Forward Cascade Research Articles

Phase ordering, topological defects, and turbulence in the three-dimensional incompressible Toner-Tu equation.

We investigate the phase-ordering dynamics of the incompressible Toner-Tu equationin three dimensions. We show that the phase ordering proceeds via defect merger events and the dynamics is controlled by the Reynolds number Re. At low Re, the dynamics is similar to that of the Ginzburg-Landau equation. At high Re, turbulence controls phase ordering. In particular, we observe a forward energy cascade from the coarsening length scale to the dissipation scale, clustering of defects, and multiscaling in velocity correlations.

Interaction between Upper-Ocean Submesoscale Currents and Convective Turbulence

Abstract The interaction between upper-ocean submesoscale fronts evolving with coherent features, such as vortex filaments and eddies, and convective turbulence generated by surface cooling of varying magnitude is investigated. Here, we decompose the flow into finescale (FS) and submesoscale (SMS) fields explicitly to investigate the energy pathways and the strong interaction between them. Most of the surface cooling flux is transferred to the FS kinetic energy through the FS buoyancy flux carried by the convective plumes. Overall, the SMS strengthens due to surface cooling. The frontogenetic tendency at the submesoscale increases, which counters the enhanced horizontal diffusion by convection-induced turbulence. Downwelling/upwelling strengthens, and the peak SMS vertical buoyancy flux increases as surface cooling is increased. Furthermore, the production of FS energy by SMS velocity gradients (the interscale transfer term, which mediates forward energy cascade) is significant, up to half of the production by convection. Examination of potential vorticity reveals that surface cooling promotes higher levels of secondary symmetric instability (SI), which coexists with the persistent baroclinic instability. The forward interscale transfer is found to increase in the regions with SI.

Turbulence kinetic energy transfers in direct numerical simulation of shock-wave–turbulence interaction in a compression/expansion ramp

A direct numerical simulation is performed for a supersonic turbulent boundary layer interacting with a compression/expansion ramp at an angle $\alpha =24^{\circ }$ , matching the same operating conditions of the direct numerical simulation by Priebe & Martín (J. Fluid Mech., vol. 699, 2012, pp. 1–49). The adopted numerical method relies on the high-order spectral difference scheme coupled with a bulk-based, low-dissipative, artificial viscosity for shock-capturing purposes (Tonicello et al., Comput. Fluids, vol. 197, 2020, 104357). Filtered and averaged fields are evaluated to study total kinetic energy transfers in the presence of non-negligible compressibility effects. The compression motions are shown to promote forward transfer of kinetic energy down the energy cascade, whereas expansion regions are more likely to experience backscatter of kinetic energy. A standard decomposition of the subgrid scale tensor in deviatoric and spherical parts is proposed to study the compressible and incompressible contributions in the total kinetic energy transfers across scales. On average, the correlation between subgrid scale dissipation and large-scale dilatation is shown to be caused entirely by the spherical part of the Reynolds stresses (i.e. the turbulent kinetic energy). On the other hand, subtracting the spherical contribution, a mild correlation is still noticeable in the filtered fields. For compressible flows, it seems reasonable to assume that the eddy-viscosity approximation can be a suitable model for the deviatoric part of the subgrid scale tensor, which is exclusively causing forward kinetic energy cascade on average. Instead, more complex models are likely to be needed for the spherical part, which, even in statistical average, provides an important mechanism for backscatter.

Comparison of feed forward and cascade forward neural networks for human action recognition

Humans can perform an enormous number of actions like running, walking, pushing, and punching, and can perform them in multiple ways. Hence recognizing a human action from a video is a challenging task. In a supervised learning environment, actions are first represented using robust features and then a classifier is trained for classification. The selection of a classifier does affect the performance of human action recognition. This work focuses on the comparison of two structures of the neural network, namely, feed forward neural network and cascade forward neural network, for human action recognition. Histogram of oriented gradients (HOG) and histogram of optical flow (HOF) are used as features for representing the actions. HOG represents the spatial features of the video while HOF gives motion features of the video. The performance of two neural network architectures is compared based on recognition accuracy. Well-known publically available datasets for action and interaction detection are used for testing. It is seen that, for human action recognition applications, feed forward neural network gives better results in terms of higher recognition accuracy than Cascade forward neural network.

λ-Navier-Stokes turbulence.

