Energy Cascade Research Articles

Ocean 2D eddy energy fluxes from small mesoscale processes with SWOT

Abstract. We investigate ocean dynamics at different scales in the Agulhas Current system, a region of important interocean exchange of heat and energy. While ocean observations and some of the most advanced climate models capture the larger mesoscale dynamics (> 100 km), the smaller-scale fronts and eddies are underrepresented. The recently launched NASA–CNES Surface Water and Ocean Topography (SWOT) wide-swath altimeter mission observes the smaller ocean geostrophic scales down to 15 km in wavelength globally. Here we will analyse different eddy diagnostics in the Agulhas Current region and quantify the contributions from the larger mesoscales observable today and the smaller scales to be observed with SWOT. Surface geostrophic diagnostics of eddy kinetic energy, strain, and energy cascades are estimated from modelled sea surface height (SSH) fields of the Massachusetts Institute of Technology general circulation model (MITgcm) latitude–longitude polar cap (LLC4320) simulation subsampled at 1/10∘. In this region, the smaller scales (<150 km) have a strong signature on the horizontal geostrophic strain rate and for all eddy diagnostics in the Western Boundary Current and along the meandering Agulhas Extension. We investigate the horizontal cascade of energy using a coarse-graining technique, and we observe that the wavelength range where the inverse cascade occurs is biased towards larger mesoscale wavelengths with today’s altimetric sampling. We also calculate the projected sampling of the eddy diagnostics under the SWOT swaths built with the NASA–CNES simulator to include the satellite position and realistic noise. For the swaths, a neural network noise mitigation method is implemented to reduce the residual SWOT random error before calculating eddy diagnostics. In terms of SSH, observable wavelengths of 15 to 20 km are retrieved after neural network noise mitigation, as opposed to wavelengths larger than 40 km before the noise reduction.

Independent-regulated double-edge Janus angular absorber for terahertz waves based on photonic edge band gaps and graphene wide-angle absorption

In this paper, three categories of Janus angle absorption structures for terahertz (THz) waves are realized by operating the edge hopping property of the photonic band gaps (PBGs) and the wide-angle absorption of graphene heterostructure. The left and right edges of the angle window are determined by the PBGs generated by photonic crystals 1 (PC1) and photonic crystals 2 (PC2), respectively. The appropriate combination of the two can obtain a transmission angle window (TAW), and the edges can be independently manipulated, which makes it possible to construct arbitrary angle filtering structures, making up for the shortage of rigid angle windows in traditional research. Graphene material has absorption potential, and when it is introduced into ternary photonic crystals 3 (PC3), high absorption at large angles will occur. The combination of PC3 and TAW will produce an absorption angle window (AAW) by using the energy cascade transmission features of photonic crystals (PCs). Contributing to the strong absorption properties, the energy transfer on both sides of PC3 is isolated. Consequently, the Janus angle absorption phenomenon will be remarkable by mirroring the PCs structures with different TAWs on both sides of PC3. Through the unique parameter design, the three relationships between the forward AAW and the backward one are investigated, that is inclusion, partial coincidence, and incoherence.

Large-scale turbulence cascade in the spiral galaxy NGC 6946

ABSTRACT The generation mechanism of compressible fluid turbulence at kiloparsec scales in the interstellar medium is a long-lasting puzzle. In this work, we explore the nature of large-scale turbulence in the external spiral galaxy NGC 6946. We use the visibility moment estimator to measure the H i column density and line-of-sight turbulent velocity power spectra combining the new observations of A array configuration of Karl G. Jansky Very Large Array (VLA) with the VLA B, C, D array observations from The H i Nearby Galaxy Survey. The estimated power spectra are obeying a power law with a slope of −0.96 ± 0.05 in column density and −1.81 ± 0.07 in line-of-sight velocity in length-scales ranging from 6 kpc to 170 pc. This points towards a forward energy cascade in the plane of the disc with a driving scale at least as large as 6 kpc. The values of the power-law indices indicate a combination of solenoidal and compressive force responsible for driving the measured turbulence. The presence of strong regular magnetic fields from the magnetic spiral arms in the galaxy is possibly contributing to the solenoidal part, while self-gravity or gravitational instability can mostly be the input for the compressive part of the forcing in the driving mechanism.

