Jerry Jose, Auguste Gires, Yelva Roustan, Ernani Schnorenberger, Ioulia Tchiguirinskaia, Daniel Schertzer
Abstract. The inherent variability in atmospheric fields, which extends over a wide range of temporal and spatial scales, also gets transferred to energy fields extracted off them. In the specific case of wind power generation, this can be seen in the theoretical power available for extraction in the atmosphere as well as the empirical power produced by turbines. Further the power produced by turbines are affected by atmospheric turbulence as well as other fields it interact with. For modelling as well as analyzing them, quantification of their variability, intermittency and correlations with other interacting fields is important. To understand the uncertainties involved in power production, power outputs from four 2MW turbines are analyzed from an operational wind farm at Pay d’Othe, 110 km southeast of Paris, France. Using simultaneously measured wind velocity from the same location, the variability in power available at the wind farm, and power produced by wind turbines were analyzed. To account for the intermittency and variability in said fields, the framework of Universal Multifractals (UM) is used. UM is a widely used, physically based, scale invariant framework for characterizing and simulating geophysical fields over a wide range of scales. While statistically analysing the power produced by the turbine, rated power acts like an upper threshold resulting in biased estimators. This is identified and quantified here using the theoretical framework of UM along with the actual sampling resolution of instruments under study. The validity of this bias in framework is further tested and illustrated using numerical simulations of fields with the same multifractal properties. Understanding instrumental thresholds and their effect in analysis is important in retrieving actual fields and modelling them, more so, in the case of power production where the uncertainties due to turbulence are already a leading challenge. This is further expanded in the second part where the influence of rainfall in power production is studied using scale invariant tools of UM and joint multifractals.
摘要大气场在时间和空间尺度上的固有变化也会转移到从大气中提取的能量场上。在风力发电的具体案例中，可以从大气中可提取的理论功率以及涡轮机产生的实际功率中看出这一点。此外，涡轮机产生的功率还会受到大气湍流和其他相互作用场的影响。为了对其进行建模和分析，必须对其可变性、间歇性以及与其他相互作用场的相关性进行量化。为了了解发电过程中的不确定性，我们分析了位于法国巴黎东南 110 公里处 Pay d'Othe 的一个运行中风电场的四台 2 兆瓦涡轮机的发电量。通过同时测量同一地点的风速，分析了风电场可用功率的变化以及风力涡轮机产生的功率。为了解释上述领域的间歇性和可变性，使用了通用多分形（UM）框架。UM 是一种广泛使用的、基于物理的、尺度不变的框架，用于描述和模拟各种尺度的地球物理场。在对涡轮机产生的功率进行统计分析时，额定功率就像一个上阈值，会导致估算值出现偏差。本文利用 UM 的理论框架和所研究仪器的实际采样分辨率，对这一偏差进行了识别和量化。通过对具有相同多分形特性的场进行数值模拟，进一步检验和说明了这一偏差框架的有效性。了解仪器阈值及其在分析中的影响，对于检索实际场并对其进行建模非常重要，尤其是在电力生产的情况下，湍流造成的不确定性已经成为一个主要挑战。在第二部分中，我们将利用尺度不变的 UM 和联合多分形工具，进一步研究降雨对发电量的影响。
{"title":"Part 1: Multifractal analysis of wind turbine power and the associated biases","authors":"Jerry Jose, Auguste Gires, Yelva Roustan, Ernani Schnorenberger, Ioulia Tchiguirinskaia, Daniel Schertzer","doi":"10.5194/npg-2024-5","DOIUrl":"https://doi.org/10.5194/npg-2024-5","url":null,"abstract":"<strong>Abstract.</strong> The inherent variability in atmospheric fields, which extends over a wide range of temporal and spatial scales, also gets transferred to energy fields extracted off them. In the specific case of wind power generation, this can be seen in the theoretical power available for extraction in the atmosphere as well as the empirical power produced by turbines. Further the power produced by turbines are affected by atmospheric turbulence as well as other fields it interact with. For modelling as well as analyzing them, quantification of their variability, intermittency and correlations with other interacting fields is important. To understand the uncertainties involved in power production, power outputs from four 2MW turbines are analyzed from an operational wind farm at Pay d’Othe, 110 km southeast of Paris, France. Using simultaneously measured wind velocity from the same location, the variability in power available at the wind farm, and power produced by wind turbines were analyzed. To account for the intermittency and variability in said fields, the framework of Universal Multifractals (UM) is used. UM is a widely used, physically based, scale invariant framework for characterizing and simulating geophysical fields over a wide range of scales. While statistically analysing the power produced by the turbine, rated power acts like an upper threshold resulting in biased estimators. This is identified and quantified here using the theoretical framework of UM along with the actual sampling resolution of instruments under study. The validity of this bias in framework is further tested and illustrated using numerical simulations of fields with the same multifractal properties. Understanding instrumental thresholds and their effect in analysis is important in retrieving