We investigate numerically the model proposed in Sahoo et al. (2017 Phys. Rev. Lett. 118, 164501) where a parameter λ is introduced in the Navier-Stokes equations such that the weight of homochiral to heterochiral interactions is varied while preserving all original scaling symmetries and inviscid invariants. Decreasing the value of λ leads to a change in the direction of the energy cascade at a critical value [Formula: see text]. In this work, we perform numerical simulations at varying λ in the forward energy cascade range and at changing the Reynolds number [Formula: see text]. We show that for a fixed injection rate, as [Formula: see text], the kinetic energy diverges with a scaling law [Formula: see text]. The energy spectrum is shown to display a larger bottleneck as λ is decreased. The forward heterochiral flux and the inverse homochiral flux both increase in amplitude as [Formula: see text] is approached while keeping their difference fixed and equal to the injection rate. As a result, very close to [Formula: see text] a stationary state is reached where the two opposite fluxes are of much higher amplitude than the mean flux and large fluctuations are observed. Furthermore, we show that intermittency as [Formula: see text] is approached is reduced. The possibility of obtaining a statistical description of regular Navier-Stokes turbulence as an expansion around this newly found critical point is discussed. This article is part of the theme issue 'Scaling the turbulence edifice (part 2)'.

Dyadic models for ideal MHD

We study two dyadic models for incompressible ideal magnetohydrodynamics, one with a uni-directional energy cascade and the other one with both forward and backward energy cascades. Global existence of weak solutions and local well-posedness are established for both models. In addition, solutions to the model with uni-directional energy cascade associated with positive initial data are shown to develop blow-up at a finite time. Moreover, a set of fixed points is found for each model. Linear instability about some particular fixed points is proved.

Inverse cascade suppression and shear-layer formation in magnetohydrodynamic turbulence subject to a guide field and misaligned rotation

Astrophysical flows are often subject to both rotation and large-scale background magnetic fields. Individually, each is known to two-dimensionalize the flow in the perpendicular plane. In realistic settings, both of these effects are simultaneously present and, importantly, need not be aligned. In this work, we numerically investigate three-dimensional forced magnetohydrodynamic turbulence subject to the competing effects of global rotation and a perpendicular background magnetic field. We focus on the case of a strong background field and find that increasing the rotation rate from zero produces significant changes in the structure of the turbulent flow. Starting with a two-dimensional inverse energy cascade at zero rotation, the flow first transitions to a forward cascade of kinetic energy, then to a shear-layer dominated regime and finally to a second shear-layer regime where the kinetic energy flux is strongly suppressed and the energy transfer is mediated by the induced magnetic field. We show that the first two transitions occur at distinct values of the Rossby number, and the third occurs at a distinct value of the Lehnert number. The three-dimensional results are confirmed using an asymptotic two-dimensional, three-component model, which allows us to extend our results to the planetary-relevant case of an arbitrary angle between the rotation vector and guide field. More generally, our results demonstrate that, when considering the simultaneous limits of strong rotation and a strong guide field, the order in which those limits are taken matters in the misaligned case.

Numerical Simulation of the Quasi-2D Turbulence on a Half Soap Bubble Heated at the Bottom

The soap bubble heated at the bottom is introduced as a novel quais two-dimensional turbulence. The curved geometry of the bubble brings the challenges for the Direct Numercial Simulations(DNS) of the turbulence on the bubble. In oder to overcome the difficulties due to the curved geometry, a numerical method based on the stereographic projection is implemented for the DNS of the soap bubble. The numerical method to compute the spectrum, the flux and the structure functions of the flows on the bubble are introduced in detail. Three different Rayleigh numbers at <inline-formula><tex-math id="M3">\begin{document}$Ra=3\times10^{7}, 3\times10^{9}, 3\times10^{11}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="amm-43-0143_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="amm-43-0143_M3.png"/></alternatives></inline-formula> are simulated based on present numerical methods. And the related spectrum, flux and structure functions are calculated. It is indicated that both the inversed energy cascade and forward enstrophy cascade are observed from all of the calculated cases. <inline-formula><tex-math id="M4">\begin{document}${\rm{Bo}}59$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="amm-43-0143_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="amm-43-0143_M4.png"/></alternatives></inline-formula> scaling law is found to fit the small scale fluctuations on the soap bubble. As the increase of Rayleigh number, the turbulent energy reduces for the large scale plumes, and the kinetic energy increases for the higher wave number structures.