Multi‐Stage Development Within Anisotropy Insight of an Anticyclone Eddy in Northwestern South China Sea in 2021

AbstractMesoscale eddies help regulate ocean energy cascades. Eddies deformation influences barotropic instability, which represents kinetic energy transfer between scales; however, the barotropic instability structure has not been well studied. We investigated an intra‐thermocline eddy (ITE) and developed a novel anisotropic method to examine the horizontal barotropic instability. The development of the ITE was monitored using a state‐of‐the‐art autonomous underwater vehicle from May to July. The ITE became trapped in June and moved eastward in July. Based on anisotropic theory, the barotropic instability was separated into isotropic and anisotropic productions. The anisotropy contained information regarding shape and mean flow feedback of the eddy. Barotropic instability was the main source for ITE eastward propagation and was dominated by anisotropic production. Following a shape and anisotropy change, the ITE gained the mean‐flow kinetic energy by the anisotropy shear production in June and by the anisotropy stretch production when moving eastward in July.

Performance analysis of a CO2 near-zero emission integrated system for stepwise recovery of LNG cold energy and GT exhaust heat

Combined cooling, heating and power (CCHP) system can further improve energy utilization efficiency while meeting diversified energy demands, and the rational use of the CCHP system is an effective way to alleviate the energy crisis. An innovative cascaded CCHP system based on the transcritical carbon dioxide cycle (TRCC) and organic Rankine cycle (ORC) has been proposed, which is designed to recover the cold energy of liquefied natural gas (LNG) and the exhaust heat from the gas turbine (GT), while achieving near-zero CO2 emissions. The simulation result demonstrates that the system achieves energy utilization efficiency, exergy efficiency and net electrical efficiency of 87.3%, 56.9% and 55.39%, respectively, with a CO2 capture rate of 79.2 kg/h under the design condition. Compared to the mentioned cogeneration systems that recover LNG cold energy and GT waste heat, the proposed system exhibits improvements in energy utilization efficiency, exergy efficiency and net electrical efficiency by 9.84%, 4.37% and 3.4%, respectively. The parameter sensitivity analysis reveals that increasing the pressure ratio of the TCO2 turbine and ORC turbine or reducing the air compressor feed temperature can improve the overall performance of the system. If the focus is solely on energy utilization efficiency and exergy efficiency, appropriately increasing the air compressor pressure ratio or reducing the gas turbine pressure ratio would be beneficial. The proposed system in the study is environmentally friendly and energy-saving, which especially suggests a direction for cold energy cascade utilization in LNG stations integrated with CCHP.

Dark matter halo mass functions and density profiles from mass and energy cascade

Halo abundance and structure play a central role for modeling structure formation and evolution. Without relying on a spherical or ellipsoidal collapse model, we analytically derive the halo mass function and cuspy halo density (inner slope of −4/3) based on the mass and energy cascade theory in dark matter flow. The hierarchical halo structure formation leads to halo or particle random walk with a position-dependent waiting time tau _g. First, the inverse mass cascade from small to large scales leads to the halo random walk in mass space with tau _gpropto m_h^{-lambda }, where m_h is the halo mass and lambda is a halo geometry parameter with predicted value of 2/3. The corresponding Fokker-Planck solution for halo random walk in mass space gives rise to the halo mass function with a power-law behavior on small scale and exponential decay on large scale. This can be further improved by considering two different lambda for haloes below and above a critical mass scale m_h^*, i.e. a double-lambda halo mass function. Second, a double-gamma density profile can be derived based on the particle random walk in 3D space with a position-dependent waiting time tau _g propto Phi (r)^{-1} propto r^{-gamma }, where Phi is the gravitational potential and r is the particle distance to halo center. Theory predicts gamma =2/3 that leads to a cuspy density profile with an inner slope of −4/3, consistent with the predicted scaling laws from energy cascade. The Press-Schechter mass function and Einasto density profile are just special cases of proposed models. The small scale permanence can be identified due to the scale-independent rate of mass and energy cascade, where density profiles of different halo masses and redshifts converge to the -4/3 scaling law (rho _h propto r^{-4/3}) on small scales. Theory predicts the halo number density scales with halo mass as propto m_h^{-1.9}, while the halo mass density scales as propto m_h^{4/9}. Results were compared against the Illustris simulations. This new perspective provides a theory for nearly universal halo mass functions and density profiles.

