the base of the ACE located at around 750-m depth. Through a ray-tracing model and dynamic analyses, this critical depth is much deeper than that of NIWs generated directly inside an ACE. By using depth–time varying stratification and relative vorticity, ray-tracing experiments further demonstrate that NIWs generated outside and passed over by an ACE can propagate to deep depths. Furthermore, energy budget analyses indicate that the net energy transfer from the ACE to NIWs plays an important role in the enhancement of downward-propagating near-inertial energy and its long-term persistence (∼45 days) in the critical layer. Within the critical layer, the enhancement of shear instability and nonlinear interactions among internal waves account for the loss of the trapped near-inertial energy and provide energy for furnishing deep ocean mixing. Significance Statement The interactions between near-inertial waves and a westward-moving anticyclonic eddy are investigated in this study. Knowledge about the propagation of near-inertial waves continues to be a topic of interest because near-inertial waves transfer energy from the mixed layer to the interior ocean, which is an important source of turbulent mixing. While much is known about how near-inertial energy propagates inside an anticyclonic eddy, few studies have examined how near-inertial energy propagates when it is generated outside an anticyclonic eddy and then enters the arriving anticyclonic eddy. In this study, the deep propagation and trapping of near-inertial energy by a westward-moving anticyclonic eddy is observed, which contributes greatly to the energy budget and the deep-ocean mixing.

Scattering mechanism of work done on an ultracold Fermi gas by a time-dependent interaction

We discuss the work done on repulsive ultracold Fermi gas via collisions tuned by a time-dependent magnetic ramp. If the interaction is strengthened during binary collisions, the kinetic energy of atoms increases with each such inelastic event. The net energy transfer via collisions is compared with the transfer via the mean field. It is found that for a weak interaction, with a scattering length shorter than the inverse mean momentum of atoms, the mean field dominates, while for a strong interaction, the majority of energy enters the gas via collisions.

Magnetosphere-Ionosphere-Thermosphere Coupling Study at Jupiter Based on Juno's First 30 Orbits and Modeling Tools.

The dynamics of the Jovian magnetosphere is controlled by the interplay of the planet's fast rotation, its solar-wind interaction and its main plasma source at the Io torus, mediated by coupling processes involving its magnetosphere, ionosphere, and thermosphere. At the ionospheric level, these processes can be characterized by a set of parameters including conductances, field-aligned currents, horizontal currents, electric fields, transport of charged particles along field lines including the fluxes of electrons precipitating into the upper atmosphere which trigger auroral emissions, and the particle and Joule heating power dissipation rates into the upper atmosphere. Determination of these key parameters makes it possible to estimate the net transfer of momentum and energy between Jovian upper atmosphere and equatorial magnetosphere. A method based on a combined use of Juno multi-instrument data and three modeling tools was developed by Wang etal. (2021, https://doi.org/10.1029/2021ja029469) and applied to an analysis of the first nine orbits to retrieve these parameters along Juno's magnetic footprint. We extend this method to the first 30 Juno science orbits and to both hemispheres. Our results reveal a large variability of these parameters from orbit to orbit and between the two hemispheres. They also show dominant trends. Southern current systems are consistent with the generation of a region of sub-corotating ionospheric plasma flows, while both super-corotating and sub-corotating plasma flows are found in the north. These results are discussed in light of the previous space and ground-based observations and currently available models of plasma convection and current systems, and their implications are assessed.

Efficient energy balancing across multiple harmonics of nonlinear normal modes

Predicting the forced responses of nonlinear systems is a topic that attracts extensive studies. The energy balancing method considers the net energy transfer in and out of the system over one period and establishes connections between forced responses and nonlinear normal modes (NNMs). In this paper, we consider the energy balancing across multiple harmonics of NNMs for predicting forced resonances. This technique is constructed by combining the energy balancing mechanism with restrictions (established via excitation scenarios) on external forcing and harmonic phase-shifts; a semi-analytical framework is derived to achieve both accurate/robust results and efficient computations. With known inputs from NNM solutions, the required forcing amplitudes to reach NNMs at resonances, along with their discrepancy, i.e. the harmonic phase-shifts, are computed via a one-step scheme. Several examples are presented for different excitation scenarios to demonstrate the applicability of this method and to show its capability in accurately predicting the existence of an isola where multiple harmonics play a significant part in the response.

