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We investigate the flow inside a 2D square cavity driven by the motion of two mutually facing walls independently sliding at different speeds. The exploration, which employs the lattice Boltzmann method (LBM), extends on previous studies that had the two lids moving with the exact same speed in opposite directions. Unlike there, here the flow is governed by two Reynolds numbers (ReT, ReB) associated to the velocities of the two moving walls. For convenience, we define a bulk Reynolds number Re and quantify the driving velocity asymmetry by a parameter a. Parameter a has been defined in the range a¿[-p/4, 0] and a systematic sweep in Reynolds numbers has been undertaken to unfold the transitional dynamics path of the two-sided wall-driven cavity flow. In particular, the critical Reynolds numbers for Hopf and Neimark-Sacker bifurcations have been determined as a function of a. The eventual advent of chaotic dynamics and the symmetry properties of the intervening solutions are also analyzed and discussed. The study unfolds for the first time the full bifurcation scenario as a function of the two Reynolds numbers, and reveals the different flow topologies found along the transitional path, This work is supported by the projects of the North‐ western Polytechnical University (No. G2021KY05103), the Natioanl Key Laboratory of Science and Technology on Aero‐ dynamic Design and Research (No. 614220121030101), the Key Laboratory of Icing and Anti/De-icing of China Aerodynamics Research and Development Center (No. IADL20210302), the Spanish Government (Nos. FIS 2016-77849-R and PID2020- 114043GB-I00), the Catalan Government (No. 2017-2017-SGR00785), and the Barcelona Supercomputing Centre (Nos. FI2017-2-002, FI-2017-3-0009, and FI-2016-3-0038), Postprint (author's final draft)

The geometrically complex mechanisms of energy transfer in the compound space of scales and positions of wall turbulent flows are investigated in a temporally evolving boundary layer. The phenomena consist of spatially ascending reverse and forward cascades from the small production scales of the buffer layer to the small dissipative scales distributed among the entire boundary layer height. The observed qualitative behaviour conforms with previous results in turbulent channel flow, thus suggesting that the observed phenomenology is a robust statistical feature of wall turbulence in general. An interesting feature is the behaviour of energy transfer at the turbulent/non-turbulent interface, where forward energy cascade is found to be almost absent. In particular, the turbulent core is found to sustain a variety of large-scale wall-parallel motions at the turbulent interface through weak but persistent reverse energy cascades. This behaviour conforms with previous results in free shear flows, thus suggesting that the observed phenomenology is a robust statistical feature of turbulent shear flows featuring turbulent/non-turbulent interfaces in general., Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Energy Technology

Author Posting. © American Geophysical Union, 2022. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research: Oceans 127(6), (2022): e2021JC017307, https://doi.org/10.1029/2021jc017307., This study examines the spatial and temporal variability of eddy kinetic energy over the Northeast Shelf using observations of surface currents from a unique array of six high frequency radar systems. Collected during summer and winter conditions over three consecutive years, the horizontal scales present were examined in the context of local wind and hydrographic variability, which were sampled concurrently from moorings and autonomous surface vehicles. While area-averaged mean kinetic energy at the surface was tightly coupled to wind forcing, eddy kinetic energy was not, and was lower in magnitude in winter than summer in all areas. Kinetic energy wavenumber spectral slopes were generally near k−5/3, but varied seasonally, spatially, and between years. In contrast, wavenumber spectra of surface temperature and salinity along repeat transect lines had sharp k−3 spectral slopes with little seasonal or inter-annual variability. Radar-based estimates of spectral kinetic energy fluxes revealed a mean transition scale of energy near 18 km during stratified months, but suggested much longer scales during winter. Overall, eddy kinetic energy was unrelated to local winds, but the up- or down-scale flux of kinetic energy was tied to wind events and, more weakly, to local density gradients., This analysis was supported by NSF grants OCE-1657896 and OCE-1736930 to Kirincich, OCE-1736709 to Flament, and OCE-1736587 to Futch. Flament is also supported by NOAAs Integrated Ocean Observing System through award NA11NOS0120039., 2023-11-21