Photoexcitation Control of Excitation Relaxation in Mixed‐Phase Ruddlesden‐Popper Hybrid Organic‐Inorganic Lead‐Iodide Perovskites

AbstractThe electronic states and exciton binding energies of layered Ruddlesden‐Popper (RP) metal‐halide perovskites can be tailored through changes of their chemical composition, yielding multi‐phase systems with complex energy cascades. Ultrafast photoexcitation relaxation with transfer dynamics into domains of increasing layer number has been reported for these materials. Here, ultrafast optical spectroscopy is used to report an unexpected excitation energy dependence of photoexcitation relaxation dynamics in mixed‐dimensional benzylammonium cesium lead iodide RP perovskite (BeA2CsPb2I7) thin films, which gives rise to spectrally broadband luminescence over the visible region. Using transient absorption and photoluminescence spectroscopy it is found that excitations, which are formed in the n = 2 RP‐phase after photoexcitation with ≈0.2 electron volt excess energy, transfer to higher layer number RP‐phases on unexpectedly slow timescales of tens of picoseconds. Further, it is observed that such excitations are initially optically passive. Notably, luminescence occurs under these conditions from multiple RP‐phases with optical bandgaps across the visible range, yielding broadband luminescence. The results hold potential for realization of broadband white‐light emitters and other light‐emitting devices.

Energy transfer and vortex structures: visualizing the incompressible turbulent energy cascade

The transfer of kinetic energy from large to small scales is a hallmark of turbulent flows. Yet, a precise mechanistic description of this transfer, which is expected to occur via an energy cascade, is still missing. Several conceptually simple configurations with vortex tubes have been proposed as a testing ground to understand the energy cascade. Here, we focus on incompressible flows and compare the energy transfer occurring in a statistically steady homogeneous isotropic turbulent (HIT) flow with the generation of fine-scale motions in configurations involving vortex tubes. We start by filtering the velocity field in bands of wavenumbers distributed logarithmically, which allows us to study energy transfer in Fourier space and also visualize the energy cascade in real space. In the case of a statistically steady HIT flow at a moderate Reynolds number, our numerical results do not reveal any significant correlation between regions of intense energy transfers and vorticity or strain, filtered in corresponding wavenumber bands, nor any simple self-similar process. In comparison, in the transient turbulent flow obtained from the interaction between two antiparallel vortex tubes, we observe a qualitatively simpler organization of the intense structures, as well as of the energy transfer. However, the correlations between energy transfer and strain are small, and point to complicated dynamics of energy transfer. By imposing a structure at large scales consisting of antiparallel vortex tubes in a statistically steady flow, we observed a picture qualitatively similar to what was observed for the transient flow, but the energy transfer statistics do not reproduce the type of triadic interactions seen in HIT. These results indicate that the specific properties of the large-scale vortical structures affect the way energy is transferred, and may not be fully representative of HIT.

Subgrid Parameterizations of Ocean Mesoscale Eddies Based on Germano Decomposition

AbstractOcean models at intermediate resolution (1/4°), which partially resolve mesoscale eddies, can be seen as Large eddy simulations of the primitive equations, in which the effect of unresolved eddies must be parameterized. In this work, we propose new subgrid models that are consistent with the physics of two‐dimensional flows. We analyze subgrid fluxes in barotropic decaying turbulence using Germano (1986, https://doi.org/10.1063/1.865568) decomposition. We show that Leonard and Cross stresses are responsible for the enstrophy dissipation, while the Reynolds stress is responsible for additional kinetic energy (KE) backscatter. We utilize these findings to propose a new model, consisting of three parts, that is compared to a baseline dynamic Smagorinsky model. The three‐component model accurately simulates the spectral transfer of energy and enstrophy and improves the representation of KE spectrum, resolved KE and enstrophy decay in a posteriori experiments. The backscattering component of the new model (Reynolds stress) is implemented both in quasi‐geostrophic and primitive equation ocean models and improves statistical characteristics, such as the vertical profile of eddy KE, meridional overturning circulation and cascades of kinetic and potential energy.

