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The westward transversal current (TC) in the southern Yellow Sea entrance was investigated during winter 2007 using a numerical ocean model. The three-dimensional structures and dynamics of the westward TC were highlighted. The model-simulated monthly mean current fields showed that the strong westward TC was limited to the upper water column (shallower than 50 m) and extended westward from 126° E to 124° E. Momentum balance analysis indicated that the westward TC was mainly regulated by a quasi-geostrophic balance. Both the sea surface elevation–related barotropic pressure gradient force and the density-related baroclinic pressure gradient force controlled the intensity and direction of the westward TC. Sensitivity model experiments focusing on tide and wind demonstrated that the westward TC was intensified when tide was ignored and was greatly weakened when wind was excluded. Lagrangian particle tracking experiments were also performed, to investigate the relationship between the Yellow Sea Warm Current and the westward TC in the frontal region. The characteristics of the water in the Yellow Sea Warm Current were affected by the properties of the water in the frontal zone, especially in the sub-surface and lower layers. The westward TC might act as an important bridge, connecting the frontal zone with the Yellow Sea Warm Current flowing along the western Yellow Sea trough.

In a recently conducted study, we developed a nano-particle sizer (NPS) that consists of a multi-port differential mobility analyzer (MP-DMA) and two multi condensation particle counters (M-CPCs) for achieving fast measurements of aerosol particles; however, the performance of MP-DMA was not detailed in the study. Therefore, the objective of this study is to perform numerical simulations to obtain the transfer function of each port in the MP-DMA, which is the main component of the NPS. We observed good agreement between the numerically obtained central particle size of each port and the experimental data under the same operating conditions. The transmission probability and resolution of each port were determined and analyzed under various conditions using the transfer function. The findings of this study shall help in understanding the advantages of NPS.

Wind-driven rain is a major concern in the design of buildings, for the sake of occupational health and safety. In particular, for facilities such as schools, the ability to identify places at risk of wind-driven rain wetting allows for mitigation and a consequent reduction in accidents due to students slipping and falling on wet patches of corridors. In this work, we analyze a corridor previously identified as a potential area of concern by the facilities management personnel for a representative school in Singapore, and we assess possible mitigation measures for their ability to prevent wind-driven rain wetting in the problem area. By using Lagrangian particle tracking methods to simulate the wind-driven rain, we are able to assess the effectiveness of different mitigation methods such as vertical and horizontal barriers which are typically installed as down-hangs or sunshades. We show that the effectiveness of horizontal and vertical barriers is dependent on raindrop size, with vertical barriers being more effective for smaller raindrop sizes and horizontal barriers for larger raindrop sizes. In addition, we simulate the implementation of an angled barrier and show that angled barriers can be more effective than either horizontal or vertical barriers alone in resolving wind-driven rain issues.

The aeroelastic response of a highly flexible wing to periodic gust excitation is determined experimentally. The integrated optical measurement approach that is applied provides combined measurements of the structural response of the wing and the unsteady flow field around it. The aeroelastic loads acting on the wing are derived from these measurements using physical models and validated against force balance measurements. It is observed that both structural and aerodynamic responses to a periodic gust excitation of a given amplitude depend strongly on the frequency of the gust. The obtained data set of results provides a complete description of the aeroelastic response that is suited as a reference for the development of aeroelastic simulation models.

The process of an intracranial aneurysm development, growth, and rupture is multifaceted and complex. In addition, clinical observations have identified the potential of thrombus formation within such aneurysms. While the underlying mechanism is not fully understood, the thrombi represent a potential risk factor for ischemic stroke. Emerging studies indicate that blood residence time (RT) is a promising hemodynamic metric associated with the aneurysm rupture and formation of intra-aneurysmal thrombi. Here, we present a methodology to experimentally evaluate both trajectory-wise and local RT based on magnetic resonance imaging (MRI) velocimetry, and apply it to in vitro flow measurements in scaled-up replicas of 9 patient-specific intracranial aneurysms. Lagrangian tracks of massless tracers are integrated from the velocity fields and averaged to return the mean RT in the aneurysm sac. This is found to be closely approximated by a simple time scale based on the sac diameter and space–time average of the aneurysmal fluid velocity. The mean RT is also correlated with the inflow time scale at the parent artery. These results also provide a basis for the estimation of RT when high-resolution hemodynamic maps are not available. With the continuous increase in accuracy and resolution enabled by progress in MRI technology, the methodology described here may in the future be applicable to in vivo data., Journal of Biomechanics, 141, ISSN:0021-9290, ISSN:1873-2380

