Turbulence Theory Research Articles

Exploring the Characteristics of Ocean Surface Winds at High Resolution With Doppler Scatterometry

AbstractOcean wind plays a fundamental role in the Earth's climate system by transporting heat, moisture, and gases globally while mediating their exchange with the ocean. How, and at what scales these processes occur is an active area of research, and modeling studies suggest that the strongest vertical transport and air‐sea exchanges occur at small scales. This paper introduces results from the S‐MODE campaign, during which a Doppler Scatterometer mapped 2D ocean vector wind on scales between 200 m and 100 km. While in an average sense, DopplerScatt wind data match classical spectra, atmospheric rolls, convection, and underlying ocean currents all drive unique wind spectra that are inconsistent with the average. Frequent observations of strong atmospheric divergence imply small‐scale vertical transport reaching 10 km/day. These results are not consistent with Kolmogorov and two‐dimensional turbulence theories due to anisotropy and divergence.

Impact of Horizontal Resolution on Simulating Eddy‐Induced Meridional Heat Transport in the Southeast Indian Ocean

AbstractThe eddy‐induced meridional heat transport (EMHT) in the Southeast Indian Ocean (SEIO) plays a crucial role in regional air–sea interactions and climate changes, but it is commonly underestimated in widely‐known models and reanalysis data sets. This study uses three experiments of the Regional Ocean Modeling System (ROMS) with varying horizontal resolutions to assess their impact on simulating EMHT in the SEIO. The results show that increasing horizontal resolution enhances the simulated EMHT with a stronger seasonal cycle. The higher horizontal resolution experiments show improvements in the association and phase difference between high‐frequency temperature and meridional velocity, both of which are the definition of EMHT. According to turbulent diffusion theory, the magnitude of EMHT is directly correlated with eddy kinetic energy (EKE). Both of them show similar vertical and temporal variations as well as spatial patterns. EKE budget analysis suggests that the improvement in EKE is primarily attributed to the enhanced baroclinic energy conversion, which indicates the EKE originated from eddy available potential energy. It is further found that the amplitude and number of mesoscale eddies are notably large in high‐resolution experiments, thereby augmenting the EKE and EMHT. Additionally, the seasonal variation in EMHT in each model experiment is tied to the number of mesoscale eddies, rather than other characteristics of them. Thus, this study provides a valuable insight into the enhancing horizontal resolution to improve the simulation of EMHT.

Statistical theory of the broadband two-plasmon decay instability

There is renewed interest in direct-drive inertial confinement fusion, following the milestone December 2022 3.15 MJ ignition result on the National Ignition Facility. A key obstacle is the control of the two-plasmon decay instability. Here, recent advances in inhomogeneous turbulence theory are applied to the broadband parametric instability problem for the first time. A novel dispersion relation is derived for the two-plasmon decay in a uniform plasma valid under broad-bandwidth laser fields with arbitrary power spectra. The effects of temporal incoherence on the instability are then studied. In the limit of large bandwidth, the well-known scaling relations for the growth rate are recovered, but it is shown that the result is more sensitive to the spectral shape of the laser pulse rather than to its coherence time. The range of wavenumbers of the excited plasma waves is shown to be substantially broadened, suggesting that the absolute instability is favoured in regions further away from the quarter critical density. The intermediate-bandwidth regime is explored numerically – the growth rate is reduced to half its monochromatic value for laser intensities of $10^{15} \ \text {W}\ \text {cm}^{-2}$ and relatively modest bandwidths of $5 \ \text {THz}$ . The instability-quenching properties of a spectrum of discrete lines spread over some bandwidth have also been studied. The reduction in the growth rate is found to be somewhat lower compared with the continuous case but is still significant, despite the fact that, formally, the coherence time of such a laser pulse is infinite.

