Lagrangian and inertial transport in atmospheric and chaotic flows

This thesis presents a compendium of publications related to transport studies analyzed from the perspective of dynamical systems. The goal is to address the role that particle properties and the flow have on the organization of trajectories and hence the transport. To observe how transport is structured, we focus on the most widely used method: the Finite Time Lyapunov Exponents. These exponents measure the separation rate of the particles starting from nearby initial positions, estimating the hyperbolicity of the trajectories. This method allows us to make a first approach to the problem, obtaining the borders or frontiers between regions with different dynamics given a simplified vision of transport. The transport structures related with this method, are called Lagrangian Coherent Structures. In the first study, the Lagrangian transport in the troposphere was analyzed. The atmospheric flow is characterized by being turbulent in a continuum of spatiotemporal scales. Within these scales, it was observed that there are structures such as the Atmospheric Rivers that maintain a spatial and temporal coherence of the order of days acting as organizers of water vapor transport and therefore dominating the dynamics of the region at the moment they occur. At the same time, the persistence and repetition of these structures, together with all the other tropospheric structures, introduce mixing into the atmosphere. Those areas in middle latitudes where these structures develop have higher mixing variability. This is mainly due to seasonal changes. However, those regions with less variability, such as the equatorial zones, the mixing and its variability on day scales, are mainly associated with inter-annual variability events such as El Ni ˜no or La Ni ˜na or the Intertropical Convergence Zone (ITCZ). In addition, the mixing information of the air masses from a climatic point of view, was used as a predictor of rainfall for the Iberian region. The Atlantic margin is characterized by an intense activity of Atmospheric Rivers, being one of the main causes of precipitation. However, the problem of determining the activity of rainfall months in advance is complex, for this reason the use of new variables as potential predictors is required. It has been obtained that the mixing, in the Atlantic region, is related to the precipitation on the Iberian Peninsula. Addressing on the second study, we focus on the influence of forces on the particles motion so the resolution of motion equation is required to obtain the trajectories they describe. The particles are modeled as small spheres with mass, but the fact that their movement is decoupled from the flow makes their trajectories depend initially on other properties such as the initial velocity. It was observed that this dependence, for certain flows, is even higher than small perturbations in its position, mainly in those regions where there is a high spatial variability of the fluid such as regions with shear. The same happens for bubbles where flotation effects appear. They are very sensitive to the inertial effects and especially to the disturbances of the radius as well as the effects of merging with other bubbles, being especially relevant in the initial instants of the movement. In addition, it has been observed that particles properties and their collective motion play a key role in the synchronization of finite-size chemical oscillators. To experimentally support some of the aforementioned behaviors, experimental data are needed to measure the trajectories of the particles. Particle Tracking Velocimetry (PTV) methods, track the trajectories of individual particles in three-dimensional space. In the last part of this thesis, we present an experimental setup and some preliminary results of trajectories of the particles mentioned above in a high turbulent flow

A method to calculate finite-time Lyapunov exponents for inertial particles in incompressible flows

The present study aims to improve the calculus of finite-time Lyapunov exponents (FTLEs) applied to describe the transport of inertial particles in a fluid flow. To this aim, the deformation tensor is modified to take into account that the stretching rate between particles separated by a certain distance is influenced by the initial velocity of the particles. Thus, the inertial FTLEs (iFTLEs) are defined in terms of the maximum stretching between infinitesimally close trajectories that have different initial velocities. The advantages of this improvement, if compared to the standard method (Shadden et al., 2005), are discussed for the double-gyre flow and the meandering jet flow. The new method allows one to identify the initial velocity that inertial particles must have in order to maximize their dispersion.This work was supported by the Ministerio de Economía y Competitividad under research grant CGL2013-45932-RS

Tagging moisture sources with Lagrangian and inertial tracers: application to intense atmospheric river events

Two Lagrangian tracer tools are evaluated for studies on atmospheric moisture sources and pathways. In these methods, a moisture volume is assigned to each particle, which is then advected by the wind flow. Usual Lagrangian methods consider this volume to remain constant and the particle to follow flow path lines exactly. In a different approach, the initial moisture volume can be considered to depend on time as it is advected by the flow due to thermodynamic processes. In this case, the tracer volume drag must be taken into account. Equations have been implemented and moisture convection was taken into account for both Lagrangian and inertial models. We apply these methods to evaluate the intense atmospheric rivers that devastated (i) the Pacific Northwest region of the US and (ii) the western Iberian Peninsula with flooding rains and intense winds in early November 2006 and 20 May 1994, respectively. We note that the usual Lagrangian method underestimates moisture availability in the continent, while active tracers achieve more realistic resultsERA-Interim data were supported by the ECMWF. This work was financially supported by Ministerio de Economía, Industria y Competitividad (CGL2017-89859-Rand CGL2013-45932-R), with contributions by the COST Action MP1305 and CRETUS strategic partnership (AGRUP2015/02). All these programs are co-funded by the ERDF (EU)S