The modeling of dilute gas-particle flows is challenging due to particle-trajectory crossing (PTC). Lagrangian particle tracking can be used, but requires a large number of parcels resulting in high computational costs. A less costly method is the Eulerian number density function (NDF) approach, based on the Boltzmann equation, often solved in terms of lower-order moments of the NDF. In this context the conditional hyperbolic quadrature method of moments (CHyQMOM) was developed and is here implemented for the first time in the OpenFOAM-7, together with high-order advection schemes and a new operator splitting procedure. The resulting solver is used to simulate different test cases: phase segregation problems, collision-less and weakly-collisional PTC flows, asymmetric and symmetric Taylor-Green vortex flow and a dilute gas-particle riser. Results, validated against analytical solutions and predictions obtained with Lagrangian particle tracking, show that the implemented CHyQMOM can be used to handle highly non-equilibrium flows.

Magnetic nanoparticles are researched intensively not only for biomedical applications, but also for industrial applications including wastewater treatment and catalytic processes. Although these particles have been shown to have interesting surface properties in their bare form, their magnetisation remains a key feature, as it allows for magnetic separation. This makes them a promising carrier for precious materials and enables recovery via magnetic fields that can be turned on and off on demand, rather than using complex (nano)filtration strategies. However, designing a magnetic separator is by no means trivial, as the magnetic field and its gradient, the separator dimensions, the particle properties (such as size and susceptibility), and the throughput must be coordinated. This is showcased here for a simple continuous electromagnetic separator design requiring no expensive materials or equipment and facilitating continuous operation. The continuous electromagnetic separator chosen was based on a current-carrying wire in the centre of a capillary, which generated a radially symmetric magnetic field that could be described using cylindrical coordinates. The electromagnetic separator design was tested in-silico using a Lagrangian particle-tracking model accounting for hydrodynamics, magnetophoresis, as well as particle diffusion. This computational approach enabled the determination of separation efficiencies for varying particle sizes, magnetic field strengths, separator geometries, and flow rates, which provided insights into the complex interplay between these design parameters. In addition, the model identified the separator design allowing for the highest separation efficiency and determined the retention potential in both single and multiple separators in series. The work demonstrated that throughputs of ~1/4 L/h could be achieved for 250–500 nm iron oxide nanoparticle solutions, using less than 10 separator units in series.

Crud has been observed on the fuel rod surfaces in a variety of fuel designs around the world, and in some limited situations fuel performance was compromised due to crud-induced power shift (CIPS) and/or crud-induced localized corrosion (CILC). It is generally believed that crud deposition depends on fuel rod surface sub-cooled nucleate boiling, coolant chemistry and the availability of particles from component corrosion or from reinserted fuel. The formation, release, and accumulation of crud on the fuel and its influence on CIPS and/or CILC is a complicated process involving multi-physics phenomena. This study uses Computational Fluid Dynamics (CFD) Lagrangian Particle Tracking (LPT) techniques in analysis of particle transfer behavior in fuel rod bundles focusing on flow swirl and turbulence impacts. It is hoped that high fidelity CFD results can provide insights into particle transfer behaviors in the bulk coolant as well as near the fuel rods, which may provide guidance for model development of lumped or integrated analysis methods. The CFD model was built based on the best practices learned from previous single-phase analyses. The LPT options, including particle injectors, forces on particles, and solver settings, were verified by comparing the simulated results to the test data from simple geometry with various particle sizes, covering deposition mechanisms in diffusion-, turbulent- and inertial-dominated regimes. The tested model then was applied to Westinghouse fuel designs with and without Intermediate Flow Mixing (IFM) grids. Particle concentration and size distributions in the coolant around fuel rods were obtained and the effects of grid induced swirl flow on particle transfer were identified. The analysis results may be included in lumped or integrated crud formation/release analysis methods. Limitations and potential improvements of this analysis method are also discussed.