Using direct numerical simulations, this thesis studies primarily fundamental aspects of homogeneous rotating turbulence. Within this context, we first investigate the transition from a split to a forward kinetic energy cascade system with a parametric study covering large aspect ratio domains, which are in the direction of rotation up to 340 times larger than the initial eddy size, and a broad range of rotation rates. This unprecedented database shows that, for fixed geometrical dimensions, the Rossby number governs the amount of energy that cascades to large scales, whereas, for a fixed Rossby number, the control parameter is given by the product between domain size along the rotation axis and forcing wavenumber. Second, we quantify the growth rate of the columnar eddies typical of rotating flows and seek for a scaling law for the energy dissipation rate. Our results indicate that the growth rate of the columnar eddies varies exponentially with the Rossby number, while, for the dissipation scaling law, an analysis based on timescales yields to a power law dependence on the Rossby number. Additionally, we also examine an inertia-gravity wave breaking in the middle-upper mesosphere. We show that optimal perturbations lead to an almost instantaneous wave breaking and secondary bursts of turbulence, a process marked by the formation of fine flow structures around the wave's least stable point. Further, we find that during the breaking events the energy dissipation rate tends to be an isotropic tensor and the local energy transfer, which is predominantly from mean to fluctuating field, is in balance with the pseudo kinetic energy dissipation rate. The latter is relevant to atmospheric flows and a case where rotation and stratification effects coexist., Aerodynamics

In order to investigate the dynamics of atmospheric turbulence, we have derived a new formulation of the spectral energy budget of kinetic and available potential energies of the atmosphere, with spherical harmonics as base functions. Compared to previous formulations, there are three main improvements: (i) the topography is taken into account, (ii) the exact three-dimensional advection terms are considered and (iii) the vertical flux is separated from the energy transfer between different spherical harmonics. Using this formulation, results from two different high resolution GCMs are analyzed: the AFES T639L24 and the ECMWF IFS T1279L91. The spectral fluxes show that the AFES, which reproduces realistic horizontal spectra with a k−5/3 inertial range at the mesoscales, simulates a strong downscale energy cascade. In contrast, neither the k−5/3 vertically integrated spectra nor the downscale energy cascade are produced by the ECMWF IFS., QC 20211001

Two studies of two-dimensional models of flows influenced by stratification and stratification/rotation are carried out in order to investigate whether a two-dimensional model can reproduce a downscale energy cascade with an associated k − 5/3 wavenumber spectrum. Firstly, a series of highly resolved numerical simulations of the classical shallow water model is carried out. A forward energy cascade is observed but the dynamics is dominated by shocks, with an associated k −2-spectrum. A theory for shallow water wave turbulence is formulated and compared to the results from the simulations. Secondly, a series of simulations of a new two-dimensional toy model is carried out, showing that the model is not generating shocks and can reproduce a downscale energy cascade with an associated k − 5/3 spectrum. The energy transfer is studied in detail in Fourier space and is compared with results from a general circulation model. An experimental study of strongly stratified turbulence at the Coriolis platform in Grenoble is carried out, with the aim of testing novel theories of stratified turbulence. Turbulence is generated by traversing an array of cylinders through a tank containing stratified salt water. Velocity is measured by Particle Image Velocimetry (PIV) and density is measured by conductivity probes. In particular, the author has developed the software system analysing the PIV images. Preliminary results from the experiment are presented. To realise the research objectives, a set of open-source software packages are developed in Python, under the umbrella of the FluidDyn project. The packages enable execution of simulations, experiments and processing of data. The codes are well documented, tested and designed to promote development and reuse., Två studier av tvådimensionella modeller av strömningar influerade av stratifiering respektive stratifiering och rotation genomförs, i syfte att undersöka huruvida en tvådimensionell modell kan reproducera en energikaskad till mindre skalor med ett associerat vågtalsspektrum av formen k−5/3. Först genomförs enserie högupplösta simuleringar av den klassiska modellen för strömningar i grunt vatten (shallow water model). En energikaskad till mindre skalor observeras,men strömningen domineras av stötar med ett associerat k−2-spektrum. Sedan genomförs en serie simuleringar av en ny tvådimensionell leksaksmodell, som visar att modellen kan reproducera en energikaskad till mindre skalor med ett associerat k−5/3-spektrum. Energiöverföringen studeras i detalj i Fourier-rummet och jämförs med resultat från en global cirkulationsmodell. En experimentell studie av starkt stratifierad turbulens genomförs vid Coriolisplattformen i Grenoble, med målet att testa nya teorier för stratifierad turbulens. Turbulensen genereras genom att traversera en rad cylindrar genom en tank innehållande stratifierat saltvatten. Hastighet mäts med Particle ImageVelocimetry (PIV) och densitet mäts med konduktivitetssonder. I synnerhet har författaren utvecklat den programvara som analyserar bilder från PIVmätningarna. Preliminära resultat från experimentet presenteras. För att realisera forskningsmålen utvecklas en mängd mjukvarupaket för öppet bruk i Python, i ett projekt med namnet FluidDyn. Paketen erbjuder möjligheter att utföra simuleringar, experiment och databehandling. Koderna är väl dokumenterade, testade och designade för att underlätta utveckling och återanvändning., QC20190902QC 20200113