Cross-beam energy transfer in direct-drive ICF. II. Theory and simulation of mitigation through increased laser bandwidth

The response of the cross-beam energy transfer instability (CBET) to laser bandwidth is investigated through a combination of theory and simulation. Existing linear theory is generalized to treat broadband lasers, demonstrating that CBET is most effectively suppressed when the bandwidth exceeds the ion-acoustic wave (IAW) frequency. It is shown that for such bandwidths, reverse (seed to pump) transfer becomes possible, which reduces the net energy transfer rapidly as bandwidth is increased. The CBET gain exponent in this regime scales with bandwidth (Δω) as Δω−3 for Gaussian or Lorentzian laser spectra with different scalings possible for other spectra. Comparison of our theory with linearized fluid and particle-in-cell simulations, performed with the laser-plasma simulation environment (LPSE) and vector particle in cell (VPIC) codes, respectively, finds that the model is accurate in the absence of nonlinear processes. However, linear analysis also finds that the IAW energy density scales as Δω−1, implying that nonlinear effects may be more difficult to control than the CBET scaling would suggest. Indeed, nonlinear effects are found to be present in VPIC simulations with high-intensity lasers, despite minimal apparent CBET. Nonlinear processes in the VPIC cases include particle trapping, the two-ion wave decay, and ion wave self-focusing. In some high intensity VPIC cases, these effects lead to net energy transfer from seed to pump and increases to backscatter stimulated Brillouin scattering reflectivities. Finally, for a given bandwidth, we show that improved control of nonlinear processes can be achieved via smoothing by spectral dispersion.

Scale interactions and anisotropy in Rayleigh–Taylor turbulence

We study energy scale transfer in Rayleigh–Taylor (RT) flows by coarse graining in physical space without Fourier transforms, allowing scale analysis along the vertical direction. Two processes are responsible for kinetic energy flux across scales: baropycnal work $\varLambda$ , due to large-scale pressure gradients acting on small scales of density and velocity; and deformation work $\varPi$ , due to multiscale velocity. Our coarse-graining analysis shows how these fluxes exhibit self-similar evolution that is quadratic-in-time, similar to the RT mixing layer. We find that $\varLambda$ is a conduit for potential energy, transferring energy non-locally from the largest scales to smaller scales in the inertial range where $\varPi$ takes over. In three dimensions, $\varPi$ continues a persistent cascade to smaller scales, whereas in two dimensions $\varPi$ rechannels the energy back to larger scales despite the lack of vorticity conservation in two-dimensional (2-D) variable density flows. This gives rise to a positive feedback loop in 2-D RT (absent in three dimensions) in which mixing layer growth and the associated potential energy release are enhanced relative to 3-D RT, explaining the oft-observed larger $\alpha$ values in 2-D simulations. Despite higher bulk kinetic energy levels in two dimensions, small inertial scales are weaker than in three dimensions. Moreover, the net upscale cascade in two dimensions tends to isotropize the large-scale flow, in stark contrast to three dimensions. Our findings indicate the absence of net upscale energy transfer in three-dimensional RT as is often claimed; growth of large-scale bubbles and spikes is not due to ‘mergers’ but solely due to baropycnal work $\varLambda$ .

Stormtime Energetics: Energy Transport Across the Magnetopause in a Global MHD Simulation

Coupling between the solar wind and magnetosphere can be expressed in terms of energy transfer through the separating boundary known as the magnetopause. Geospace simulation is performed using the Space Weather Modeling Framework (SWMF) of a multi-ICME impact event on February 18–20, 2014 in order to study the energy transfer through the magnetopause during storm conditions. The magnetopause boundary is identified using a modified plasma β and fully closed field line criteria to a downstream distance of −20Re. Observations from Geotail, Themis, and Cluster are used as well as the Shue 1998 model to verify the simulation field data results and magnetopause boundary location. Once the boundary is identified, energy transfer is calculated in terms of total energy flux K, Poynting flux S, and hydrodynamic flux H. Surface motion effects are considered and the regional distribution of energy transfer on the magnetopause surface is explored in terms of dayside X>0, flank X<0, and tail cross section X=Xmin regions. It is found that total integrated energy flux over the boundary is nearly balanced between injection and escape, and flank contributions dominate the Poynting flux injection. Poynting flux dominates net energy input, while hydrodynamic flux dominates energy output. Surface fluctuations contribute significantly to net energy transfer and comparison with the Shue model reveals varying levels of cylindrical asymmetry in the magnetopause flank throughout the event. Finally existing energy coupling proxies such as the Akasofu ϵ parameter and Newell coupling function are compared with the energy transfer results.