Energy cascades in rapidly rotating and stratified turbulence within elongated domains

We study forced, rapidly rotating and stably stratified turbulence in an elongated domain using an asymptotic expansion at simultaneously low Rossby number $\mathit {Ro}\ll 1$ and large domain height compared with the energy injection scale, $h=H/\ell _{in}\gg 1$ . The resulting equations depend on the parameter $\lambda =(h \mathit {Ro} )^{-1}$ and the Froude number $\mathit {Fr}$ . An extensive set of direct numerical simulations (DNS) is performed to explore the parameter space $(\lambda,\mathit {Fr})$ . We show that a forward energy cascade occurs in one region of this space, and a split energy cascade outside it. At weak stratification (large $\mathit {Fr}$ ), an inverse cascade is observed for sufficiently large $\lambda$ . At strong stratification (small $\mathit {Fr}$ ) the flow becomes approximately hydrostatic and an inverse cascade is always observed. For both weak and strong stratification, we present theoretical arguments supporting the observed energy cascade phenomenology. Our results shed light on an asymptotic region in the phase diagram of rotating and stratified turbulence, which is difficult to attain by brute-force DNS.

Different mechanisms for the seasonal variations of the mesoscale eddy energy in the South China Sea

Using a recently developed functional analysis tool, Multiscale Window Transform (MWT) and the MWT-based theory of canonical transfer, this study investigates the dynamical processes responsible for the seasonal variability of the mesoscale eddies in the South China Sea (SCS). A three-scale energetics framework is employed, in which the original fields are decomposed into subfields on a nonstationary background flow window, a mesoscale eddy window and a high-frequency synoptic eddy window. Three local regions of high mesoscale eddy kinetic energy (EKE) levels, namely, the southwest of Taiwan Island (SWT), the southeast of Vietnam (SEV) and the northeast of the Natuna Island (NEN), are identified. The seasonal cycles of the mesoscale EKE in the three regions are not in phase, with peaks occurring around January, October and December, respectively. By diagnosing the canonical transfers between the background flow and the mesoscale eddies, we find that the seasonal cycle of the eddy variability in the SWT region is due to a mixed instability (baroclinic and barotropic instabilities), while barotropic instability plays a dominant role in determining the EKE seasonality in the SEV and NEN regions. This is quite different from the previous argument that baroclinic instability dominates the seasonal EKE in the SCS. The three-scale framework further reveals that high-frequency synoptic motions act to dissipate the lower-frequency mesoscale eddies through forward energy cascades. Besides the internal processes, external wind forcing is also found to influence the seasonal eddy variability, but is only limited to the NEN region. Our results highlight different mechanisms controlling the seasonal modulations of the mesoscale eddies in different regions of the SCS.

Flow structures, nonlinear inertial waves and energy transfer in rotating spheres

We investigate flow structures, nonlinear inertial waves and energy transfer in a rotating fluid sphere, using a Galerkin spectral method based on helical-wave decomposition (HWD). Numerical simulations of flows in a sphere are performed with different system rotation rates, where a large-scale forcing is employed. For the case without system rotation, the intense vortex structures are tube-like. When a weak rotation is introduced, small-scale structures are reduced and vortex tubes tend to align with the rotation axis. As the rotation rate increases, a large-scale anticyclonic vortex structure is formed near the rotation axis. The structure is shown to be led by certain geostrophic modes. When the rotation rate further increases, a cyclone and an anticyclone emerge from the top and bottom of the boundary, respectively, where two quasi-geostrophic equatorially symmetric inertial waves dominate the flow. Based on HWD, effects of spherical confinement on rotating turbulence are systematically studied. It is found that the forward cascade becomes weaker as the rotation increases. When the rotation rate becomes larger than some critical value, dual energy cascades emerge, with an inverse cascade at large scales and a forward cascade at small scales. Finally, the flow behavior near the boundary is studied, where the average boundary layer thickness gets smaller when system rotation increases. The flow behavior in the boundary layer is closely related to the interior flow structures, which create significant mass flux between the boundary layer and the interior fluid through Ekman pumping.

Existence of positive skewness of velocity gradient in early transition

In the statistical point of view, the skewness of the longitudinal velocity gradient is usually related to energy transfer in turbulence, for example, the Kolmogorov forward energy cascade in fully developed turbulence implies negative skewness, while Gaussian random noise and infinitesimal perturbations lead to zero skewness. We show by two DNS cases that, in the early transition stage, the skewness can be positive, in contrast to the energy cascade in equilibrium turbulence.