actual fields and modelling them, more so, in the case of power production where the uncertainties due to turbulence are already a leading challenge. This is further expanded in the second part where the influence of rainfall in power production is studied using scale invariant tools of UM and joint multifractals.","PeriodicalId":54714,"journal":{"name":"Nonlinear Processes in Geophysics","volume":"6 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139667165","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract. In recent years, concerns have been raised regarding the intensification and increase of extreme weather events such as torrential rainfall and typhoons. To mitigate the damage caused by weather-induced disasters, recent studies have started developing weather control technologies to lead the weather to a desirable direction with feasible manipulations. This study proposes introducing the model predictive control (MPC), an advanced control method explored in control engineering, into the framework of the control simulation experiment (CSE). In contrast to previous CSE studies, the proposed method explicitly considers physical constraints such as the maximum allowable manipulations within the cost function of the MPC. As the first step toward applying the MPC to real weather control, this study performed a series of MPC experiments with the Lorenz-63 model. Our results showed that the Lorenz-63 system can be led to the positive regime with control inputs determined by the MPC. Furthermore, the MPC significantly reduced necessary forecast length compared to earlier CSE studies. It was beneficial to select a member showing a larger regime shift for the initial state when dealing with uncertainty in initial states.
{"title":"Leading the Lorenz-63 system toward the prescribed regime by model predictive control coupled with data assimilation","authors":"Fumitoshi Kawasaki, Shunji Kotsuki","doi":"10.5194/npg-2024-4","DOIUrl":"https://doi.org/10.5194/npg-2024-4","url":null,"abstract":"<strong>Abstract.</strong> In recent years, concerns have been raised regarding the intensification and increase of extreme weather events such as torrential rainfall and typhoons. To mitigate the damage caused by weather-induced disasters, recent studies have started developing weather control technologies to lead the weather to a desirable direction with feasible manipulations. This study proposes introducing the model predictive control (MPC), an advanced control method explored in control engineering, into the framework of the control simulation experiment (CSE). In contrast to previous CSE studies, the proposed method explicitly considers physical constraints such as the maximum allowable manipulations within the cost function of the MPC. As the first step toward applying the MPC to real weather control, this study performed a series of MPC experiments with the Lorenz-63 model. Our results showed that the Lorenz-63 system can be led to the positive regime with control inputs determined by the MPC. Furthermore, the MPC significantly reduced necessary forecast length compared to earlier CSE studies. It was beneficial to select a member showing a larger regime shift for the initial state when dealing with uncertainty in initial states.","PeriodicalId":54714,"journal":{"name":"Nonlinear Processes in Geophysics","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139667534","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Samuel George Hartharn-Evans, Marek Stastna, Magda Carr
Abstract. While well-established energy-based methods of quantifying diapycnal mixing in process-study numerical models are often used to provide information about when mixing occurs, and how much mixing has occurred, describing how and where this mixing has taken place remains a challenge. Moreover, methods based on sorting the density field struggle when the model is under-resolved and when there is uncertainty as to the definition of the reference density when bathymetry is present. Here, an alternative method of understanding mixing is proposed. Paired histograms of user-selected variables (which we abbreviate USPs (user-controlled scatter plots)) are employed to identify mixing fluid and are then used to display regions of fluid in physical space that are undergoing mixing. This paper presents two case studies showcasing this method: shoaling internal solitary waves and a shear instability in cold water influenced by the nonlinearity of the equation of state. For the first case, the USP method identifies differences in the mixing processes associated with different internal solitary wave breaking types, including differences in the horizontal extent and advection of mixed fluid. For the second case, the method is used to identify how density and passive tracers are mixed within the core of the asymmetric cold-water Kelvin–Helmholtz instability.