Shear layer synchronization of aerodynamically isolated opposite cavities due to acoustic resonance excitation

Flow over rectangular cavities can become unstable and excite the acoustic modes of the surrounding duct, resulting in severe noise and vibration. In this work, acoustic resonance excitation by two opposite and aerodynamically isolated rectangular cavities is experimentally and numerically investigated to identify the effect of the flow-acoustic coupling on the synchronization of shear layer instabilities. Compressible unsteady Reynolds-averaged Navier–Stokes simulation is used to model the self-excitation of resonance and characterize the fully coupled flow and acoustic fields. Moreover, the location and the strength of the acoustic sources and sinks are evaluated using Howe's integral formulation of the aerodynamic sound. It is revealed that double symmetric cavities generate a higher rate of acoustic energy transfer due to the synchronization of the shear layer instabilities over the two cavities in an antisymmetric pattern, leading to a stronger acoustic resonance than all other cases. On the other hand, the two shear layers over two opposite cavities with different aspect ratios were mismatched in phase and vortex convection velocity. As a result, the net energy transfer in an asymmetric cavity configuration occurred at a similar rate to a single rectangular cavity, driving a weaker acoustic resonance excitation.

Scale dependence and cross-scale transfer of kinetic energy in compressible hydrodynamic turbulence at moderate Reynolds numbers

We investigate properties of the scale dependence and cross-scale transfer of kinetic energy in compressible three-dimensional hydrodynamic turbulence, by means of two direct numerical simulations of decaying turbulence with initial Mach numbers M = 1/3 and M = 1, and with moderate Reynolds numbers, R_lambda ~ 100. The turbulent dynamics is analyzed using compressible and incompressible versions of the dynamic spectral transfer (ST) and the Karman-Howarth-Monin (KHM) equations. We find that the nonlinear coupling leads to a flux of the kinetic energy to small scales where it is dissipated; at the same time, the reversible pressure-dilatation mechanism causes oscillatory exchanges between the kinetic and internal energies with an average zero net energy transfer. While the incompressible KHM and ST equations are not generally valid in the simulations, their compressible counterparts are well satisfied and describe, in a quantitatively similar way, the decay of the kinetic energy on large scales, the cross-scale energy transfer/cascade, the pressure dilatation, and the dissipation. There exists a simple relationship between the KHM and ST results through the inverse proportionality between the wave vector k and the spatial separation length l as k l ~ 3^1/2. For a given time the dissipation and pressure-dilatation terms are strong on large scales in the KHM approach whereas the ST terms become dominant on small scales; this is owing to the complementary cumulative behavior of the two methods. The effect of pressure dilatation is weak when averaged over a period of its oscillations and may lead to a transfer of the kinetic energy from large to small scales without a net exchange between the kinetic and internal energies. Our results suggest that for large-enough systems there exists an inertial range for the kinetic energy cascade ...

Local Coupling and Conversion of Surface Waves due to Earth’s Rotation. Part 2: Numerical Examples

Summary Rotation of the Earth affects the propagation of seismic waves. The global coupling of spheroidal and toroidal modes by the Coriolis force over time is described by normal-mode theory. The local action of the Coriolis force on the propagation of surface waves can be described by coefficients for the coupling between propagating Rayleigh and Love waves as derived by (Landau & Lifshitz 1959). Using global wavefield simulations we show how the Coriolis force leads to coupling and conversion between both surface wave types depending on latitude, propagation direction, frequency, and local velocity structure. Surface wave coupling is most efficient for periods where the modes have similar phase velocities, a condition that is equivalent to the selection rules of the angular degree in the normal-mode framework, a phenomenon that we refer to as resonant coupling. In the time-domain, resonant coupling gradually converts energy from one wave type–Rayleigh waves or Love wave–into the other, which then propagates independently. Due to the lateral heterogeneity, the condition of equal phase velocity renders the rotational coupling location-dependent. East-west oriented ray path segments and segments at high latitudes (across the Poles) only weakly couple the fundamental mode Rayleigh and Love waves while coupling is strongest for propagation along the meridians across the equator. At 250 s period, where Love and Rayleigh waves have similar phase velocities, the net energy transfer from Rayleigh to Love wave reaches about 10% for one orbit.

