Energy Cascade Research Articles

Direct numerical simulation of bubble rising in turbulence

We describe the rising trajectory of bubbles in isotropic turbulence and quantify the slowdown of the mean rise velocity of bubbles with sizes within the inertial subrange. We perform direct numerical simulations of bubbles, for a wide range of turbulence intensity, bubble inertia and deformability, with systematic comparison with the corresponding quiescent case, with Reynolds number at the Taylor microscale from 38 to 77. Turbulent fluctuations randomise the rising trajectory and cause a reduction of the mean rise velocity $\tilde {w}_b$ compared with the rise velocity in quiescent flow $w_b$ . The decrease in mean rise velocity of bubbles $\tilde {w}_b/w_b$ is shown to be primarily a function of the ratio of the turbulence intensity and the buoyancy forces, described by the Froude number $Fr=u'/\sqrt {gd}$ , where $u'$ is the root-mean-square velocity fluctuations, $g$ is gravity and $d$ is the bubble diameter. The bubble inertia, characterised by the ratio of inertial to viscous forces (Galileo number), and the bubble deformability, characterised by the ratio of buoyancy forces to surface tension (Bond number), modulate the rise trajectory and velocity in quiescent fluid. The slowdown of these bubbles in the inertial subrange is not due to preferential sampling, as is the case with sub-Kolmogorov bubbles. Instead, it is caused by the nonlinear drag–velocity relationship, where velocity fluctuations lead to an increased average drag. For $Fr > 0.5$ , we confirm the scaling $\tilde {w}_b / w_b \propto 1 / Fr$ , as proposed previously by Ruth et al. (J. Fluid Mech., vol. 924, 2021, p. A2), over a wide range of bubble inertia and deformability.

In-situ observations of the three-dimensional energy cascade rate and Yaglom flux in the Earth’s magnetosheath

Abstract Measuring the energy cascade rate in space plasmas is a challenging task for several reasons. This quantity is (i) inherently three-dimensional (ii) scale-dependent, (iii) anisotropic in the interplanetary plasma, and (iv) requires measurements of plasma parameters in at least four points. Here, it is shown how three of these problems have been addressed by applying the novel lag polyhedra derivative ensemble (LPDE) technique to the magnetospheric multiscale (MMS) mission in the Earth’s magnetosheath. In particular, this technique solves the full vectorial Yaglom equation, handling problem (i), does not require the assumption of isotropy, solving problem (iii), while the application to MMS addresses constraint (iv).

The generalized quasilinear approximation of two-dimensional Rayleigh–Bénard convection

In the generalized quasilinear approximation (GQLA) (Marston et al., Phys. Rev. Lett., vol. 116, 2016, 214501), a threshold wavenumber ( $k_0$ ) in the direction of translational symmetry segregates the total into large- ( $l$ ) and small-scale ( $h$ ) fields. While the governing equation for the large-scale field is fully nonlinear, that for the small scales is linearized with respect to the large-scale field. In addition, some nonlinear triad interactions are omitted in the GQLA. Herein, the GQLA is applied to two-dimensional planar Rayleigh–Bénard convection (RBC). A scale separation between the large-scale convection rolls and small-scale turbulent fluctuations is typical in RBC. The present work explores the efficacy of GQLA in capturing the scale-by-scale energy transfer processes in RBC. The initial condition for the GQLA simulations was either the statistically stationary state obtained in direct numerical simulation (DNS) or random fluctuations superimposed on the linear conductive temperature profile and $\boldsymbol {u}=0$ . The GQLA simulations can capture the convection rolls for $k_0$ larger than or equal to the dominant wavenumber for thermal driving of the flow ( $k_0 \ge k_{\hat {Q}}$ ). Additionally, the GQLA emulates the fully nonlinear dynamics for $k_0$ larger than or equal to the first harmonic of the convection-roll wavenumber ( $k_0 \ge 2k_{roll}$ ). In the intermediate regime with $2k_{roll} > k_0 \ge k_{\hat {Q}}$ , the dynamics captured in GQLA simulations is different from the DNS. In DNS, two primary energy transfer processes dominate: (i) the energy transfer to/from the convection rolls and (ii) the scale-by-scale inverse kinetic energy and forward thermal energy cascades mediated by the convection rolls. The fully nonlinear dynamics is emulated by GQLA when these energy transfer processes are faithfully reproduced. Utilizing the framework of altering the triad interactions in GQLA, an additional intrusive calculation, including target triad interactions, is performed here to study their influence. This intrusive calculation shows that the convection rolls are not captured in GQLA for $k_0 < k_{\hat {Q}}$ because of the exclusion of the $h \to l \to l$ and $l \to h \to h$ triad interactions in GQLA. The inclusion of these triad interactions in the intrusive calculation yields the convection rolls, and the reproduced dynamics is similar to that of the intermediate GQLA regime with $2k_{roll} > k_0 \ge k_{\hat {Q}}$ .