{"title":"A new approach to understanding fluid mixing in process-study models of stratified fluids","authors":"Samuel George Hartharn-Evans, Marek Stastna, Magda Carr","doi":"10.5194/npg-31-61-2024","DOIUrl":"https://doi.org/10.5194/npg-31-61-2024","url":null,"abstract":"Abstract. While well-established energy-based methods of quantifying diapycnal mixing in process-study numerical models are often used to provide information about when mixing occurs, and how much mixing has occurred, describing how and where this mixing has taken place remains a challenge. Moreover, methods based on sorting the density field struggle when the model is under-resolved and when there is uncertainty as to the definition of the reference density when bathymetry is present. Here, an alternative method of understanding mixing is proposed. Paired histograms of user-selected variables (which we abbreviate USPs (user-controlled scatter plots)) are employed to identify mixing fluid and are then used to display regions of fluid in physical space that are undergoing mixing. This paper presents two case studies showcasing this method: shoaling internal solitary waves and a shear instability in cold water influenced by the nonlinearity of the equation of state. For the first case, the USP method identifies differences in the mixing processes associated with different internal solitary wave breaking types, including differences in the horizontal extent and advection of mixed fluid. For the second case, the method is used to identify how density and passive tracers are mixed within the core of the asymmetric cold-water Kelvin–Helmholtz instability.","PeriodicalId":54714,"journal":{"name":"Nonlinear Processes in Geophysics","volume":"10 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139589636","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract. The evolution of multifractal structures in physical processes, for instance, climatology, seismology or volcanology, contributes to detecting changes in the corresponding phenomena. The evolution of the multifractal structure of volcanic emissions of low, moderate, and high energy (Colima, México years 2013–2015) contributes to this research to detect quite evident signs of the immediacy of possible dangerous emissions of high energy close to 8.0x108 J. These signs are manifested by the evolution of six multifractal parameters: the central Hölder exponent (α0), the maximum and minimum Hölder exponents (αmax, αmin) the multifractal amplitude (W= αmax-αmin), the multifractal asymmetry (γ = [αmax-α0]/[α0-αmin]) and the complexity index, CI, which is defined as the addition of normalised values of α0, W and γ. The results of the adapted Gutenberg-Richter seismic law to volcanic emissions of energy, as well as the corresponding skewness and standard deviation of the volcanic emission data, also contribute to confirming the results obtained using multifractal analysis. The obtained results, based on multifractal structure, adaptation of Gutenberg-Richter law to volcanic emissions, and basic statistical parameters, could be assumed as relevant to prevent a forthcoming volcanic episode of high energy, which could be additionally quantified by an appropriate forecasting algorithm.
{"title":"Multifractal structure and Gutenberg-Richter parameter associated with volcanic emissions of high energy in Colima, México (years 2013–2015)","authors":"Marisol Monterrubio-Velasco, Xavier Lana, Raúl Arámbula-Mendoza","doi":"10.5194/npg-2024-2","DOIUrl":"https://doi.org/10.5194/npg-2024-2","url":null,"abstract":"<strong>Abstract.</strong> The evolution of multifractal structures in physical processes, for instance, climatology, seismology or volcanology, contributes to detecting changes in the corresponding phenomena. The evolution of the multifractal structure of volcanic emissions of low, moderate, and high energy (Colima, México years 2013–2015) contributes to this research to detect quite evident signs of the immediacy of possible dangerous emissions of high energy close to 8.0x10<sup>8</sup> J. These signs are manifested by the evolution of six multifractal parameters: the central Hölder exponent (α<sub>0</sub>), the maximum and minimum Hölder exponents (α<sub>max</sub>, α<sub>min</sub>) the multifractal amplitude (<em>W</em>= α<sub>max</sub>-α<sub>min</sub>), the multifractal asymmetry (γ = [α<sub>max</sub>-α<sub>0</sub>]/[α<sub>0</sub>-α<sub>min</sub>]) and the complexity index, CI, which is defined as the addition of normalised values of α<sub>0</sub>, <em>W</em> and γ. The results of the adapted Gutenberg-Richter seismic law to volcanic emissions of energy, as well as the corresponding skewness and standard deviation of the volcanic emission data, also contribute to confirming the results obtained using multifractal analysis. The obtained results, based on multifractal structure, adaptation of Gutenberg-Richter law to volcanic emissions, and basic statistical parameters, could be assumed as relevant to prevent a forthcoming volcanic episode of high energy, which could be additionally quantified by an appropriate forecasting algorithm.","PeriodicalId":54714,"journal":{"name":"Nonlinear Processes in Geophysics","volume":"4 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139553450","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Vivian A. Montiforte, Hans E. Ngodock, Innocent Souopgui