Fluctuation theorem and extended thermodynamics of turbulence.

Turbulent flows are out-of-equilibrium because the energy supply at large scales and its dissipation by viscosity at small scales create a net transfer of energy among all scales. This energy cascade is modelled by approximating the spectral energy balance with a nonlinear Fokker-Planck equation consistent with accepted phenomenological theories of turbulence. The steady-state contributions of the drift and diffusion in the corresponding Langevin equation, combined with the killing term associated with the dissipation, induce a stochastic energy transfer across wavenumbers. The fluctuation theorem is shown to describe the scale-wise statistics of forward and backward energy transfer and their connection to irreversibility and entropy production. The ensuing turbulence entropy is used to formulate an extended turbulence thermodynamics.

Stochastic electron acceleration in relativistic laser pulse and stationary periodic electric and magnetic fields

The mechanisms of stochastic electron acceleration in relativistic laser pulses and stationary periodic electric and magnetic fields are investigated by employing a new Hamiltonian approach. The new Hamiltonian is the dephasing rate between the electron and laser pulse such that it is time independent when the stationary fields are absent. The physics underlying stochastic electron motion is clearly revealed, and the conditions for triggering stochastic instability are obtained by finding the Chirikov-like mapping. It demonstrates that if the amplitudes of the stationary fields exceed some threshold values, the Hamiltonian can be randomly changed, and thus, net energy transfer between electrons and the laser radiation are possible. The maximum electron energy gained from the stochastic motion has a weak dependence on the amplitude of stationary fields and can significantly exceed the vacuum ponderomotive energy. All these analytical results have been confirmed by the numerical simulations.

Work done on a single-particle gas during an adiabatic compression and expansion process.

We compute the average work done by an external agent, driving a piston at constant speed, over a single-particle gas going through an adiabatic compression and expansion process. To do so, we get the analytical expression relating the number of collisions between the piston and the particle with the position of the piston during the process. The ergodicity breaking of the system during the process is identified as the source of its irreversibility. In addition, we observe that by using particular initial distributions for the state of the particle, it is possible to preclude the possibility of a net energy transfer from the agent to the particle during the process.

Large eddy simulation investigation of the canonical shock–turbulence interaction

High resolution large eddy simulations (LES) are performed to study the interaction of a stationary shock with fully developed turbulent flow. Turbulent statistics downstream of the interaction are provided for a range of weakly compressible upstream turbulent Mach numbers $M_{t}=0.03{-}0.18$, shock Mach numbers $M_{s}=1.2{-}3.0$ and Taylor-based Reynolds numbers $Re_{\unicode[STIX]{x1D706}}=20{-}2500$. The LES displays minimal Reynolds number effects once an inertial range has developed for $Re_{\unicode[STIX]{x1D706}}>100$. The inertial range scales of the turbulence are shown to quickly return to isotropy, and downstream of sufficiently strong shocks this process generates a net transfer of energy from transverse into streamwise velocity fluctuations. The streamwise shock displacements are shown to approximately follow a $k^{-11/3}$ decay with wavenumber as predicted by linear analysis. In conjunction with other statistics this suggests that the instantaneous interaction of the shock with the upstream turbulence proceeds in an approximately linear manner, but nonlinear effects immediately downstream of the shock significantly modify the flow even at the lowest considered turbulent Mach numbers.

Observed Energy Exchange between Low-Frequency Flows and Internal Waves in the Gulf of Mexico

AbstractA long-term mooring array deployed in the northern Gulf of Mexico is used to analyze energy exchange between internal waves and low-frequency flows. In the subthermocline (245–450 m), there is a noticeable net energy transfer from low-frequency flows, defined as having a period longer than six inertial periods, to internal waves. The magnitude of energy transfer rate depends on the Okubo–Weiss parameter of low-frequency flows. A permanent energy exchange occurs only when the Okubo–Weiss parameter is positive. The near-inertial internal waves (NIWs) make major contribution to the energy exchange owing to their energetic wave stress and relatively stronger interaction with low-frequency flows compared to the high-frequency internal waves. There is some evidence that the permanent energy exchange between low-frequency flows and NIWs is attributed to the partial realization of the wave capture mechanism. In the periods favoring the occurrence of the wave capture mechanism, the horizontal propagation direction of NIWs becomes anisotropic and exhibits evident tendency toward that predicted from the wave capture mechanism, leading to pronounced energy transfer from low-frequency flows to NIWs.