On the Growth and Evolution of Nocturnal Ionospheric Irregularities Using HF Radar Observations Along With Digisonde and GNSS Data Over Trivandrum, India

AbstractThe growth and evolution of nocturnal ionospheric plasma irregularities are analyzed over the geomagnetic equatorial station Trivandrum (8.5°N, 77°E, dip latitude 1.9°N) using multi‐instrumental techniques during various seasons of moderate and high solar activity periods. Irregularities are classified into three categories based on their structure and the vertical extent of radar backscattered echoes as Bottom Type, Top Side, and Bottom Type‐Top Side structures. The presence or absence of energy cascading across different scale sizes is identified from the presence of irregularities as Equatorial Spread F (ESF) in digisonde, scintillation in GNSS and backscattered echoes in HF radar with the signals manifesting sequentially or otherwise in these instruments. Threshold values of the duration (2.25 hr) and altitudinal extent (430 km) of ESF irregularities (observed with the digisonde) required for effective energy cascading across scale sizes are identified. The bottom type irregularity layers are observed to form in the equatorial region, Trivandrum, when the post‐sunset F region height varied within the range of 280–370 km which is broader in comparison to those observed at low latitudes. An empirical model is developed using post‐sunset ionospheric height to predict the maximum altitudinal extent of ESF irregularities. This serves as an indicator of the energy cascading process across scale sizes. The altitudinal extent of irregularities predicted by the empirical model also serves as a proxy for the occurrence of plasma bubbles, which has significant adverse implications for communication and navigation systems.

Research on control strategy of electric vehicle thermal management system motor

Abstract The low efficiency and difficulty in low-temperature heating are the challenges currently faced by the thermal management system of new energy vehicles. A multi-heat source vehicle thermal management system for waste heat cascade recovery and utilization was proposed, and the performance of the vehicle thermal management system was studied through a combination of component testing and one-dimensional simulation. Based on a one-dimensional simulation model, the characteristics of the motor waste heat source are analyzed. The increase in the inlet water temperature of the motor coolant will lead to enhanced heat dissipation of the motor to the air, resulting in a waste of motor waste heat. Based on the results of the analysis, an energy cascade management strategy is constructed. The optimal heating mode is selected by collecting temperature signals such as motors, and the cut-off valve is controlled through logic gates to achieve flexible switching of different modes. The system effectively reduces the energy consumption of thermal management systems, which is of great significance for developing thermal management systems for new energy vehicles.

A two-stage deep learning architecture for detection global coastal and offshore submesoscale ocean eddy using SDGSAT-1 multispectral imagery