Conceived as a major new tool for climate studies, the Surface Water and Ocean Topography (SWOT) satellite mission will launch in late 2021 and will retrieve the dynamics of the oceans upper layer at an unprecedented resolution of a few kilometers. During the calibration and validation (CalVal) phase in 2022, the satellite will be in a 1- day-repeat fast sampling orbit with enhanced temporal resolution, sacrificing the spatial coverage. This is an ideal opportunity - unique for many years to come - to coordinate in situ experiments during the same period for a focused study of fine scale dynamics and their broader roles in the Earth system. Key questions to be addressed include the role of fine scales on the ocean energy budget, the connection between their surface and internal dynamics, their impact on plankton diversity, and their biophysical dynamics at the ice margin.

Price dynamics of speculative markets is one of the most complex phenomena in economics. Already the statistical description turns out to be difficult. The most prominent characteristic of the distribution of logarithmic price differences (returns) Δy for a given time delay Δt is its lepto- kurtosis, i.e., the pronounced frequencies with which both small and large returns occur. Proper modelling of this effect is of practical relevance for risk management. The kurtosis of the return distribution is largest for Δt of the order of minutes and decreases monotonically with increasing Δt, accompanied by an according change in the form of the distribution [1, 2]. Simultaneously, the variance of the distribution increases: it depends on the time delay according to a power law ((Δy)2) ~ Δt ε2.

A turbulent flow is composed of swirling eddies of many sizes. Energy, which is added to the flow at the larger scales, is transferred down through consecutively smaller eddies until the scale is small enough that viscous forces dominate, at which point the energy is dissipated. The mechanism by which energy is transferred down the scales of eddies is generally described as eddy break-up, but the process of eddies breaking into smaller eddies has never been directly observed. The objective of this research is to identify and visualize eddies and their breakage into smaller eddies in numerically simulated isotropic turbulence flows. A corre- lation vector is defined at each point in space, based upon the dot product of velocity over spatial distance. This function shows eddies as the result of correlation over the entire field for each point, in contrast to ear- lier eddy identification techniques which focus only on local properties of the flow, such as kinetic energy magnitude. The resultant correlation field shows blobs of high correlation, which can be interpreted as the kernel of a coherent structure in the flow. These kernels can be seen splitting into smaller kernels over time — an indication of the turbulent energy cascade at work. Making use of the Biot-Savart law, the veloc- ity field associated with a coherent blob of correlation is generated from the associated vorticity field. The reconstructed velocity field is vortex-like in structure, and appears to break into two separate vortices as the kernel separates into two distinct kernels, yielding a visualization of turbulent eddy dynamics in real space — the first step towards the visualization of the turbulent energy cascade., Molecular Science & Technology