Abstract. Advanced numerical data assimilation (DA) methods, such as the four-dimensional variational (4DVAR) method, are elaborate and computationally expensive. Simpler methods exist that take time-variability into account, providing the potential of accurate results with a reduced computational cost. Recently, two of these DA methods were proposed for a nonlinear ocean model. The first method is Diffusive Back and Forth Nudging (D-BFN) which has previously been implemented in several complex models, most specifically, an ocean model. The second is the Concave-Convex Nonlinearity (CCN) method provided by Larios and Pei that has a straightforward implementation and promising results. D-BFN is less costly than a traditional variational DA system but it requires integrating the model forward and backward in time over a number of iterations, whereas CCN only requires integration of the forward model once. This paper will investigate if Larios and Pei's CCN algorithm can provide competitive results with the already tested D-BFN within simple chaotic models. Results show that observation density and/or frequency, as well as the length of the assimilation window, significantly impact the results for CCN, whereas D-BFN is fairly adaptive to sparser observations, predominately in time.
摘要先进的数值数据同化（DA）方法，如四维变分法（4DVAR），既复杂又耗费计算成本。现有的简化方法考虑了时间可变性，有可能在降低计算成本的同时获得准确的结果。最近，针对一个非线性海洋模型提出了两种此类 DA 方法。第一种方法是 Diffusive Back and Forth Nudging (D-BFN)，该方法之前已在多个复杂模型（尤其是海洋模型）中实施。第二种方法是 Larios 和 Pei 提出的凹凸非线性（CCN）方法，该方法实施简单，效果良好。D-BFN 比传统的变分法系统成本更低，但它需要在多次迭代中对模型进行前后积分，而 CCN 只需对前向模型进行一次积分。本文将研究 Larios 和 Pei 的 CCN 算法能否在简单混沌模型中提供与已测试过的 D-BFN 相媲美的结果。结果表明，观测密度和/或频率以及同化窗口的长度会对 CCN 的结果产生重大影响，而 D-BFN 对较稀疏的观测（主要是时间观测）具有相当的适应性。
{"title":"A Comparison of Two Nonlinear Data Assimilation Methods","authors":"Vivian A. Montiforte, Hans E. Ngodock, Innocent Souopgui","doi":"10.5194/npg-2024-3","DOIUrl":"https://doi.org/10.5194/npg-2024-3","url":null,"abstract":"<strong>Abstract.</strong> Advanced numerical data assimilation (DA) methods, such as the four-dimensional variational (4DVAR) method, are elaborate and computationally expensive. Simpler methods exist that take time-variability into account, providing the potential of accurate results with a reduced computational cost. Recently, two of these DA methods were proposed for a nonlinear ocean model. The first method is Diffusive Back and Forth Nudging (D-BFN) which has previously been implemented in several complex models, most specifically, an ocean model. The second is the Concave-Convex Nonlinearity (CCN) method provided by Larios and Pei that has a straightforward implementation and promising results. D-BFN is less costly than a traditional variational DA system but it requires integrating the model forward and backward in time over a number of iterations, whereas CCN only requires integration of the forward model once. This paper will investigate if Larios and Pei's CCN algorithm can provide competitive results with the already tested D-BFN within simple chaotic models. Results show that observation density and/or frequency, as well as the length of the assimilation window, significantly impact the results for CCN, whereas D-BFN is fairly adaptive to sparser observations, predominately in time.","PeriodicalId":54714,"journal":{"name":"Nonlinear Processes in Geophysics","volume":"334 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139590099","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Amandine Kaiser, Nikki Vercauteren, Sebastian Krumscheid
Abstract. Numerical weather prediction and climate models encounter challenges in accurately representing flow regimes in the stably stratified atmospheric boundary layer and the transitions between them, leading to an inadequate depiction of regime occupation statistics. As a consequence, existing models exhibit significant biases in near-surface temperatures at high latitudes. To explore inherent uncertainties in modeling regime transitions, the response of the near-surface temperature inversion to transient small-scale phenomena is analyzed based on a stochastic modeling approach. A sensitivity analysis is conducted by augmenting a conceptual model for near-surface temperature inversions with randomizations that account for different types of model uncertainty. The stochastic conceptual model serves as a tool to systematically investigate which types of unsteady flow features may trigger abrupt transitions in the mean boundary layer state. The findings show that the incorporation of enhanced mixing, a common practice in numerical weather prediction models, blurs the two regime characteristic of the stably stratified atmospheric boundary layer. Simulating intermittent turbulence is shown to provide a potential workaround for this issue. Including key uncertainty in models could lead to a better statistical representation of the regimes in long-term climate simulation. This would help to improve our understanding and the forecasting of climate change in high-latitude regions.