Submesoscale ocean eddies are essential oceanic phenomenon that control and influence the ocean energy cascade. Most existing eddy detection methods rely on low-resolution satellite altimeter data, which fail to capture submesoscale ocean features and oceanographic phenomena in shallow water. Introducing high-resolution multispectral data can alleviate these problems, yet it has been largely overlooked. A generalized and efficient deep learning architecture that combines developments in deep learning with Sustainable Development Goals Science Satellite 1 (SDGSAT-1) multispectral data from earth observations offers a potential pathway for more fine detection of ocean eddies. Considering that oceanic eddy exhibits spatially sparse characteristics on high-resolution remote sensing scenes, the oceanic eddy detection (OED) model suitable for global coastal and offshore regions is divided into two stages: eddy information judgment and eddy position determination. Correspondingly, SDGSAT-1 multispectral data from November 2021 to December 2022 were carried out to construct two submesoscale eddy datasets for training and testing each stage model. The union validation of multiple metrics demonstrates that the proposed OED model and its stage models achieve state-of-the-art (SOTA) performance, especially in optically complex coastal and offshore waters. We applied the model to real-world scenes captured by SDGSAT-1 in 2023, and found that the detected results were mainly located at the water depth below 200 m. The authenticity of the recognition results is validated using sea surface chlorophyll concentration, temperature, and topography data, indicating that the OED model has achieved remarkable effectiveness under various sea conditions. In addition, the temporal distributions and statistical characteristics of detected submesoscale eddies are analyzed over an extended period (November 2021 to November 2023). Finally, HISEA-2, Landsat-9, and Sentinel-2 served as testing grounds to validate the generalization of the proposed methodology, with experimental results demonstrating that the OED model possesses significant developmental potential for multi-source remote sensing data. This paper presents a comprehensive deep learning framework for the global-scale detection of submesoscale eddies and underscores the pivotal role of high-resolution multispectral imagery as an innovative data source for global coastal and offshore eddy identification.

Gas Transfer Across Air‐Water Interfaces in Inland Waters: From Micro‐Eddies to Super‐Statistics

AbstractIn inland water covering lakes, reservoirs, and ponds, the gas exchange of slightly soluble gases such as carbon dioxide, dimethyl sulfide, methane, or oxygen across a clean and nearly flat air‐water interface is routinely described using a water‐side mean gas transfer velocity , where overline indicates time or ensemble averaging. The micro‐eddy surface renewal model predicts , where is the molecular Schmidt number, is the water kinematic viscosity, and is the waterside mean turbulent kinetic energy dissipation rate at or near the interface. While has been reported across a number of data sets, others report large scatter or variability around this value range. It is shown here that this scatter can be partly explained by high temporal variability in instantaneous around , a mechanism that was not previously considered. As the coefficient of variation in increases, must be adjusted by a multiplier that was derived from a log‐normal model for the probability density function of . Reported variations in with a macro‐scale Reynolds number can also be partly attributed to intermittency effects in . Such intermittency is characterized by the long‐range (i.e., power‐law decay) spatial auto‐correlation function of . That varies with a macro‐scale Reynolds number does not necessarily violate the micro‐eddy model. Instead, it points to a coordination between the macro‐ and micro‐scales arising from the transfer of energy across scales in the energy cascade.

Two-dimensional Rayleigh–Bénard convection without boundaries

We study the effects of Prandtl number $\mathit {Pr}$ and Rayleigh number $\mathit {Ra}$ in two-dimensional Rayleigh–Bénard convection without boundaries, i.e. with periodic boundary conditions. For Prandtl numbers in the range $10^{-3} \leqslant \mathit {Pr} \leqslant 10^2$ , the viscous dissipation scales as $\epsilon _\nu \propto \mathit {Pr}^{1/2}\mathit {Ra}^{-1/4}$ , which is based on the observation that enstrophy $\langle {\omega ^2}\rangle \propto \mathit {Pr}^0 \mathit {Ra}^{1/4}$ , and the Nusselt number tends to follow the ‘ultimate’ scaling $\mathit {Nu} \propto \mathit {Pr}^{1/2}\mathit {Ra}^{1/2}$ for all values of $\mathit {Pr}$ considered. The inverse cascade of kinetic energy forms the power-law spectrum $\hat {E}_u(k) \propto k^{-2.3}$ , which is close to $k^{-11/5}$ proposed by the Bolgiano–Obukhov (BO) scaling. The potential energy flux is not constant, in contrast to one of the main assumptions underlying the BO phenomenology. So, the direct cascade of potential energy forms the power-law spectrum $\hat {E}_\theta (k) \propto k^{-1.2}$ , which deviates from the expected $k^{-7/5}$ . Finally, at $\mathit {Pr} \to 0$ and $\infty$ , we find that the dynamics is dominated by vertically oriented elevator modes that grow without bound, even at high Rayleigh numbers and with large-scale dissipation present.