Three-dimensional shear-flow instability saturation via stable modes

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

Multiscale dynamics in streamwise-rotating channel turbulence

In this paper the multiscale dynamics of streamwise-rotating channel turbulence is studied through direct numerical simulations. Using the generalized Kolmogorov equation, we find that as rotation becomes stronger, the turbulence in the buffer layer is obviously reduced by the intense spatial turbulent convection. On the contrary, in other layers, the turbulence is strengthened mainly by the modified production peak, the intense spatial turbulent convection and the suppressed forward energy cascades. It is also discovered that under a system rotation, small- and large-scale inclined structures have different angles with the streamwise direction, and the difference is strengthened with increasing rotation rates. The multiscale inclined structures are further confirmed quantitatively through a newly defined angle based on the velocity vector. Through the budget balance of Reynolds stresses and the hairpin vortex model, it is discovered that the Coriolis force and the pressure–velocity correlation are responsible for sustaining the inclined structures. The Coriolis force directly decreases the inclination angles but indirectly induces inclined structures in a more predominant way. The pressure–velocity correlation term is related to the strain rate tensor. Finally, the anisotropic generalized Kolmogorov equation is used to validate the above findings and reveals that the multiscale behaviours of the inclined structures are mainly induced by the mean spanwise velocity gradients.

A model-free optimal operation strategy of diversified demands-park integrated energy system considering energy cascade utilization

In order to improve the energy efficiency of park integrated energy system, this work proposes a model-free optimal operation strategy of diversified demands-park integrated energy system considering energy cascade utilization. First, by considering diversified demands of various users for energy, an energy cascade utilization mode and its corresponding multi-dimensional energy supply and demand balance equation is developed. Moreover, in view of the above structure, a model-free DD-PIES optimal operation strategy is further proposed. Among them, the model-free approach is realized on the basis of the interaction between agent and environment, combined with sufficient exploration and consequences learning of its behavior through experience. Compared to the previous works, this proposed strategy has good self-learning ability for multiple uncertainties of renewable energy and energy demand, and cuts down on inefficient exploration during the training process, while guarantee the security during the execution of actions by the agent. Finally, the rationality and validity of the proposed strategy in reducing operating cost and improving energy efficiency of the system are verified by a case study.

Effect of a canopy patch made of streamwise-oriented plates on turbulence in an open-channel flow

AbstractThe paper examines the flow through a highly porous canopy patch made of streamwise-oriented thin plates arranged in a staggered configuration and placed in a rough-bed open channel. This patch geometry contrasts with the patches made of bluff bodies, which are nearly exclusively used in the literature. Particle Image Velocimetry was used to measure the flow upstream, within and downstream of the patch. The canopy patch has the effect of drastically reducing the turbulence level of the incoming flow, especially the turbulence shear stress, which is reduced by 85%. Spectral analysis of the velocity shows that the reduction in turbulent kinetic energy occurs at all length scales. Yet, at the entrance of the patch, the energy from the smallest scales up to the scale of the water surface increases. This suggests a spectral shortcut mechanism by which the large-scale structures of the incoming flow are disintegrated by the group of plates instead of decaying through the energy cascade. The increased small-scale turbulent energy then dissipates through the patch.

Viscous effects on gas-liquid hydrodynamics for bubble size determinations in different Newtonian and non-Newtonian fluids using a CFD-PBM model