{"title":"Sensitivity of the polar boundary layer to transient phenomena","authors":"Amandine Kaiser, Nikki Vercauteren, Sebastian Krumscheid","doi":"10.5194/npg-31-45-2024","DOIUrl":"https://doi.org/10.5194/npg-31-45-2024","url":null,"abstract":"Abstract. Numerical weather prediction and climate models encounter challenges in accurately representing flow regimes in the stably stratified atmospheric boundary layer and the transitions between them, leading to an inadequate depiction of regime occupation statistics. As a consequence, existing models exhibit significant biases in near-surface temperatures at high latitudes. To explore inherent uncertainties in modeling regime transitions, the response of the near-surface temperature inversion to transient small-scale phenomena is analyzed based on a stochastic modeling approach. A sensitivity analysis is conducted by augmenting a conceptual model for near-surface temperature inversions with randomizations that account for different types of model uncertainty. The stochastic conceptual model serves as a tool to systematically investigate which types of unsteady flow features may trigger abrupt transitions in the mean boundary layer state. The findings show that the incorporation of enhanced mixing, a common practice in numerical weather prediction models, blurs the two regime characteristic of the stably stratified atmospheric boundary layer. Simulating intermittent turbulence is shown to provide a potential workaround for this issue. Including key uncertainty in models could lead to a better statistical representation of the regimes in long-term climate simulation. This would help to improve our understanding and the forecasting of climate change in high-latitude regions.","PeriodicalId":54714,"journal":{"name":"Nonlinear Processes in Geophysics","volume":"64 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139495235","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Irina I. Rypina, Lawrence J. Pratt, Michael Dotzel
Abstract. Although the movement and aggregation of microplastics at the ocean surface have been well studied, less is known about the subsurface. Within the Maxey–Riley framework governing the movement of small, rigid spheres with high drag in fluid, the aggregation of buoyant particles is encouraged in vorticity-dominated regions. We explore this process in an idealized model that is qualitatively reminiscent of a 3D eddy with an azimuthal and overturning circulation. In the axially symmetric state, buoyant spherical particles that do not accumulate at the top boundary are attracted to a loop consisting of periodic orbits. Such a loop exists when drag on the particle is sufficiently strong. For small, slightly buoyant particles, this loop is located close to the periodic fluid parcel trajectory. If the symmetric flow is perturbed by a symmetry-breaking disturbance, additional attractors for small, rigid, slightly buoyant particles may arise near periodic orbits of fluid parcels within the resonance zones created by the disturbance. Disturbances with periodic or quasiperiodic time dependence may produce even more attractors, with a shape and location that recurs periodically. However, not all such loops attract, and rigid particles released in the vicinity of one loop may instead be attracted to a nearby attractor. Examples are presented along with mappings of the respective basins of attraction.