The method of iterative particle reconstruction (IPR), introduced by Wieneke (Meas Sci Technol 24:024008, 2013), constitutes a major step toward Lagrangian particle tracking in densely seeded flows (Schanz et al. in Exp Fluids 57:1–27, 2016). Here we present novel approaches in several key aspects of the algorithm, which, in combination, triple the working range of IPR in terms of particle image densities. The updated method is proven to be fast, accurate and robust against image noise and other imaging artifacts. Most of the proposed changes to the original processing are easy to implement and come at low computational cost. Furthermore, a bundle adjustment scheme that simultaneously updates the 3D locations of all particles and the camera calibrations is introduced. While the particle position optimization proved to be more effective using localized ‘shake’ schemes, this so-called global shake scheme constitutes an effective measure to correct for decalibrations and vibrations, acting as an in-situ single-image volume-self-calibration. Further optimization strategies using such approaches are conceivable. Graphic abstract

In this study, a new image calibration approach is presented that corrects arbitrary optical distortions by utilizing non-parametric, 3D disparity fields. A calibration plate with a high spatial resolution (i.e., high density of calibration marks) was used to identify optical distortions that remain after the initial calibration, which were then used to create a correction field for the pinhole or polynomial mapping functions. Results from a pipe flow experiment with four cameras using volume self-calibration (VSC) and Shake-the-Box Lagrangian particle tracking (STB LPT) are presented and the impact of the improved calibration is discussed. Using the calibration marks with the correction field, distortions of initially more than 20 pixels are reduced below 1 pixel. Using VSC with the correction field allows further reduction of average calibration disparities below 0.02 pixels (maximum 0.5 pixels), whereas without a correction field the remaining average disparity is much higher at 1 pixel (maximum 5 pixels). STB analysis of the data shows a considerable higher spatial resolution at the pipe wall and a consistent spatial distribution of the number of detected particles in the measurement volume.

Lagrangian Particle Tracking (LPT) has become a near-standard approach for performing accurate 3D flow measurements, thanks notably to the technical breakthroughs brought by the Iterative Particle Reconstruction (IPR: Wieneke, 2013) and Shake-the-Box (STB: Schanz et.al, 2016) procedures. These decisive progresses have triggered a number of studies relative to the eduction of flow kinematics and dynamics based on particle trajectory analyses. Novara & Scarano (2013), and others, focused on polynomial approximations of the trajectories, which analytically provide the material derivatives used to estimate pressure gradients. In particular, approximations based on second order polynomials fits of a small number of particle positions are used in commercially available softwares and among research teams as a straightforward solution to obtain the first and second order derivatives with a limited effect of the measurement noise. Additionally the analyses conducted during the 2020 LPT challenge (Leclaire, 2020 ; Sciacchitano, 2020) have addressed the performance of methodologies used by different groups with respect to second order trajectory fits for both multi-pulse and four-pulse (Novara et. al, 2016) LPT cases. On more advanced theoretical grounds, Geseman et. al (2016) have proposed the trackfit approach using penalized B-splines with considerations on the time-varying acceleration rate (i.e. jolt or jerk) and spectral content of noisy particle tracks

International audience; Recent developments in time-resolved Particle Tracking Velocimetry (4D-PTV) consistently improved tracking accuracy and robustness. We propose a novel technique named "Lagrangian coherent predictor" to estimate particle positions within the 4D-PTV algorithm. We add spatial and temporal coherency information of neighbour particles to predict a single trajectory using Lagrangian Coherent Structures (LCS). We found that even a weak signal from coherent neighbour motions improves particle prediction accuracy in complex flow regions. We applied Finite Time Lyapunov Exponent (FTLE) to quantify local boundaries (i.e. ridges) of coherent motions. Synthetic analysis of the wake behind a smooth cylinder at Reynolds number equal to 3900 showed enhanced estimation compared with the recent predictor functions employed in 4D-PTV. Results of the experimental study of the same flow configuration are reported. We compared predicted positions with the optimised final positions of Shake The Box (STB). It was found that the Lagrangian coherent predictor succeeded in estimating particle positions with minimum deviation to the optimised positions.