Climatology of Lyapunov exponents : the link between atmospheric rivers and large-scale mixing variability

Large-scale tropospheric mixing and Lagrangian transport properties have been analyzed for the long-term period 1979–2014 in terms of the finite-time Lyapunov exponents (FTLEs).Wind field reanalyses from the European Centre for Medium-Range Weather Forecasts were used to calculate the Lagrangian trajectories of large ensembles of particles. Larger values of the interannual and intra-annual mixing variabilities highlight the El Niño Southern Oscillation, the storm track, or the Intertropical Convergence Zone among other largescale structures. The mean baroclinic instability growth rate and the mean atmospheric river occurrence show large correlation values with the FTLE climatology as an indication of their influence on tropospheric mixing in the midlatitudes. As a case study, the role that land-falling atmospheric rivers have on large-scale tropospheric mixing and the precipitation rates observed in Saharan Morocco and the British Isles has been analyzed. The atmospheric river contribution to tropospheric mixing is found to decrease from 15% in Saharan Morocco to less than 5% for the UK and Ireland regions, in agreement with their contribution to precipitation that is 40% larger in the former than in the latter regionThis work was financially supported by Ministerio de Economía y Competitividad and Xunta de Galicia (CGL2013-45932-R, GPC2015/014) and contributions by the COST Action MP1305 and CRETUS Strategic Partnership (AGRUP2015/02). All these programs are co-funded by ERDF (EU)S

Influence of finite-time Lyapunov exponents on winter precipitation over the Iberian Peninsula

Seasonal forecasts have improved during the last decades, mostly due to an increase in understanding of the coupled ocean–atmosphere dynamics, and the development of models able to predict the atmosphere variability. Correlations between different teleconnection patterns and severe weather in different parts of the world are constantly evolving and changing. This paper evaluates the connection between winter precipitation over the Iberian Peninsula and the large-scale tropospheric mixing over the eastern Atlantic Ocean. Finite-time Lyapunov exponents (FTLEs) have been calculated from 1979 to 2008 to evaluate this mixing. Our study suggests that significant negative correlations exist between summer FTLE anomalies and winter precipitation over Portugal and Spain. To understand the mechanisms behind this correlation, summer anomalies of the FTLE have also been correlated with other climatic variables such as the sea surface temperature (SST), the sea level pressure (SLP) or the geopotential. The East Atlantic (EA) teleconnection index correlates with the summer FTLE anomalies, confirming their role as a seasonal predictor for winter precipitation over the Iberian PeninsulaThis work was financially supported by the Ministerio de Economía y Competitividad and Xunta de Galicia (CGL2013-45932-R, GPC2015/014), and contributions by COST Action MP1305 and the CRETUS Strategic Partnership (AGRUP2015/02). All these programs are co-funded by the ERDF (EU). The support of Office of Naval Research grant no. N00014-16-1-2492 is also acknowledgedS

Evaluation of the moisture sources in two extreme landfalling atmospheric river events using an Eulerian WRF tracers tool

A new 3-D tracer tool is coupled to the WRF model to analyze the origin of the moisture in two extreme atmospheric river (AR) events: the so-called Great Coastal Gale of 2007 in the Pacific Ocean and the Great Storm of 1987 in the North Atlantic. Results show that between 80 and 90 % of moisture advected by the ARs, and a high percentage of the total precipitation produced by the systems have a tropical origin. The tropical contribution to precipitation is in general above 50 % and largely exceeds this value in the most affected areas. Local convergence transport is responsible for the remaining moisture and precipitation. The ratio of tropical moisture to total moisture is maximized as the cold front arrives on land. Vertical cross sections of the moisture content suggest that the maximum in tropical humidity does not necessarily coincide with the low-level jet (LLJ) of the extratropical cyclone. Instead, the amount of tropical humidity is maximized in the lowest atmospheric level in southern latitudes and can be located above, below or ahead of the LLJ in northern latitudes in both analyzed casesThis work has been founded by the Ministerio de Economía y Competitivad (CGL2013-45932-R) from the Spanish Government and its mobility grants for pre-doc researchers. Funding for Dominguez and Hu comes from NASA grant NNX14AD77GS

Measurements of the energy dissipation rate in homogeneous turbulence using dense 3D Lagrangian Particle Tracking and FlowFit

We present measurements of the full velocity gradient tensor and all volumetric dissipation rate elements based on dense fields of fluid particle trajectories in homogeneous turbulence at Re ~270 and ~370 in a Kármán flow between two counter-rotating disks with impellers. Applying the Shake-The-Box (STB) Lagrangian Particle Tracking (LPT) algorithm, we are able to instantaneously track up to 80.000 particles in a volume of 40 x 40 x 15 mm³. The mean interparticle distance is lower than 7 Kolmogorov lengths for the Re_lambda ~270 case. A data assimilation scheme (FlowFit) with continuity and Navier-Stokes- constraints is used to interpolate the scattered velocity and acceleration data by a continuous 3D B-Spline representation, enabling to recover (locally) the smallest flow scales. In the presentation, we show Lagrangian velocity and acceleration statistics, as well as the Eulerian counterparts on velocity gradients and pressure fields. We compute the energy dissipation rate directly by making use of quadruples of particle trajectories in close proximity (r < 3 eta) and compare it to indirect approaches using second-order velocity- and velocityacceleration structure functions in the inertial subrange