Intensification of submesoscale frontogenesis and forward energy cascade driven by upper-ocean convergent flows

Upper-ocean fronts are an important component of the global climate system, regulating both the oceanic energy cycle and material transports. In the common paradigm, upper-ocean fronts are generated by frontogenesis at the mesoscale (20–300 km), driven predominantly by confluent horizontal flows initiated by a background straining field. However, the mechanisms by which this frontogenesis extends down to and influences the submesoscale (0.2–20 km), which dominates vertical transports in the ocean, are still understudied. Here, we provide direct observational evidence that submesoscale frontogenesis, defined as the rate at which submesoscale buoyancy gradients intensify, is closely linked to convergent flows. Analysis of year-long measurements by a mooring array in the North Atlantic indicates that both the upper-ocean frontogenetic rate and the horizontal convergence exhibit strong seasonality and scale dependence, with larger magnitudes in winter and at smaller horizontal scales (down to at least 2 km). The frontogenetic rate is found to correlate more strongly with horizontal convergence as the scale decreases, suggesting that convergent flows are the main driver of submesoscale frontogenesis. Crucially, a rapid forward cascade of kinetic energy and enhanced vertical velocities preferentially occur during periods of submesoscale frontogenesis. Our findings highlight a mechanism underpinning the key role of submesoscale fronts in the oceanic kinetic energy cascade and as a focus of vertical transports, and call for a parameterization of such effects in climate-scale ocean models.

Evaluation of an Unsteady Yaw, Gust, and Broadband Turbulence Generation System for Closed-Loop Automotive Wind Tunnels

<div>This study investigates the flow characteristics in the test section of a model-scale, three-quarters open-jet, closed-loop return wind tunnel equipped with a novel device featuring three subsystems to generate transient yaw, gusts, and turbulence. The effect of each subsystem on the resulting turbulent and unsteady flows is evaluated individually and simultaneously. It is demonstrated that this new turbulence generation system can generate yaw distributions with standard deviations ranging from 2.1° to 8.0°. This replicates a wide range of on-road yaw behavior. Additionally, the subsystems can activate transient yaw events and unsteady gusts. Frequency sweeping was demonstrated to fill a wide range of low-frequency spectra, which helps recreate the on-road flow spectra in wind tunnels. Unsteady gusts of more than 15% of the mean flow velocity were achieved. The active turbulence subsystem generates turbulence levels from a few percent, passively, to over 20% intensity levels actively, with tailorable levels depending on input parameters to the active grid. Combined, the subsystems were demonstrated to achieve a wide range of yaw distributions with different standard deviations and features of the on-road turbulence spectrum, from low-frequency events to broadband turbulence with significant inertial subrange within the model-scale wind tunnel.</div>

Modeling of Liquefied Natural Gas Cold Power Generation for Access to the Distribution Grid

Cold energy generation is an important part of liquefied natural gas (LNG) cold energy cascade utilization, and existing studies lack a specific descriptive model for LNG cold energy transmission to the AC subgrid. Therefore, this paper proposes a descriptive model for the grid-connected process of cold energy generation at LNG stations. First, the expansion kinetic energy transfer of the intermediate work mass is derived and analyzed in the LNG unipolar Rankine cycle structure, the mathematical relationship between the turbine output mechanical power and the variation in the work mass flow rate and pressure is established, and the variations in the LNG heat exchanger temperature difference, seawater flow rate, and the turbine temperature difference in the cycle system are investigated. Secondly, based on the fifth-order equation of state of the synchronous generator, the expressions of its electromagnetic power, output AC frequency, and voltage were analyzed. Finally, the average equivalent models of the machine-side and grid-side converters are established using a direct-fed grid-connected structure, thus forming a descriptive model of the overall drive process. The ORC model is built in Aspen HYSIS to obtain the time series expression of the torque output of the turbine; based on the ORC output torque, the permanent magnet synchronous generator (PMGSG) as well as the direct-fed grid-connected structure are built in MATLAB/Simulink, and the active power and current outputs of the grid-following-type voltage vector control method and the grid-forming-type power-angle synchronous control method are also verified.