Oceanic Mesoscale Eddy Depletion Catalyzed by Internal Waves

AbstractThe processes leading to the depletion of oceanic mesoscale kinetic energy (KE) and the energization of near‐inertial internal waves are investigated using a suite of realistically forced regional ocean simulations. By carefully modifying the forcing fields we show that solutions where internal waves are forced have ∼ less mesoscale KE compared with solutions where they are not. We apply a coarse‐graining method to quantify the KE fluxes across time scales and demonstrate that the decrease in mesoscale KE is associated with an internal wave‐induced reduction of the inverse energy cascade and an enhancement of the forward energy cascade from sub‐to super‐inertial frequencies. The integrated KE forward transfer rate in the upper ocean is equivalent to half and a quarter of the regionally averaged near‐inertial wind work in winter and summer, respectively, with the strongest fluxes localized at surface submesoscale fronts and filaments.

The Role of Phylogenetics in Unravelling Patterns of HIV Transmission towards Epidemic Control: The Quebec Experience (2002-2020).

Phylogenetics has been advanced as a structural framework to infer evolving trends in the regional spread of HIV-1 and guide public health interventions. In Quebec, molecular network analyses tracked HIV transmission dynamics from 2002–2020 using MEGA10-Neighbour-joining, HIV-TRACE, and MicrobeTrace methodologies. Phylogenetics revealed three patterns of viral spread among Men having Sex with Men (MSM, n = 5024) and heterosexuals (HET, n = 1345) harbouring subtype B epidemics as well as B and non-B subtype epidemics (n = 1848) introduced through migration. Notably, half of new subtype B infections amongst MSM and HET segregating as solitary transmissions or small cluster networks (2–5 members) declined by 70% from 2006–2020, concomitant to advances in treatment-as-prevention. Nonetheless, subtype B epidemic control amongst MSM was thwarted by the ongoing genesis and expansion of super-spreader large cluster variants leading to micro-epidemics, averaging 49 members/cluster at the end of 2020. The growth of large clusters was related to forward transmission cascades of untreated early-stage infections, younger at-risk populations, more transmissible/replicative-competent strains, and changing demographics. Subtype B and non-B subtype infections introduced through recent migration now surpass the domestic epidemic amongst MSM. Phylodynamics can assist in predicting and responding to active, recurrent, and newly emergent large cluster networks, as well as the cryptic spread of HIV introduced through migration.

Diagnosing Cross‐Scale Kinetic Energy Exchanges From Two Submesoscale Permitting Ocean Models

AbstractFine‐scale motions (&lt;100 km) contribute significantly to the exchanges and dissipation of kinetic energy in the upper ocean. However, knowledge of ocean kinetic energy at fine‐scales (in terms of density and transfers) is currently limited due to the lack of sufficient observational data sets at these scales. The sea‐surface height measurements of the upcoming Surface Water and Ocean Topography (SWOT) altimeter mission should provide information on kinetic energy exchanges in the upper ocean down to 10–15 km. Numerical ocean models, able to describe ocean dynamics down to ∼10 km, have been developed in anticipation of the SWOT mission. In this study, we use two state‐of‐the‐art, realistic, North Atlantic simulations, with horizontal resolutions ∼1.5 km, to investigate the distribution and exchanges of kinetic energy at fine‐scales in the open ocean. Our results show that the distribution of kinetic energy at fine‐scales approximately follows the predictions of quasigeostrophic dynamics in summertime but is somewhat consistent with submesoscale fronts‐dominated regimes in wintertime. The kinetic energy spectral fluxes are found to exhibit both inverse and forward cascade over the top 1,000 m, with a maximum inverse cascade close to the average energy‐containing scale. The forward cascade is confined to the ocean surface and shows a strong seasonality, both in magnitude and range of scales affected. Our analysis further indicates that high‐frequency motions (&lt;1 day) play a key role in the forward cascade and that the estimates of the spectral fluxes based on geostrophic velocities fail to capture some quantitative aspects of kinetic energy exchanges across scales.

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

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.

WITHDRAWN: Prediction of water quality in municipal distribution system

In this study Feed Forward Back propagation (FFBP) and Cascade Feed Forward Back propagation (CFBP) algorithms have been compared for prediction of water quality in the distribution systems, so as make it tomeet the standards of sustainability. These algorithms have been used for forecasting Water Quality Index (WQI) in various zones of municipal distribution system by using pH, alkalinity, hardness, dissolved oxygen (DO), total solids (TS) and MPN as the input variables. Different ANN models were developed using training data set and tested in order to determine optimum number of neurons in the hidden layer, best fitting transfer function, optimum length of training dataset and best suited ANN algorithm. Further the developed ANN models were compared with multiple linear regression (MLR) technique, which is a commonly used statistical technique for modelling water quality variables. The study revealed that ANN model outperforms multiple regression technique for prediction of water quality in the distribution system and it is a robust tool for understanding the poorly defined relations between water quality variables and WQI in municipal distribution system.