Often, culturing during bioprocessing generates severe conditions that modify the viscosity of the culture media. The change in viscosity leads to different microenvironments governed by viscous effects-mediated hydrodynamics. For example, different bubble size distributions are dispersed inside a bioreactor due to viscous effects. Traditionally, the mathematical modeling framework used in numerical simulation of the bubble size distribution in (bio)reactors is based on breakup and coalescence models valid only in the inertial subrange of turbulence. Hence, applying the traditional models for breakup and coalescence in viscous fluids can result in inaccurate model predictions because the dissipation subrange of turbulence is not considered. This work focuses on the numerical prediction of the bubble size in a stirred bioreactor using the concept of the complete energy spectrum of turbulence to enable viscous effects in the breakup and coalescence models. The breakup and coalescence models are used within the population balance equation (PBE), coupled with computational fluid dynamics (CFD). The emphasis of the PBE-CFD simulations is placed on gas–liquid hydrodynamics aspects related to viscous Newtonian and non-Newtonian fluids applications. In bioreactor zones where viscosity effects occur, the use of the complete energy spectrum of turbulence facilitates the calculation of the transition between dissipation and inertial subranges of turbulence. It is shown that the numerical simulations captured viscous effects-mediated hydrodynamics. Considering these findings, using the complete energy spectrum of turbulence in PBE-CFD simulations is a promising approach for numerical bubble size prediction.

A Physical Model for the Observed Inverse Energy Cascade in Typhoon Boundary Layers

AbstractThe knowledge of the observed inverse energy cascade in typhoon boundary layers holds significant implications for understanding the formation, enhancement, and deformation of typhoons. This study reveals that the observed inverse energy cascade originates from the rapid rotation of typhoons. The transition from the direct energy cascade regime to the inverse energy cascade regime can be characterized by the Zeman length scale. The turbulence structures behave as two dimensional above the Zeman length scale. Through symmetry analysis, it is discovered that the ratio of the inverse energy cascade flux to the direct energy cascade flux is proportional to the turbulence Rossby number with a power of −2. These findings offer a framework for incorporating the inverse energy cascade into the turbulence parameterizations and improving typhoon modeling.

Comparison of various dual-temperature zones space heating systems based on energy cascade utilization principle

The high efficiency heating system is crucial in ensuring both residents and buildings remain comfortably warm during cold seasons, providing not only a comfortable living environment but also contributing to health, productivity, and overall well-being. Based on the energy cascade utilization principle, three multi-temperature zone space heating systems were introduced firstly, namely warm air (WA), radiator combined with fresh air (RA + FA), and floor combined with fresh air (FL + FA) in this research. The detailed energetic and exergetic models of these space heating systems were developed to investigate and compare the system performance under various operated conditions, including the fresh air, supply air, radiator, and floor temperatures. The results showed that the energy efficiency ratio (EER) value increased first and then decreased with the supply air temperature increasing for the WA, while the EER of the RA + FA and FL + FA decreased with the floor and radiator temperatures increasing. The maximal EER for the WA, FL + FA, and RA + FA system were 2.96, 3.52, and 3.43 under selected conditions. Besides, the WA system outperformed the RA + FA system in terms of exergy efficiency, and the WA system exergy efficiency ranged from 22 to 28% under selected conditions. Lastly, for the FL + FA system, the system exergy loss increased by approximately 0.016–0.018 kW/°C for the floor temperature, and the values were 0.024 kW/°C for fresh air temperature.

Multi-scale reconstruction of turbulent rotating flows with proper orthogonal decomposition and generative adversarial networks

Data reconstruction of rotating turbulent snapshots is investigated utilizing data-driven tools. This problem is crucial for numerous geophysical applications and fundamental aspects, given the concurrent effects of direct and inverse energy cascades. Additionally, benchmarking of various reconstruction techniques is essential to assess the trade-off between quantitative supremacy, implementation complexity and explicability. In this study, we use linear and nonlinear tools based on the proper orthogonal decomposition (POD) and generative adversarial network (GAN) for reconstructing rotating turbulence snapshots with spatial damages (inpainting). We focus on accurately reproducing both statistical properties and instantaneous velocity fields. Different gap sizes and gap geometries are investigated in order to assess the importance of coherency and multi-scale properties of the missing information. Surprisingly enough, concerning point-wise reconstruction, the nonlinear GAN does not outperform one of the linear POD techniques. On the other hand, the supremacy of the GAN approach is shown when the statistical multi-scale properties are compared. Similarly, extreme events in the gap region are better predicted when using GAN. The balance between point-wise error and statistical properties is controlled by the adversarial ratio, which determines the relative importance of the generator and the discriminator in the GAN training.

