Energy Cascade Research Articles

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.

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, we show 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).

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.

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.

Probing the physics of star formation (ProPStar)

Context. Turbulence is a key component of molecular cloud structure. It is usually described by a cascade of energy down to the dissipation scale. The power spectrum for subsonic incompressible turbulence is ∝k−5/3, while for supersonic turbulence it is ∝k−2. Aims. We determine the power spectrum in an actively star-forming molecular cloud, from parsec scales down to the expected magnetohydrodynamic (MHD) wave cutoff (dissipation scale). Methods. We analyzed observations of the nearby NGC 1333 star-forming region in three different tracers to cover the different scales from ∼10 pc down to 20 mpc. The largest scales are covered with the low-density gas tracer 13CO (1–0) obtained with a single dish, the intermediate scales are covered with single-dish observations of the C18O (3–2) line, while the smallest scales are covered in H13CO+ (1–0) and HNC (1–0) with a combination of NOEMA interferometer and IRAM 30m single-dish observations. The complementarity of these observations enables us to generate a combined power spectrum covering more than two orders of magnitude in spatial scale. Results. We derive the power spectrum in an active star-forming region spanning more than 2 decades of spatial scales. The power spectrum of the intensity maps shows a single power-law behavior, with an exponent of 2.9 ± 0.1 and no evidence of dissipation. Moreover, there is evidence that the power spectrum of the ions to have more power at smaller scales than the neutrals, which is opposite to the theoretical expectations. Conclusions. We show new possibilities for studying the dissipation of energy at small scales in star-forming regions provided by interferometric observations.

Rugged magneto-hydrodynamic invariants in weakly collisional plasma turbulence: Two-dimensional hybrid simulation results

Aims. We investigated plasma turbulence in the context of solar wind. We concentrated on properties of ideal second-order magneto-hydrodynamic (MHD) and Hall MHD invariants. Methods. We studied the results of a two-dimensional hybrid simulation of decaying plasma turbulence with an initial large cross helicity and a negligible magnetic helicity. We investigated the evolution of the combined energy and the cross, kinetic, mixed, and magnetic helicities. For the combined (kinetic plus magnetic) energy and the cross, kinetic, and mixed helicities, we analysed the corresponding Kármán-Howarth-Monin (KHM) equation in the hybrid (kinetic proton and fluid electron) approximation. Results. The KHM analysis shows that the combined energy decays at large scales. At intermediate scales, this energy cascades (from large to small scales) via the MHD non-linearity and this cascade partly continues via Hall coupling to sub-ion scales. The cascading combined energy is transferred (dissipated) to the internal energy at small scales via the resistive dissipation and the pressure-strain effect. The Hall term couples the cross helicity with the kinetic one, suggesting that the coupled invariant, referred to here as the mixed helicity, is a relevant turbulence quantity. However, when analysed using the KHM equations, the kinetic and mixed helicities exhibit very dissimilar behaviours to that of the combined energy. On the other hand, the cross helicity, in analogy to the energy, decays at large scales, cascades from large to small scales via the MHD+Hall non-linearity, and is dissipated at small scales via the resistive dissipation and the cross-helicity equivalent of the pressure-strain effect. In contrast to the combined energy, the Hall term is important for the cross helicity over a wide range of scales (even well above ion scales). In contrast, the magnetic helicity is scantily generated through the resistive term and does not exhibit any cascade.

Modified stochastic diffusion particle-tracking model (MSDPTM) incorporating energy cascade theory and eddy intermittency for suspended sediment transport in open channel flow.

This study presents a modified stochastic diffusion particle tracking model (MSDPTM) that incorporates energy cascade theory to more accurately simulate suspended sediment transport. The impact of turbulent eddies on sediment particles is an intermittent process, which is also considered in this study. The study examines the time correlation between eddies using eddy turnover time and finds that closer-scale eddies exhibit higher correlations than those farther apart. The statistical properties of particle movement, such as the ensemble mean and variance of particle trajectories, have been calculated and compared with the stochastic diffusion particle tracking model (SDPTM) results. Notably, MSDPTM with intermittency demonstrates a significantly larger ensemble mean of particle trajectories in the streamwise direction than other particle tracking models. The proposed model is validated through comparison with available data, showing its enhanced performance. The results of the simulation indicate that MSDPTM outperforms SDPTM, especially when the intermittency effect of eddies is considered.