Over the past 30 years, the Eddy Dissipation Concept (EDC) has been widely applied in the industry for the numerical simulations of turbulent combustion problems. The success of the EDC is mainly due to its ability to incorporate detailed chemical mechanisms at an affordable computational cost compared to some other models. Detailed kinetic schemes are necessary in order to capture turbulent flames where there is strong coupling between the turbulence and chemical kinetics. Such flames are found in Moderate and Intense Low-oxygen Dilution (MILD) combustion, where chemical time scales are increased compared with conventional combustion, mainly because of slower reactions (due to the dilution of reactants). Recent modelling studies have highlighted limitations of the standard EDC model when applied to the simulation of MILD systems, noticeably a significant overestimation of temperature levels. Modifications of the model coefficients were proposed to account for the specific features of MILD combustion, i.e. an extension of the reaction region and the reduction of maximum temperatures. The purpose of the present paper is to provide functional expressions showing the dependency of the EDC coefficients on dimensionless flow parameters such as the Reynolds and Damköhler numbers, taking into account the specific features of the MILD combustion regime, where the presence of hot diluent and its influence on the flow and mixing fields impacts on the reaction rate and thermal field. The approach is validated using detailed experimental data from flames stabilized on the Adelaide Jet in Hot Co-flow (JHC) burner at different co-flow compositions (3%, 6% and 9% O2 mass fraction) and fuel-jet Reynolds numbers (5000, 10,000 and 20,000). Results show promising improvement with respect to the standard EDC formulation, especially at diluted conditions and medium to low Reynolds numbers. © 2015 Elsevier Ltd.

Two codes have been developed and implemented for use on massively parallelsuper computers to simulate two-dimensional and quasi-geostrophic turbulence.The codes have been found to scale well with increasing resolution and width ofthe simulations. This has allowed for the highest resolution simulations of twodimensionaland quasi-geostrophic turbulence so far reported in the literature.The direct numerical simulations have focused on the statistical characteristicsof turbulent cascades of energy and enstrophy, the role of coherent vorticesand departures from universal scaling laws, theoretized more than 40 yearsago. In particular, the investigations have concerned the enstrophy and energycascades in forced and decaying two-dimensional turbulence. Furthermore, theapplicability of Charney’s hypotheses on quasi-geostrophic turbulence has beentested. The results have shed light on the flow evolution at very large Reynoldsnumbers. The most important results are the robustness of the enstrophycascade in forced and decaying two-dimensional turbulence, the sensitivity toan infrared Reynolds number in the spectral scaling of the energy spectrumin the inverse energy cascade range, and the validation of Charney’s predictionson the dynamics of quasi-geostrophic turbulence. It has also been shownthat the scaling of the energy spectrum in the enstrophy cascade is insensitiveto intermittency in higher order statistics, but that corrections apply to the”universal” Batchelor-Kraichnan constant, as a consequence of large-scale dissipationanomalies following a classical remark by Landau (Landau & Lifshitz1987). Another finding is that the inverse energy cascade is maintained bynonlocal triad interactions, which is in contradiction with the classical localityassumption., QC 20101029

Our long-term scientific goal is to better understand the mechanisms by which mixing occurs in the ocean so that we can develop improved parameterizations of mixing for ocean models. Mixing within the stratified ocean is our particular focus, as the complex interplay of internal waves from a variety of sources and turbulence makes this a current locus of uncertainty. In this project, our broad focus is on the energy sources of nonlinear internal waves (NLIWs) in a complex environment of strong internal tides and abrupt topography (continental shelf and slope). We expect a rapid evolution of internal tides and NLIWs, and aim to understand their dynamics, energy cascade, and role in mixing. The primary objectives of the project are as follows: (1) to identify the generation sites and understand the generation mechanism of NLIWs, (2) to understand the evolution of NLIW interactions with abrupt topography, (3) to quantify the energy budget and energy cascade from internal tides to NLIWs, and (4) to quantify the seasonal variation of the energy of NLIWs near Dongsha Plateau in the northern South China Sea (SCS). Our particular interest is to understand the energy cascade from barotropic tides, internal tides, and NLIWs to turbulence mixing in the northern SCS, and to understand the evolution of NLIWs interacting with the shoaling continental slope. Our approach is to take direct observations of NLIWs near Dongsha Island, where NLIWs are often captured in satellite images. Primary platforms include an ADV Lagrangian Float; an array of bottom-mounted ADCP moorings; and shipboard EK500, marine radar, ADCP, and CTD. Our main goals are to quantify the energy budget and evolution of NLIWs across the rapidly shoaling continental slope and the gentle plateau near Dongsha Island, and to quantify the seasonal variation of NLIW characteristics.