Single-mode wave decay

The usual approach on electrostatic wave decay process for a weak beam-plasma system considers two different wave modes interplaying, the Langmuir and ion-sound mode. In the present paper, a single-mode approach is shown to be feasible for conditions where the respective dispersion relations undergo topological changes. Numerical solutions for the dispersion relation of a beam-plasma system are presented, supporting the modeling of an analytic dispersion relation of a single wave mode. This wave mode is accounted for in the kinetic equations for particles and waves, which rule the evolution of the system. The results are compared against the two-wave mode approach using Langmuir and ion-sound waves, within the context of weak turbulence theory. It is found that the single-mode approach can account for the basic features of particles and waves, since the single mode exhibits both low and high frequency regions, which ultimately play the roles of ion-sound and Langmuir modes, respectively.

Conceptualizing Injured Partners’ Relational Uncertainty Following Marital Infidelity: A Relational Turbulence Theory Perspective

ABSTRACT The current research utilizes relational turbulence theory (RTT) to examine the associations between relational uncertainty and the cognitive, emotional, and communicative responses of injured partners who had recently experienced marital infidelity. Individuals in marital relationships who experienced partner infidelity in the past year and had not terminated their relationship were recruited to complete an online survey (N = 305). Results from structural equation modeling indicated that injured partners’ commitment and growth belief were negatively associated with self uncertainty and commitment was positively associated with relationship uncertainty. Self, partner, and relationship uncertainty corresponded with cognitive, emotional, and communicative responses to infidelity in different ways. Additionally, perceptions of infidelity severity and distributive communication contributed to injured partners’ experience of relational turbulence. The research has theoretical implications for applying RTT to the context of marital infidelity and practical implications for targeted support for individuals navigating infidelity.

Convective and Orographic Origins of the Mesoscale Kinetic Energy Spectrum

AbstractThe mesoscale spectrum describes the distribution of kinetic energy in the Earth's atmosphere between length scales of 10 and 400 km. Since the first observations, the origins of this spectrum have been controversial. At synoptic scales, the spectrum follows a −3 spectral slope, consistent with two‐dimensional turbulence theory, but a shallower −5/3 slope was observed at the shorter mesoscales. The cause of the shallower slope remains obscure, illustrating our lack of understanding. Through a novel coarse‐graining methodology, we are able to present a spatio‐temporal climatology of the spectral slope. We find convection and orography have a shallowing effect and can quantify this using “conditioned spectra.” These are typical spectra for a meteorological condition, obtained by aggregating spectra where the condition holds. This allows the investigation of new relationships, such as that between energy flux and spectral slope. Potential future applications of our methodology include predictability research and model validation.

Ordering of time scales predicts applicability of quasilinear theory in unstable flows

We discuss the applicability of quasilinear-type approximations for a turbulent system with a large range of spatial and temporal scales. We consider a paradigm fluid system of rotating convection with vertical and horizontal temperature gradients. In particular, the interaction of rotation with the horizontal temperature gradient drives a ‘thermal wind’ shear flow whose strength is controlled by the horizontal temperature gradient. Varying this parameter therefore systematically alters the ordering of the shearing time scale, the convective time scale and the correlation time scale. We demonstrate that quasilinear-type approximations work well when the shearing time scale or the correlation time scale is sufficiently short. In all cases, the generalised quasilinear approximation systematically outperforms the quasilinear approximation. We discuss the consequences for statistical theories of turbulence interacting with mean gradients.

A physical stochastic model of near-surface fluctuating wind fields

Modeling and simulation of atmospheric turbulence in coastal areas has emerged as a prominent area of research in recent years. This study presents a physical stochastic model to describe the horizontal coherence of fluctuating wind fields within the physical stochastic modeling frame. Based on the one-dimensional stochastic Fourier spectrum and isotropic turbulence theory, the horizontal coherence for fluctuating wind fields is expressed as a random function, with its probability information determined by the physical mechanism/background. The proposed physical stochastic model directly depicts the stochastic time series thereby enabling it to capture all probability information in detail comprehensively. The proposed model is numerically validated with the measured data obtained from an observation array constructed in Southeast China. This investigation holds significant potential for its application in wind-resistance design and reliability assessment of long-span structures.