A cascade hybrid PSO feed-forward neural network model of a biomass gasification plant for covering the energy demand in an AC microgrid

Agriculture and forestry crop residues represent more than half of the world's residual biomass; these residues turn into synthesis gas (syngas) and are used for power generation. Including Syngas Gensets into hybrid renewable microgrids for electricity generation is an interesting alternative, especially for rural communities where forest and agricultural waste are abundant. However, energy demand is not constant throughout the day. The variations in the energy demand provoke changes in both gasification plant efficiency and biomass consumption. This paper presents an Artificial Neural Network (ANN) based model hybridized with a Particle Swarm Optimization (PSO) algorithm for a Biomass Gasification Plant (BGP) that allows estimating the amount of biomass needed to produce the required syngas to meet the energy demand. The proposed model is compared with two traditional models of ANNs: Feed Forward Back Propagation (FF-BP) and Cascade Forward Propagation (CF-P). ANNs are trained in MATLAB software using a set of historical real data from a BGP located in the Distributed Energy Resources Laboratory of the Universitat Politècnica de València in Spain. The model performance is validated using the Mean Squared Error (MSE) and linear regression analysis. The results show that the proposed model performs 23.2% better in terms of MSE than de other models. The tunning parameters of the optimal PSO algorithm for this application were found. Finally, the model was validated to predict the necessary biomass and syngas to cover the energy demand.

Spatial and Temporal Characteristics of the Submesoscale Energetics in the Gulf of Mexico

AbstractThe submesoscale energetics of the eastern Gulf of Mexico (GoM) are diagnosed using outputs from a 1/48° MITgcm simulation. Employed is a recently developed, localized multiscale energetics formalism with three temporal-scale ranges (or scale windows), namely, a background flow window, a mesoscale window, and a submesoscale window. It is found that the energy cascades are highly inhomogeneous in space. Over the eastern continental slope of the Campeche Bank, the submesoscale eddies are generated via barotropic instability, with forward cascades of kinetic energy (KE) following a weak seasonal variation. In the deep basin of the eastern GoM, the submesoscale KE exhibits a seasonal cycle, peaking in winter, maintained via baroclinic instability, with forward available potential energy (APE) cascades in the mixed layer, followed by a strong buoyancy conversion. A spatially coherent pool of inverse KE cascade is found to extract energy from the submesoscale KE reservoir in this region to replenish the background flow. The northern GoM features the strongest submesoscale signals with a similar seasonality as seen in the deep basin. The dominant source for the submesoscale KE during winter is from buoyancy conversion and also from the forward KE cascades from mesoscale processes. To maintain the balance, the excess submesoscale KE must be dissipated by smaller-scale processes via a forward cascade, implying a direct route to finescale dissipation. Our results highlight that the role of submesoscale turbulence in the ocean energy cycle is region and time dependent.

Lattice Boltzmann Method for Marangoni forcing soap film

Marangoni surface tension forcing soap film is numerically solved by Lattice Boltzmann Method (LBM). A delicate false force term in the LBM equation is proposed to describe the Marangoni forcing soap film. The validity of LBM is elucidated by the linear theory of surface tension profile as a function of the vertical position of the soap film. The effect of thickness on the statistical behaviors of the Marangoni forcing soap film is discussed from three aspects: the energy spectrum, energy transfer and intermittency. It is found that the scaling behavior of energy spectrum is independent of the scaling constant of thickness [Formula: see text] where the range of [Formula: see text] is from 0.2 to 0.3. The scaling behavior of energy spectrum is [Formula: see text], which is in accordance with the Kraichnan theory in the inverse cascade. In the large-scale range, the energy flux cascades to the small scale which is called as a forward cascade process. In this scale range, more energy flux cascades to the small scale when the value of [Formula: see text] becomes larger. On the contrary, the backward cascade is involved in the small-scale range of the thinned film where more energy transfers to the large scale as the value of [Formula: see text] is smaller. The intermittency measured by PDF of the velocity increment exists in the turbulent soap film. The universal scaling law of the velocity structure function is identical with the 3D S-L intermittency model and our 2D intermittency theory.