Depth profiling of implanted D in silicates: Contribution of solar wind protons to water in the Moon and terrestrial planets

The solar wind protons implanted in silicate material and combined with oxygen are considered crucial for forming OH/H O on the Moon and other airless bodies. This process may also have contributed to hydrogen delivery to planetary interiors through the accretion of micrometre-sized dust and planetesimals during early stages of the Solar System. This paper experimentally investigates the depth distribution of solar wind protons in silicate materials and explores the mechanisms that influence this profile. We simulated solar wind irradiation by implanting 3 keV D ions in three typical silicates (olivine, pyroxene, and plagioclase) at a fluence of sim 1.4 × 10 ions/cm . Fourier transform infrared spectroscopy was used to analyse chemical bond changes, while transmission electron microscopy (TEM) characterised microstructural modifications. Nanoscale secondary ion mass spectrometry (NanoSIMS) was employed to measure the D/ O ratio and determine the depth distribution of implanted deuterium. The newly produced OD band (at 2400–2800 cm –1 ) in the infrared spectrum reveals the formation of O–D bonds in the irradiated silicates. The TEM and NanoSIMS results suggest that over 73<!PCT!> of the implanted D accumulated in fully amorphous rims with a depth of 70 nm, while 25<!PCT!> extended inwards to sim 190 nanometres, resulting in partial amorphisation. The distribution of these deuterium particles is governed by the collision processes of the implanted particles, which involve factors such as initial energy loss, cascade collisions, and channelling effects. Furthermore, up to 2<!PCT!> of the total implanted D penetrated the intact lattice via diffusion, reaching depths ranging from hundreds of nanometres to several micrometres. Our results suggest that implanted solar wind protons can be retained in silicate interiors, which may significantly affect the hydrogen isotopic composition in extraterrestrial samples and imply an important source of hydrogen during the formation of terrestrial planets.

Transportation of Liquefied Natural Gas (LNG) via Long-Distance Low-Temperature Pipeline and Cascade Utilization of Cold Energy

In addition to methane, liquefied natural gas (LNG) typically contains valuable light hydrocarbons such as ethane, propane, and butane. Establishing LNG receiving stations for imported LNG can effectively alleviate regional energy supply-demand conflicts, optimize energy consumption structures, promote sustainable regional economic development, and improve ecological environments. The technology for long-distance low-temperature pipeline transportation of LNG facilitates the efficient transfer and cascading utilization of the cold energy contained in LNG, allowing for deep coupling with cold networks and natural gas pipelines, thereby promoting the integrated development of LNG, cold energy, and natural gas transportation. This paper systematically summarizes the current status of LNG long-distance low-temperature pipeline transportation technology, cold energy cascading utilization technology, pipeline regulation technology, and multi-network integration technology. It analyzes the key challenges these technologies face under new strategies and looks ahead to future development trends, aiming to provide scientific insights and directions for the application of LNG long-distance low-temperature transportation and multi-network integration in China.