Ground failure and soil erosion caused by bursting of buried water pipeline: experimental and numerical investigations

Pressurized water pipelines buried in an urban environment are prone to bursting failures, threatening public safety and traffic convenience. The limited studies in literature just focused on soil fluidization while few studies considered ground failure, shear strain, soil erosion and the influence of leakage locations during pipe bursts. In this study, extensive experimental tests along with a finite difference method – discrete element method (FDM-DEM) solid–fluid coupling analysis were conducted to investigate these issues. It was disclosed that the failure development during pipe bursts can be divided into three stages, i.e., seepage diffusion, erosion cavity expansion, and soil fluidization. By digital image correlation (DIC) analysis of the experimental results, a wedge-shaped displacement zone in ground was identified, with peak shear strain near its boundaries. Moreover, it was revealed that leakage locations affected the expansion origin of erosion cavity; as the burial depths increased, the ground heave range increased linearly; the maximum water outflow distance was closely related to the internal pressures of buried pipeline, which could be modeled by a square root formula based on turbulent jet theory. Mesoscopic analyses revealed that finer particles were more susceptible to erosion during pipe bursts because of the low possibility of forming strong connections with surrounding particles. The findings yielded from this study can enhance the understanding of pipe bursts and help professionals mitigate potential damage.

Scaling Law of Flow and Heat Transfer Characteristics in Turbulent Radiative Rayleigh-Bénard Convection of Optically Thick Media

Radiative natural convection is of vital importance in the process of energy storage, power generation, and thermal storage technology. As the attenuation coefficients of many heat transfer media in these fields are high enough to be considered as optically thick media, like nanofluids or molten salts in concentrated solar power or phase change thermal storage, Rosseland approximation is commonly used. In this paper, we delve into the impact of thermal radiation on the Rayleigh-Bénard (RB) convection. Theoretical analysis has been conducted by modifying the Grossmann-Lohse (GL) model. Based on turbulent dissipation theory, the corresponding scaling laws in four main regimes are proposed. Direct numerical simulation (DNS) was also performed, revealing that radiation exerts a notable influence on both flow and heat transfer, particularly on the formation of large-scale circulation. By comparing with DNS results, it is found that due to the presence of radiation, the modified Nu scaling law in small Pr range of the GL model is more suitable for predicting the transport characteristics of optical thick media with large Pr. The maximum deviation between the results of DNS and prediction model is about 10%, suggesting the summarized scaling law can effectively predict the Nu of radiative RB convection.

Dynamic and Daily Partner-Specific Processes of Relationship Uncertainty and Enacted Relationship Talk

Guided by relational turbulence theory (RTT), this intensive longitudinal study examined how within-person daily fluctuations in relationship uncertainty corresponded with individuals’ decisions to engage in daily enacted relationship talk. Using a person-specific approach, this study also examined how individuals’ attachment insecurity predicted within-person differences in month-long processes predicted by RTT. College-aged dating partners ( N = 202, between-person) reported their attachment proclivities in a pre-test survey and subsequently reported on their relationship uncertainty and enacted relationship talk once per day over a period of 30 consecutive days ( N = 5,240, within-person). Results indicated that on days when individuals experienced elevated relationship uncertainty, they engaged in less relationship talk than they typically did. Additionally, we found that individuals with more volatility (intraindividual variability) and inertia (day-to-day carryover) in relationship uncertainty throughout the month enacted less relationship talk on average. Finally, results indicated that attachment insecurity predicted person-specific month-long processes consistent with RTT.

Using the Boundary Element Method for airfoil trailing edge noise prediction

This study investigates two aspects of the prediction of trailing edge noise from an airfoil using the Boundary Element Method to solve the scattering phenomenon. The first one consists in defining the surface pressure spectrum near the trailing edge as a source for the turbulent boundary layer-trailing edge interaction, using either an empirical model or one-dimensional turbulent boundary layer theory. The second aspect focuses on the capability of the Boundary Element Method to handle general boundary conditions. It is applied to predict the noise emitted by a porous trailing edge. This work is conducted in the context of aerodynamic noise from wind turbine blades, but has a wider range of engineering applications.