Flow structure dynamics with extreme dissipation events in homogeneous turbulence – an experimental investigation using shake-the-box and flowfit

Since the introduction of the Richardson-Kolmogorov cascade a picture of turbulence has been created that intrinsically connects a (in general) directional down-scaling process featuring vortical flow structures with the overall energy transfer finally ending into viscous dissipation at the smallest scales of the cascade. In turbulent flows at sufficient Reynolds number intermittency of extreme dissipation events is accompanied by strong enstrophy events and both have a close relationship to the pressure Laplacian. The aim of the present investigation is to analyze the temporal dynamics of flow structures generating extreme dissipation events. Conditional ensemble averages and Lagrangian viewpoints shall complement this topological study. We present measurements of the full velocity gradient tensor and all elements of the dissipation rate based on dense fields of fluid particle trajectories in homogeneous turbulence at Re~270 and ~370 in a von Kármán flow between two counter-rotating propellers. Applying the Shake-The-Box (STB) particle tracking algorithm [1], we are able to instantaneously track up to ~100.000 particles in a measurement volume of 50 x 50 x 15 mm³. The mean inter-particle distance is lower than 7 Kolmogorov lengths. The data assimilation scheme FlowFit [2] with continuity and Navier-Stokes- constraints is used to interpolate the scattered velocity and acceleration data by continuous 3D B-Splines in a cubic grid, enabling to recover (locally) the smallest flow scales. We compute the energy dissipation rate directly by using local velocity gradient information gained by FlowFit at midpoints of particle tetrahedra in close proximity of a few Kolmogorov lengths and compare it to known inertial range approaches using two-point statistics

Validation of a Lagrangian model for large-scale macroplastic tracer transport using mussel-peg in NW Spain (Ría de Arousa)

Marine debris is a growing problem in recent years due to population growth around the world. The incorrect management of plastic waste causes these bodies reach the seas and oceans, becoming a worldwide problem. Once they reach the seas and oceans, they begin a long period of degradation, moving from a macro state (plastics whose diameter is greater than 0.5 cm) to a micro state (diameter less than 0.5 cm). The microplastics spread throughout the oceans, entering the food chain of marine species and, subsequently, of humans. Therefore, it is important to stop the problem while it remains at the macroscale. In this work, a validation of a recently developed Lagrangian computational model to track the movement of macro plastics in seas and oceans is presented. This validation is performed on a regional scale, in the Ría de Arousa, one of the most important estuaries for mussel cultivation in northwestern Spain. During mussel cultivation in rafts, a type of floating plastic stick are released, the mussel-pegs. The potential of this study is that we can compare the accumulation results of the model with the accumulation data collected on the Galician beaches. In a general framework, the influence of wind on the spatial distribution of the accumulations given by the model was observed. For the monitoring data, similar results were found for the accumulation trends over the entire total period. For the monthly representation, some discrepancies were observed. These differences can be attributed to particular synoptic situations, poor reproduction of the coastline or to the very orientation of the study area with respect to the intertidal dynamicsWe gratefully acknowledge financial support by CleanAtlantic Interreg Project (EAPA 46/2016) and Xunta de Galicia under Research Grant No. 2021-PG036-1S

Effects of anisotropy on the geometry of tracer particle trajectories in turbulent flows

Using curvature and torsion to describe Lagrangian trajectories gives a full description of these as well as an insight into small and large time scales as temporal derivatives up to order 3 are involved. One might expect that the statistics of these properties depend on the geometry of the flow. Therefore, we calculated curvature and torsion probability density functions (PDFs) of experimental Lagrangian trajectories processed using the Shake-the-Box algorithm of turbulent von Kármán flow, Rayleigh-Bénard convection and a zero-pressuregradient boundary layer over a flat plate. The results for the von-Kármán flow compare well with experimental results for the curvature PDF and numerical simulation of homogeneous and isotropic turbulence for the torsion PDF. For the experimental Rayleigh-Bénard convection, the power law tails found agree with those measured for von-Kármán flow. Results for the logarithmic layer within the boundary layer differ slightly, we give some potential explanation below. To detect and quantify the effect of anisotropy either resulting from a mean flow or large-scale coherent motions on the geometry or tracer particle trajectories, we introduce the curvature vector. We connect its statistics with those of velocity fluctuations and demonstrate that strong large-scale motion in a given spatial direction results in meandering rather than helical trajectories