Energy transfer from internal solitary waves to turbulence via high-frequency internal waves: seismic observations in the northern South China Sea

Abstract. The shoaling and breaking of internal waves (IWs) are critical processes in the ocean's energy cascade and mixing. Using seismic data, we observed high-frequency internal waves (HIWs), which were primarily distributed in the depth range of 79–184 m. Their amplitude scale is O (10 m), with half-height widths ranging from 154 to 240 m. The shoaling thermocline and gentle slope with a low internal Iribarren number suggest that observed high-frequency internal waves are likely a result of fission. The remote sensing data support this point. Instability estimations showed that, due to the strong vertical shear, the Richardson number (Ri) in the range of 20–30 km was less than 0.25, and Kelvin–Helmholtz (KH) billows can be found in the seismic transect, suggesting that these waves were unstable and might dissipate rapidly. We used the seismic data to estimate diapycnal mixing, and we found that the HIWs can enhance diapycnal mixing, averaging 10−4 m2 s−1. The maximum mixing value is up to 10−3 m2 s−1, and it is associated with the breaking of IWs caused by the strong shear. The results show a new energy cascade route from shoaling internal solitary waves (ISWs) to turbulence, i.e., the fission of ISWs into HIWs, which improves our knowledge of ISW energy dissipation and their roles in improved mixing in the northern South China Sea.

Analysis of Wind Power Fluctuation in Wind Turbine Wakes Using Scale-Adaptive Large Eddy Simulation

In large wind farms, the interaction of atmospheric turbulence and wind turbine wakes leads to complex vortex dynamics and energy dissipation, resulting in reduced wind velocity and subsequent loss of wind power. This study investigates the influence of vortex stretching on wind power fluctuations within wind turbine wakes using scale-adaptive large eddy simulation. The proper orthogonal decomposition method was employed to extract the most energetic contributions to the wind power spectra. Vertical profiles of mean wind speed, Reynolds stresses, and dispersive stresses were analyzed to assess energy dissipation rates. Our simulation results showed excellent agreement when compared with wind tunnel data and more advanced numerical models, such as the actuator line model and the actuator line model with hub and tower effects. This highlights the important role of coherent and energetic flow components in the spectral behavior of wind farms. The findings indicate a persistent energy cascading length scale in the wake of wind turbines, emphasizing the vertical transport of energy to turbine blades. These results complement existing literature and provide new insights into the dynamics of wind turbine wakes and their impact on wind farm performance.

Assessment of a multiphase formulation of one-dimensional turbulence using direct numerical simulation of a decaying turbulent interfacial flow

The interaction between turbulence and surface tension is studied numerically using the one-dimensional-turbulence (ODT) model. ODT is a stochastic model simulating turbulent flow evolution along a notional one-dimensional line of sight by applying instantaneous maps that represent the effects of individual turbulent eddies on property fields. It provides affordable high resolution of interface creation and property gradients within each phase, which are key for capturing the local behavior as well as overall trends, and has been shown to reproduce the main features of an experimentally determined regime diagram for primary jet breakup. Here ODT is used to investigate the interaction of turbulence with an initially planar interface. The notional flat interface is inserted into a periodic box of decaying homogeneous isotropic turbulence, simulated for a variety of turbulent Reynolds and Weber numbers. Unity density and viscosity ratios serve to focus solely on the interaction between fluid inertia and the surface-tension force. Statistical measures of interface surface density and spatial structure along the direction normal to the initial surface are compared to corresponding direct-numerical-simulation (DNS) data. Allowing the origin of the lateral coordinate system to follow the location of the median interface element improves the agreement between ODT and DNS, reflecting the absence of lateral nonvortical displacements in ODT. Beyond the DNS-accessible regime, ODT is shown to obey the predicted parameter dependencies of the Kolmogorov critical scale in both the inertial and dissipative turbulent-cascade subranges. Notably, the probability density function of local fluctuations of the critical scale is found to collapse to a universal curve across both subranges. Published by the American Physical Society 2024

Subgrid-scale model considering the inverse energy cascade using an artificial neural network