Structural and Dynamical Quality Assessment of Gap‐Filled Sea Surface Temperature Products

AbstractPrevious studies that intercompared global Level‐4 (L4) sea surface temperature (SST) analyses were centered on the assessment of the accuracy and bias of SST by comparing them with independent near‐surface Argo profile temperature data. This type of assessment is centered on the absolute value of SST rather than on SST spatial properties (gradients), which is more relevant to the study of oceanographic features (e.g., fronts, eddies, etc.) and ocean dynamics. Here, we use, for the first time, the spectrum of singularity exponents to assess the structural and dynamical quality of different L4 gap‐filled products based on the multifractal theory of turbulence. Singularity exponents represent the geometrical projection of the turbulence cascade, and its singular spectrum can be related to the probability density function of the singularity exponents normalized by the scale. Our results reveal that the different schemes used to produce the L4 SST products generate different singularity spectra, which are then used to identify a potential loss of dynamical information or structural coherence. This new diagnostic constitutes a valuable tool to assess the structural quality of SST products and can support data satellite SST producers efforts to improve the interpolation schemes used to generate gap‐filled SST products.

Self-similarity and the direct (enstrophy) cascade in forced two-dimensional fluid turbulence

In the absence of large-scale coherent structures, a widely used statistical theory of two-dimensional turbulence developed by Kraichnan, Leith, and Batchelor (KLB) predicts a power-law scaling for the energy, $E(k)\propto k^\alpha$ with an integral exponent $\alpha ={-3}$ , in the inertial range associated with the direct cascade. A power-law scaling is also observed in the presence of coherent structures, but the scaling exponent becomes fractal and often differs substantially from the value predicted by the KLB theory. Here we present a dynamical theory that sheds new light on the relationship between the spatial and temporal structure of the large-scale flow and the scaling of small-scale structures representing filamentary vorticity. Specifically, we find hyperbolic regions of the large-scale flow to play a key role in the flux of enstrophy between scales. Small-scale vorticity in these regions can be described by dynamically self-similar solutions of the Euler equation, which explains the power-law scaling. Furthermore, we find that correlations between different hyperbolic regions are responsible for the emergence of fractal scaling exponents.

A longitudinal test of relational turbulence theory and serial arguments in romantic relationships

Abstract Relational turbulence theory (RTT) suggests that people perceive their romantic relationships as turbulent when they experience interactions that manifest the deleterious effects of relational uncertainty and altered patterns of interdependence. RTT also positions communication in these episodes as associated with subsequent relational uncertainty and qualities of interdependence. Using three-wave panel data collected at three-week intervals, this study evaluates (a) how communication in serial argument episodes predict relationship parameters (i.e., relational uncertainty and qualities of interdependence), (b) how relationship parameters predict serial argument occurrence, directness, and valence, and (c) whether over time variability in qualities of serial argument communication predict subsequent relational turbulence. Results indicated limited support for reciprocal, between-wave associations between relationship qualities and serial argument communication; however, over time variability in the valence of serial argument communication was associated with higher levels of relational turbulence after 6 weeks. Implications for RTT and research on serial arguments are discussed.

Hidden turbulence in van Gogh's The Starry Night

Turbulent skies have often inspired artists, particularly in the iconic swirls of Vincent van Gogh's The Starry Night. For an extended period, debate has raged over whether the flow pattern in this masterpiece adheres to Kolmogorov's theory of turbulence. In contrast to previous studies that examined only part of this painting, all and only the whirls/eddies in the painting are taken into account in this work, following the Richardson–Kolmogorov's cascade picture of turbulence. Consequently, the luminance's Fourier power spectrum spontaneously exhibits a characteristic −5/3 Kolmogorov-like power-law. This result suggests that van Gogh had a very careful observation of real flows, so that not only the sizes of whirls/eddies in The Starry Night but also their relative distances and intensity follow the physical law that governs turbulent flows. Moreover, a “–1”-like power-law persists in the spectrum below the scales of the smallest whirls, hinting at Batchelor-type scalar turbulence with a high Schmidt number. Our study, thus, unveils the hidden turbulence captured within The Starry Night.