This paper aims at analysing the behaviour of particle localisation error in 3D Lagrangian Particle Tracking (LPT) techniques, with a particular emphasis on general properties, independent of a specific algorithm. Based on the hypothesis that in LPT algorithms, errors on the image formation models are solely due to random noise, we show/prove the existence of a best achievable root mean square error (RMSE) on particle localisation, that, for a setup at a given seeding density, depends only on the noise level. We provide a procedure to estimate this lower bound, and show that it can only be reached if there are no missed detections; further on, we establish a link between localisation error and fraction of missed particles. We illustrate the consistency of this model on the results of the recent First Challenge on LPT (see ISPIV21 papers by Leclaire et al. and Sciacchitano et al.)

This paper proposes a data reconstruction of homogeneous turbulent flow combined machine learning (ML) approach using experimental Lagrangian Particle Tracking (LPT) data with Shake-The-Box (STB). The LPT with STB was adopted to measure a von Kármán flow with a homogeneous turbulent region in the center [1]. The STB results have been stored and a temporal filter using 3rd order B-splines has been applied with optimal weighting coefficients to be used as input for FlowFit data assimilation method [2]. FlowFit data was used as ground truth to train ML algorithm. The low-resolved data of the velocity and acceleration field was reconstructed using an Adaptive Neuro-Fuzzy Inference System (ANFIS) with the downsampled LPT data as an input to predict homogeneous turbulent flow [3]. The training process can be mathematically regarded as an optimization problem to determine the weighting factor.

Examining the behaviour of dense suspensions has proven to be difficult, both experimentally and numerically. Using super water–absorbent polymer, PIV measurement was successfully conducted in a hydrogel suspension with a volume fraction (VF) of Φ =20% (see Zhang and Rival, 2018). However, due to the slightly refractive index mismatch, the image quality will degrade significantly as the particle loading of the hydrogel is increased. In order to achieve flow measurements in suspensions with high volume fractions, non-optical based techniques such as ultrasound imaging velocimetry (UIV) should be implemented. UIV has been developed for fluid dynamics applications and embraced by many researchers to study fluid flows (Gurung and Poelma, 2016; Jeronimo et al., 2019). Although, UIV provides useful information about the flow physics, it is unable to provide Lagrangian quantities such as particle trajectories, which is a key parameter to study entrainment and particle-wall interactions.

This work presents the main results of the first Lagrangian Particle Tracking challenge, conducted within the framework of the European Union’s Horizon 2020 project HOMER (Holistic Optical Metrology for Aero-Elastic Research), grant agreement number 769237. The challenge, jointly organised by the research groups of DLR, ONERA and TU Delft, considered a synthetic experiment reproducing the wall-bounded flow in the wake of a cylinder which was simulated by LES. The participants received the calibration images and sets of particle images acquired by four virtual cameras, and were asked to produce as output the particles positions, velocities and accelerations (when possible) at a specific time instant. Four different image acquisition strategies were addressed, namely two-pulse (TP), four-pulse (FP) and time-resolved (TR) acquisitions, each with varying tracer particle concentrations (or number of particles per pixel, ppp). The participants’ outputs were analysed in terms of percentages of correctly reconstructed particles, missed particles, ghost particles, correct tracks and wrong tracks, as well as in terms of position, velocity and acceleration errors, along with their distributions. The analysis of the results showed that the best-performing algorithms allow for a correct reconstruction of more than 99% of the tracer particles with positional errors below 0.1 pixels even at ppp values exceeding 0.15, whereas other algorithms are more prone to the presence of ghost particles already for ppp < 0.1. While the velocity errors remained contained within a small percentage of the bulk velocity, acceleration errors as large as 50% of the actual acceleration magnitude were retrieved.