Submesoscale Processes in the Northern Red Sea: Insights From Underwater Glider Observations

AbstractThe critical role of oceanic submesoscale currents in promoting energy cascade and modulating biogeochemical processes as well as the heat budget in the upper ocean has gained wide recognition. Although high‐resolution numerical simulations have enabled qualitative investigation of the spatiotemporal variability of submesoscale processes in the north Red Sea (NRS), observational evidence remains scarce. This study investigated the submesoscale processes in the NRS through field observations of underwater gliders. High‐resolution glider and satellite observation data sets reveal the spatiotemporal variation characteristics of submesoscale fronts and deepen mixed layer depth during winter. Diagnosis of potential vorticity (PV) and classifications of submesoscale instabilities demonstrate conducive conditions for the mixed layer baroclinic, gravitational, and symmetric instability. The significant negative PV induced by atmospheric cooling associated with robust fronts promotes the development of submesoscale processes. Combining the Omega equation with biogeochemical observations suggests that coherent pathways via submesoscale processes lead to the vertical transport of biomass and oxygen patches, supplying nutrients into the euphotic layer and ventilating hypoxic waters at depths. These results demonstrate the fundamental role of submesoscale processes in the ocean dynamics of the NRS.

A conical spiral methanol steam reforming reactor for spectral splitting-based concentrating photovoltaic-thermochemical hybrid production

The spectral beam splitting (SBS) photovoltaic-thermochemical hybrid system improves the solar thermal energy grade through photon energy cascade distribution and methanol steam reforming (MSR) reaction. Given the deficiency of MSR reactor development for dish-concentrating SBS systems, the conical spiral structure is introduced to the receiver/reactor in this work, thus facilitating efficient absorption of circular beams and ameliorating the adaptability of the production. Based on specially designed spectral beam splitter, the Monte Carlo ray tracing (MCRT) method is employed to simulate the non-imaging optical process and optimized reflective cone structure. Thermodynamics and kinetic models of the reactor are established and experimentally validated. The analysis results show that the reflective cone advances the optical efficiency of the reactor to 76.95%, and the conical spiral structure helps to enhance heat and mass transfer for utilization of the catalytic space. The mid/low-temperature reaction prefers a solution flow rate of less than 1.53 mL·s-1 and a water-methanol ratio of 1.4-1.9, with the maximum solar thermochemical conversion rate of 54.5%. Moreover, the upgrading in photothermal and photovoltaic heat exceeds respectively 0.62 and 8.97 at less than 600 W·m-2 of irradiation, demonstrating the adaptive potential of the reactor. In summary, the research results contribute to broadening the operating conditions of the hybrid production and the full-spectrum penetration of solar energy in distributed scenarios.

Complex flow field analysis in Multi-Shaft stirred Reactors: Dynamics of Wave-Vortex coupling revealed by POD and DMD methods

Insufficient understanding of complex flow structures in multi-shaft stirred reactors hinders industrial adoption. In this work, Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD) methods were used to analyze the Large-Eddy Simulation (LES) results of the stationary and rotating zones for three types of stirred reactors, including multi-shaft configurations. The results indicate that the flexible spatial distribution of the impellers in multi-shaft stirred reactors enhances fluid interactions, leading to the superior performance in energy cascading, flow field self-regulation, and wave-vortex coupling. Frequency analysis of single modes underscores DMD’s efficacy in interpreting complex flow phenomena. Based on this, the DMD modal coefficients were fitted to equations, clarifying the development process of wave-vortex coupling within the stirred reactors. Additionally, by integrating fundamental fluid mechanics equations with the outcomes of the DMD method, a wave-vortex coupling model was developed, which is anticipated to yield a more accurate representation of the flow field.