Energy cascade in a far-from-equilibrium inhomogeneous trapped Bose gas obtained by power spectrum analysis

Energy cascade in a far-from-equilibrium inhomogeneous trapped Bose gas obtained by power spectrum analysis

Distributed low-carbon operational optimization model of an integrated energy system based on ladder carbon trading and integrated demand response

ABSTRACT Integrated energy system (IES) has become significant in the global energy revolution because of its unique advantage of promoting clean energy use and improving energy efficiency. However, its low-carbon operational optimization and capacity allocation challenges have sharply increased because, as its scale continuously grows, its inherent strongly coupled multi energy flow and high nonlinearity characteristics have become more prominent. This study proposes a distributed low-carbon operational optimization mechanism for an IES using integrated demand response (IDR) and ladder carbon trading (LCT). First, a low-carbon IES was modeled as a coupled model between energy operators (EO) that contain combined cooling, heating, and power systems (CCHP) and flexible users (FU) based on the Stackelberg game. Second, the operational optimization model was formulated as a source-load synergistic operation scheduling mechanism based on IDR and the LCT. Finally, the strategy of each stakeholder was obtained using a modified distributed algorithm of genetic algorithm nested quadratic programming (GA-QP). The effectiveness of the proposed model was verified through a case study. The economic benefits for each stakeholder improved, as confirmed through the experimental results. The energy cost of the FU decreased by 4.42%, and the revenue from energy sales of the EO increased by 11.9%; renewable energy was prioritized for consumption, with a consumption rate of 100%; the total output of the core devices for energy cascade utilization increased by 15.6%, significantly improving energy supply efficiency; the total carbon emissions decreased by 8.64%; and power and heat loss rates were 0% and 0.00059%, respectively. Highlights With the rapid development of renewable energy, The integrated energy system relies on its inherent operational advantages of high flexibility, high toughness, and multi energy coupling cascade utilization, demonstrates unique advantages in serving as a clean and renewable energy carrier and adapting to the development of distributed energy The energy cost of flexible users has decreased by 4.42%, and the revenue from energy sales of energy operators has increased by 11.9%; Renewable energy is prioritized for consumption, with a consumption rate of 100%; The total output of the core devices for energy cascade utilization has increased by 15.6%, significantly improving energy supply efficiency; The total carbon emissions decreased by 8.64%, both power and heat loss rates are 0%, the error rate of energy supply is 0.00059% Based on the above research, this paper is established a distributed low-carbon operation optimization model for Integrated energy system coupled the EO that contain CCHP and the FU based on Stackelberg game In view of the gradual deepening of the coupling degree of the IES, the increasingly obvious characteristics of multi-agent, the difficulty of centralized scheduling to protect the interests of each independent entity, and the inadequacy of the system’s energy cascade utilization advantages, this paper establishes a bilateral distributed operation optimization model based on Game theory In response to the insufficient utilization of the advantages of multi energy coupling in existing research on IES, insufficient attention paid to the interaction between supply and demand on both sides of the system, and insufficient enthusiasm of users as independent entities to participate in system operation scheduling, this article adopts a integrated demand response as the load side operation scheduling strategy

REGULARITIES OF HYDROCHEMICAL DYNAMICS IN A TWO-DIMENSIONAL TURBULENT FLOW OF NATURAL WATER

The variability of the composition and properties of natural waters, which creates numerous difficulties in water use, cannot always be explained by the influence of external influencing factors, such as weathering or leaching of rocks, a change in the phases of the water regime, etc. This is especially true for subdiurnal and subhourly quality variability, which can be caused by complex, previously unknown dynamic hydrochemical processes. Such a conclusion follows from the results of the study of turbidity and pH of natural water given in the work, obtained with an increased frequency of measurements. These results indicate the existence of a quasi-cyclic change in the controlled parameters with different periods, from every minute to daily. The study of observational data allows us to make an assumption that in this case the hydrochemical dynamics is due to direct and reverse energy cascades in a two-dimensional turbulent flow of natural water, in which the impurity subsystem is prone to stratification.