{"title":"Aggregation of slightly buoyant microplastics in 3D vortex flows","authors":"Irina I. Rypina, Lawrence J. Pratt, Michael Dotzel","doi":"10.5194/npg-31-25-2024","DOIUrl":"https://doi.org/10.5194/npg-31-25-2024","url":null,"abstract":"Abstract. Although the movement and aggregation of microplastics at the ocean surface have been well studied, less is known about the subsurface. Within the Maxey–Riley framework governing the movement of small, rigid spheres with high drag in fluid, the aggregation of buoyant particles is encouraged in vorticity-dominated regions. We explore this process in an idealized model that is qualitatively reminiscent of a 3D eddy with an azimuthal and overturning circulation. In the axially symmetric state, buoyant spherical particles that do not accumulate at the top boundary are attracted to a loop consisting of periodic orbits. Such a loop exists when drag on the particle is sufficiently strong. For small, slightly buoyant particles, this loop is located close to the periodic fluid parcel trajectory. If the symmetric flow is perturbed by a symmetry-breaking disturbance, additional attractors for small, rigid, slightly buoyant particles may arise near periodic orbits of fluid parcels within the resonance zones created by the disturbance. Disturbances with periodic or quasiperiodic time dependence may produce even more attractors, with a shape and location that recurs periodically. However, not all such loops attract, and rigid particles released in the vicinity of one loop may instead be attracted to a nearby attractor. Examples are presented along with mappings of the respective basins of attraction.","PeriodicalId":54714,"journal":{"name":"Nonlinear Processes in Geophysics","volume":"14 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139483819","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract. Analytic solutions for the Advection-Diffusion equation have been explored in diverse scientific and engineering domains, aiming to understand transport phenomena, including heat and mass diffusion, along with the movement of water resources. Precipitation, a vital component of water resources, presents a modeling challenge due to the complex interplay between advection-diffusion effects and source terms. This study aims to improve the modeling of nonlinearly evolving precipitation fields by specifically addressing advection-diffusion equations with time-varying source terms. Utilizing analytic solutions derived through the integral transform technique, we modeled the time-varying source term and investigated the correlation between advection-diffusion and source term effects. While the growth of the field is mainly influenced by the amplitude, size, and timescale of the source term, it can be modulated by advection and diffusion effects. When the timescale of source injection is significantly shorter than the dynamic scale of the system, advection and diffusion effects become independent of the field growth. Conversely, when the timescale of source term injection is sufficiently long, the system evolution primarily depends on advection and diffusion effects. In turbulent regimes with strong diffusion and weak advection effects, a quasi-equilibrium state between growth and decay can be established by regulating the decay caused by advection. However, in regimes where advection effects are crucial, the decay process predominates over the growth process.
{"title":"Application of Advection-Diffusion Equation for Nonlinearly Evolving Precipitation Field","authors":"Ji-Hoon Ha","doi":"10.5194/npg-2023-28","DOIUrl":"https://doi.org/10.5194/npg-2023-28","url":null,"abstract":"<strong>Abstract.</strong> Analytic solutions for the Advection-Diffusion equation have been explored in diverse scientific and engineering domains, aiming to understand transport phenomena, including heat and mass diffusion, along with the movement of water resources. Precipitation, a vital component of water resources, presents a modeling challenge due to the complex interplay between advection-diffusion effects and source terms. This study aims to improve the modeling of nonlinearly evolving precipitation fields by specifically addressing advection-diffusion equations with time-varying source terms. Utilizing analytic solutions derived through the integral transform technique, we modeled the time-varying source term and investigated the correlation between advection-diffusion and source term effects. While the growth of the field is mainly influenced by the amplitude, size, and timescale of the source term, it can be modulated by advection and diffusion effects. When the timescale of source injection is significantly shorter than the dynamic scale of the system, advection and diffusion effects become independent of the field growth. Conversely, when the timescale of source term injection is sufficiently long, the system evolution primarily depends on advection and diffusion effects. In turbulent regimes with strong diffusion and weak advection effects, a quasi-equilibrium state between growth and decay can be established by regulating the decay caused by advection. However, in regimes where advection effects are crucial, the decay process predominates over the growth process.","PeriodicalId":54714,"journal":{"name":"Nonlinear Processes in Geophysics","volume":"20 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139470798","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-01-15DOI: 10.5194/egusphere-2023-3164
Evgeny Kadantsev, Evgeny Mortikov, Andrey Glazunov, Nathan Kleeorin, Igor Rogachevskii
Abstract. The dissipation rates of the basic turbulent second-order moments are the key parameters controlling turbulence energetics and spectra, turbulent fluxes of momentum and heat, and playing a vital role in turbulence modelling. In this paper, we use the results of Direct Numerical Simulations (DNS) to evaluate dissipation rates of the basic turbulent second-order moments and revise the energy and flux-budget turbulence closure model for stably stratified turbulence. We delve into the theoretical implications of this approach and substantiate our closure hypotheses through DNS data. We also show why the concept of down-gradient turbulent transport becomes incomplete when applied to the vertical turbulent flux of potential temperature under very stable stratification. We reveal essential feedback between turbulent kinetic energy, the vertical flux of buoyancy and turbulent potential energy, which is responsible for maintaining shear-produced stably stratified turbulence up to extreme static stability.