Theory and Modelling of Isotropic Turbulence: From Incompressible through Increasingly Compressible Flows

Homogeneous isotropic turbulence (HIT) has been a useful theoretical concept for more than fifty years of theory, modelling, and calculations. Some exact results are revisited in incompressible HIT, with special emphasis on the 4/5 Kolmogorov law. The finite Reynolds number effect (FRN), which yields corrections to that law, is investigated, using both Kármán–Howarth-type equations and a statistical spectral closure of the Eddy-Damped Quasi-Normal Markovian (EDQNM)-type. This discussion offers an opportunity to give an extended review of such spectral closures, from weak turbulence, as in wave turbulence theory, to a strong one. Extensions of the 4/5 or 4/3 Kolmogorov/Monin laws to anisotropic cases, such as stably stratified and MHD turbulence, are briefly touched on. Before addressing more recent work on compressible isotropic turbulence, the simplest case of quasi-incompressible turbulence subjected to externally imposed isotropic compression or dilatation is presented. Rapid distortion theory is found to be a poor model in this isotropic case, in contrast with its relevance in strongly anisotropic flow cases. Accordingly, a fully nonlinear approach based on a rescaling of all fluctuating variables is used, in order to show its interplay with the linear operator. This opens the discussion on the cases of homogeneous incompressible turbulence, where RDT and nonlinear models are relevant, provided that anisotropy is accounted for. Finally, isotropic compressible flows of increasing complexity are considered. Recent studies using weak turbulence theory, modelling, and DNS are discussed. A final unpublished study involves interactions between the solenoidal mode, inherited from incompressible turbulence, and the acoustic and entropic modes, which are specific to the compressible problem. An approach to acoustic wave turbulence, with resonant triads, is revisited on this occasion.

Personal Recollections on Jack Herring and Developments in Theory of Turbulence, Atmospheric Sciences, and Computational Fluid Dynamics

The majority of articles in this Special Issue illuminate various aspects of Jack Herring’s contributions to the theory of turbulence, atmospheric sciences, and computational fluid dynamics (CFD), be it through his publications, presentations, collaborations, work with colleagues and students, or personal contacts [...]

A Variant of the Local Similarity Theory and Approximations of Vertical Profiles of Turbulent Moments of the Atmospheric Convective Boundary Layer

The approximation of the turbulent moments of the atmospheric convective layer is based on a variant of the local similarity theory using the concepts of the semi-empirical theory of Prandtl turbulence. In the proposed variant of the local similarity theory, the second moment of vertical velocity and the “spectral” Prandtl mixing length are used as basic parameters. This approach allows us to extend Prandtl’s theory to turbulent moments of vertical velocity and buoyancy and additionally offer more than ten new approximations. The comparison of the proposed approximation with other variants of the theory of local similarity is considered. It is shown that the selected basic parameters significantly improve the agreement between the local similarity approximations and experimental data. The approximations are consistent with observations in the turbulent convective layer of the atmosphere, the upper boundary of which nearly corresponds to the lower boundary of the temperature inversion. Analytical approximations of local similarity can find applications in the construction of high-order moment closures in the vortex of resolving numerical turbulence models, as well as in the construction of “mass-flux” parametrization.

Transition from weak turbulence to collapse turbulence regimes in the Majda-McLaughlin-Tabak model.

It is well known that wave collapses can emerge from the focusing one-dimensional (1D) Majda-McLaughlin-Tabak (MMT) model as a result of modulational instability. However, how these wave collapses affect the spectral properties and statistics of the wave field has not been adequately studied. We undertake this task by simulating the forced-dissipated 1D MMT model over a range of forcing amplitudes. Our results show that when the forcing is weak, the spectrum agrees well with the prediction by wave turbulence theory with few collapses in the field. As the forcing strength increases, we see an increase in the occurrence of collapses, together with a transition from a power-law spectrum to an exponentially decaying spectrum. Through a spectral decomposition, we find that the exponential spectrum is dominated by the wave collapse component in the nonintegrable MMT model, which is in analogy to a soliton gas in integrable turbulence.