Particle Tracking Velocimetry (PTV) or Lagrangian Particle Tracking (LPT) picked up a lot of interest over the last years due to their ability to acquire global flow fields at high spatial and temporal resolution. The most recent research focused mainly on algorithmic advancements in order to increase the obtainable data density and on its application to new flow cases. Only a small amount of studies tried to quantify the measurement uncertainties linked to these volumetric measurement approaches. Within this contribution we want to present how to acquire measurement uncertainties for the position, velocity and acceleration for each data point along a trajectory by means of linear regression analysis tools. Based on these uncertainties, an adaptive filtering approach is introduced, which eliminates the user’s choice of the filter kernel length and which automatically determines its optimal value.

Advanced Lagrangian Particle Tracking methods (such as the STB algorithm (Schanz et al. 2016)) are a very useful tool for uncovering properties of flow. As a measurement technique, the results of such methods are perturbed by different sources of errors and noise. This work addresses the problem of optimal filtering of particle tracks as well as estimating uncertainties of derived quantities such as location, velocity and acceleration of observed particles. The behavior and performance of this new filtering method (“TrackFit”), first introduced at Gesemann et al. (2016) is analyzed and compared to the Savitzky–Golay filter (Savitzky and Golay (1964)) which is commonly used for these purposes. The optimal choice of parameters of this filtering method as well as the uncertainty quantification of the reconstructed tracks can be extracted from a spectral analysis of the recorded raw particle tracking data. This is in contrast to a Savitzky–Golay filter where the choice of parameters might often be driven by experience and gut feeling. Estimating the power spectral density (PSD) of the particle trajectory signals for the purpose of optimal filtering parameter selection represents a challenge due to possibly short trajectory signals. In the following work we will present a method for PSD estimation that is applicable in this scenario. In addition, we show that regardless of the choice of Savitzky–Golay filter parameters, the resulting filter will not approximate the ideal noise reduction filter well unlike the “TrackFit” described in this work.

An experimental methodology is proposed for the study of aeroelastic systems. The approach locally evaluates the forces involved in Collar’s triangle, namely aerodynamic, elastic, and inertial forces. The position of flow tracers as well as of markers on the object surface is monitored by a volumetric PIV system. From the recorded images, the flow tracers and surfare markers are separated based on their optical characteristics. The resulting images are then analysed by Lagrangian particle tracking. The inertial and elastic forces are obtained solely analysing the motion and the deformation of the solid object, whereas the aerodynamic force distribution is obtained via the pressure-from-PIV technique. Experiments are conducted on a benchmark problem of fluid-structure interaction, featuring a flexible panel installed at the trailing edge of a cylinder. A polynomial fit of the markers’ positions is carried out to determine the panel’s instantaneous shape, from which the inertial and elastic forces are evaluated. The pressure loads on the panel are determined via solution of the Poisson equation for pressure, imposing adaptive boundary conditions that comply with the panel. The simultaneous measurement of the three forces allows to assess the equilibrium of forces, and in turn to close Collar’s triangle.

Lagrangian particle tracking Shake-the-box (STB) method (Schanz et al., 2016) acquires the 3D positions of tracer particles from the temporal sequences of their 2D projection images even for rather high seeding densities. Approximation of tracks by analytical functions (Gesemann, 2015) provides an accurate evaluation of tracers’ local velocity and acceleration. This data, which is obtained on non-regular grid, can be used to estimate local pressure fluctuations based on the Navier–Stokes equation. The present paper describes a grid-free least-squares method for the gradients and pressure evaluation based on irregularly scattered LPT data with random noise minimization.

The dispersal of marine organisms is a critical process for the maintenance of biodiversity and ecosystem functioning across a seascape. Understanding the patterns of habitat connectivity that arise from the movement of multiple species can highlight the role of regional processes in maintaining local community structure. However, quantifying the probability and scale of dispersal for marine organisms remains a challenge. Here, we use a biophysical model to simulate dispersal, and we conduct a network analysis to predict connectivity patterns across scales for the community of invertebrates associated with seagrass habitat in British Columbia, Canada. We found many possible connections and few isolated habitat meadows, but the probability of most connections was low. Most habitat connections occurred within 3 days of dispersal time over short distances, indicating potential limits to long distance dispersal and little effect of species-specific dispersal abilities on the potential spatial extent of habitat connectivity. We then highlight the different roles that individual seagrass meadows can play in maintaining network connectivity. We also identify clusters of connected meadows and use these clusters to estimate the spatial scale of community dynamics. The connectivity patterns generated by our dispersal simulations highlight the importance of considering marine communities in their broad seascape context, with applications for the prioritization and conservation of habitat that maintains connectivity.