摘要基本湍流二阶矩耗散率是控制湍流能谱、湍流动量和热量通量的关键参数，在湍流建模中起着至关重要的作用。本文利用直接数值模拟（DNS）结果评估了基本湍流二阶矩的耗散率，并修正了稳定分层湍流的能量和通量预算湍流闭合模型。我们深入探讨了这种方法的理论意义，并通过 DNS 数据证实了我们的封闭假设。我们还说明了为什么在非常稳定的分层条件下，下梯度湍流输运的概念在应用于潜在温度的垂直湍流通量时会变得不完整。我们揭示了湍动动能、浮力垂直通量和湍动势能之间的基本反馈，它是维持剪切产生的稳定分层湍流直至极端静态稳定的原因。
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Pub Date : 2024-01-12DOI: 10.5194/egusphere-2024-92
Linghan Meng, Haibin Song, Yongxian Guan, Shun Yang, Kun Zhang, Mengli Liu
Abstract. From July to September 2009, a set of multi-channel seismic data was collected in the northern shelf area of the South China Sea. After the data was processed, we observed a series of shoaling events on one of the survey lines, including high-frequency internal waves, high-mode nonlinear internal waves, and shear instability. Using theoretical results from previous numerical simulations and field observations, coupled with local temperature and salinity data, we analyzed their depth distribution, waveform characteristics, and formation mechanisms, and discussed the influence of seafloor topography and stratification on the shoaling of solitary internal waves. We estimated the mixing parameters of seawater using a parameterization scheme based on hydrographic data and seismic data, respectively. And we found that the diapycnal mixing caused by these shoaling events in the shelf area were about 3.5 times greater than those on the slope. Consequently, the fission of internal solitary waves and the induced shear instability serve as significant mechanisms for the energy dissipation of internal solitary waves at the slope and shelf of the South China Sea. Additionally, the high-frequency internal waves generated during shoaling might also have a crucial role in this process.
{"title":"High-frequency Internal Waves, High-mode Nonlinear Waves and K-H Billows on the South China Sea's Shelf Revealed by Marine Seismic Observation","authors":"Linghan Meng, Haibin Song, Yongxian Guan, Shun Yang, Kun Zhang, Mengli Liu","doi":"10.5194/egusphere-2024-92","DOIUrl":"https://doi.org/10.5194/egusphere-2024-92","url":null,"abstract":"<strong>Abstract.</strong> From July to September 2009, a set of multi-channel seismic data was collected in the northern shelf area of the South China Sea. After the data was processed, we observed a series of shoaling events on one of the survey lines, including high-frequency internal waves, high-mode nonlinear internal waves, and shear instability. Using theoretical results from previous numerical simulations and field observations, coupled with local temperature and salinity data, we analyzed their depth distribution, waveform characteristics, and formation mechanisms, and discussed the influence of seafloor topography and stratification on the shoaling of solitary internal waves. We estimated the mixing parameters of seawater using a parameterization scheme based on hydrographic data and seismic data, respectively. And we found that the diapycnal mixing caused by these shoaling events in the shelf area were about 3.5 times greater than those on the slope. Consequently, the fission of internal solitary waves and the induced shear instability serve as significant mechanisms for the energy dissipation of internal solitary waves at the slope and shelf of the South China Sea. Additionally, the high-frequency internal waves generated during shoaling might also have a crucial role in this process.","PeriodicalId":54714,"journal":{"name":"Nonlinear Processes in Geophysics","volume":"54 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139461340","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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