Two related projects were funded sequentially under the same grant number. The first was to conduct an experiment near DongSha Island, using the Lagrangian float, to understand the energy cascade from barotropic tides, internal tides, nonlinear internal waves, to turbulence mixing in the northern South China Sea. Results are reported. The second was to analyze observations of data taken in the vicinity of the Kuroshio path from Luzon Strait to the southern East China Sea. Results are reported.

Direct numerical simulations of stably and strongly stratified turbulent flows with Reynolds number Re >> 1 and horizontal Froude number F-h << 1 are presented. The results are interpreted on the basis of a scaling analysis of the governing equations. The analysis suggests that there are two different strongly stratified regimes according to the parameter R = ReFh2. When R >> 1, viscous forces are unimportant and l(v) scales as l(v) similar to U/N (U is a characteristic horizontal velocity and N is the Brunt-Vaisala frequency) so that the dynamics of the flow is inherently three-dimensional but strongly anisotropic. When R << 1, vertical viscous shearing is important so that l(v) similar to l(h)/Re-1/2 (l(h) is a characteristic horizontal length scale). The parameter R is further shown to be related to the buoyancy Reynolds number and proportional to (l(O)/eta)(4/3), where l(O) is the Ozmidov length scale and eta the Kolmogorov length scale. This implies that there are simultaneously two distinct ranges in strongly stratified turbulence when R >> 1: the scales larger than l(O) are strongly influenced by the stratification while those between l(O) and eta are weakly affected by stratification. The direct numerical simulations with forced large-scale horizontal two-dimensional motions and uniform stratification cover a wide Re and F-h, range and support the main parameter controlling strongly stratified turbulence being R. The numerical results are in good agreement with the scaling laws for the vertical length scale. Thin horizontal layers are observed independently of the value of R but they tend to be smooth for R < 1, while for R > 1 small-scale three-dimensional turbulent disturbances are increasingly superimposed. The dissipation of kinetic energy is mostly due to vertical shearing for R < 1 but tends to isotropy as R increases above unity. When R < 1, the horizontal and vertical energy spectra are very steep while, when R > 1, the horizontal spectra of kinetic, QC 20100525

Mesoscale intrathermocline eddies play an important role in transferring heat, salinity, and momentum in large-scale flows, actively influencing the general circulation of the ocean. Nevertheless, the factors controlling the longevity and coherence of mesoscale eddies are much debated. One of the key questions is the relative significance of double diffusion and turbulence in the dispersion of mesoscale variability. Several observational studies have implicated the lateral intrusions, driven by double-diffusive mixing, in the ultimate disintegration of eddies. However, observational limitations precluded unambiguous quantification of the impact of interleaving on the basis of field measurements. To the best of our knowledge, this research presents the first intrusion-resolving numerical simulation of a mesoscale eddy. This study is focused on the dynamics of a Mediterranean eddy (meddy). Double diffusion and turbulence of various strengths are applied to both static and dynamic (rotating) eddies in order to isolate the effects and determine the dominant players. The prominent findings of this study are threefold: (1) Double diffusion is a key process in dissipating an eddy. (2) Lateral diffusivity values calculated from the numerical simulations fall within the range of observed values. (3) A static eddy dissipates in a very different manner from a dynamic eddy, which underscores inherent limitations of intrusion modeling in quiescent background states. Finally, it should be emphasized that while the key physical processes at play are illustrated here on a specific example of meddies, the broader implications of our findings are much more fundamental and far-reaching. It is our belief that this study provides a clue to one of the long-standing problems in physical oceanography, namely, the link between the basin-scale forcing of the ocean by air-sea fluxes and the dissipation of energy and thermal variance at the microscale., http://archive.org/details/dynamicsstabilit1094551618, Outstanding Thesis, Lieutenant Commander, United States Navy, Approved for public release; distribution is unlimited.