For the closure of the subgrid-scale (SGS) stress tensor, an artificial neural network (ANN)-based SGS model that takes account of the inverse energy cascade in isotropic turbulence is developed. The data required for training this ANN-based SGS model are provided by direct numerical simulation of isotropic turbulence with an inverse energy cascade. Two input features, the root mean square of the rate-of-strain tensor and the product of the eigenvalues of the rate-of-strain tensor, are employed to characterize the inverse energy cascade. An a priori test reveals that the ANN-based model adequately predicts the SGS stress tensor in the backward energy transfer process, and the predictive capability of the gradient model is found to be slightly poorer than that of the ANN-based model, while that of the Smagorinsky model is not satisfactory. In comparison with the gradient model, the ANN-based model even predicts a few backward energy transfer events in the stage of excessive energy dissipation. In addition, the off-diagonal component of the SGS stress tensor, rather than the diagonal component, may be intimately associated with the inverse energy cascade. The ANN-based SGS model presented here is expected to provide inspiration for future investigations of the construction of SGS models that take account of the inverse energy cascade.

Energy balance and scale truncation of the approximate deconvolution with correction

We present the similarity theory of Approximate Deconvolution with Correction (ADC) - a member of the recently proposed family of turbulence models called LES-C. This model stems from a combination of a well-known Approximate Deconvolution Model (ADM) with a defect correction procedure. We derive the energy equality for the ADC in a way that highlights the enhanced accuracy of the ADC, as compared to the ADM. Using the proposed definitions of the ADC energy and dissipation rates, we investigate the energy cascade of the ADC; we show that it correctly predicts the energy cascade in the inertial range, and acts to dissipate the small scales at a higher rate than the ADM. The micro-scale of the ADC is then found; we prove it to be larger than the micro-scale of the ADM, which also explains the previously established efficiency of the ADC.

A transformer-based convolutional method to model inverse cascade in forced two-dimensional turbulence

The present work proposes a novel transformer-based convolutional neural network (TransCNN) method to effectively model the inverse energy cascade in two dimensional (2D) turbulence. The TransCNN structure combines large-scale features extracted by transformer with small-scale features from convolutional layers, thus is considered suitable for multi-scale modeling. The novel TransCNN method has been applied to model sub-grid scale (SGS) stress for large-eddy simulation (LES) of 2D turbulence, under the extremely challenging situation that the LES grid is too coarse to resolve the external forcing scale. The data-driven model trained by the novel TransCNN structure is compared to two deep CNN models with varying complexities. All models exhibit proficiency during a priori tests. Notably, TransCNN surpasses its counterparts in predictive accuracy and generalizability in a posteriori tests. An investigation into the receptive fields reveals that the TransCNN model can efficiently leverage global information with the transformer structure, which is key to its superior performance in representing the inverse energy cascade in the 2D turbulent simulations.

Distinct Impacts of Topographic versus Planetary PV Gradients on Baroclinic Turbulence

Abstract The impacts of topographic versus planetary potential vorticity (PV) gradients on fully developed geostrophic turbulence are often treated as dynamically equivalent in theoretical understanding and parameterizations of ocean mesoscale turbulence. Using a suite of homogeneous, two-layer quasigeostrophic (QG) turbulence simulations, we identify similarities and distinctions of topographic versus planetary PV gradients in modulating turbulent eddy energy and fluxes. We show that, while an elevated background PV gradient can suppress geostrophic turbulence, a positive (negative) bottom slope with respect to the orientation of isopycnal slope barotropizes (debarotropizes) the turbulent energy at large scales, which contrasts with a dynamically inert planetary PV gradient in the modewise energy transfer. Then, in the presence of weak bottom drag, a positive slope energizes large-scale along-slope jets and limits small-scale barotropic eddies, both of which yield stronger eddy suppression effects than from a planetary PV gradient; by contrast, a negative slope hinders along-slope jet formation by enhancing the dual-energy cascade cycling, which alleviates the topographic suppression on eddies. In the presence of strong bottom drag, a positive slope elevates barotropic eddy energy, which further enhances the eddy-driven fluxes; by contrast, a negative slope confines turbulent energy to the baroclinic mode, which is strongly damped, causing further weakened turbulent energy and eddy fluxes. A flow regime captured by linear QG theories also emerges as the turbulent energy cascade is jointly suppressed by negative slopes and strong bottom drag. This study provides insights into parameterizing mesoscale eddy effects across sloping bathymetry in predictive ocean models.