Impinging jets are widely used for heat and mass transfer because they are applicable to any type of body and can be easily implemented. They are also used in various industrial fields and design techniques. Previous research investigated e.g. a jet impinging onto a flat surface. However, since most of the mechanical parts have curvature on their surface, it is necessary to study more detailed properties of the jet impinging on a curved surface using advanced measurements. Therefore, in this study, three-dimensional flow structures of a round jet impinging on a convex cylinder surface were measured using volumetric Lagrangian particle tracking (LPT).

International audience; This communication describes how datasets for the 1st challenge on Lagrangian Particle Tracking (LPT) and Data Assimilation (DA), held in 2020 and organized within the UE-funded H2020 project HOMER, have been generated. The physical situation, a turbulent wall-bounded flow in the wake of a cylinder, has been simulated using LES with the ONERA HPC solver FASTS. The free-stream and momentum thickness Reynolds numbers were respectively of 665,000 and 4,150; the boundary layer thickness upstream of the cylinder was roughly of 60 mm, with a cylinder diameter of 10 mm, located with a gap of 10 mm from the wall. Virtual particles have been seeded and propagated in the flow using the LES velocity, within the simulation. A virtual experimental domain has been considered downstream of the cylinder, for which a virtual four-camera setup has been used, leading to LPT images. Several acquisition types (two-pulse, four-pulse and time-resolved) and a range of seeding densities have been considered. Depending on the acquisition type, either the particles positions only, or also their velocities and acceleration, have been requested to participants to the challenge. For the DA challenge, particle trajectories have been provided as input, while the requested output consisted in the velocity, velocity gradient and pressure on a prescribed 3D mesh embedded in the experimental domain. Further work is presently underway to complete the website hosting the datasets, towards a full benchmark portal with automatic evaluation, conceived to be progressively completed with other test cases in the long run.; Cette communication présente les principes de la génération des jeux de données formant la base du 1er challenge sur le suivi de particules lagrangien (LPT) et l'assimilation de données (DA), qui s'est tenu en 2020 et était organisé dans le cadre du projet UE H2020 HOME. La situation physique, celle d'un écoulement turbulent pariétal dans le sillage d'un cylindre, a été simulée à l'aide du code HPC FASTS de l'ONERA. L'écoulement était caractérisé par un nombre de Reynolds infini de 665000, et un nombre de Reynolds basé sur l'épaisseur de quantité de mouvement de 4150. L'épaisseur de couche limite était d'environ 60 mm, le diamètre du cylindre étant de 10 mm, placé à 10 mm de hauteur par rapport à la paroi. Des particules virtuelles ont été générées puis propagées à l'aide des vitesses de la LES, de façon intégrée dans la simulation. Un domaine expérimental virtuel a été considéré à l'aval du cylindre, visualisé par un système de quatre caméras virtuelles, menant aux imagers LPT. Différents types d'acquisition (deux pulses, quatre pulses et résolu en temps), et une gamme de différentes densités d'ensemencement ont été considérées. Selon le type d'acquisition, les participants au challenge devaient fournir les positions des particules uniquement, ou bien également leurs vitesses et accélérations. Pour le challenge DA, les trajectoires des particules ont été fournies en entrée, la sortie consistant en la vitesse, le gradient de vitesse et la pression de l'écoulement sur une grille 3D contenue dans le domaine expérimental. Un travail est actuellement en cours pour étendre les capacités du site web utilisé pour télécharger les données, en le rendant capable de fournir une évaluation automatique des données uploadées ainsi qu'un classement des performances ; il sera conçu pour pouvoir être étendu régulièrement à de nouveaux jeux de données.

In the evaluation of Lagrangian particle tracking (LPT) measurement data the use of spatially binned flow statistics in the form of one, two or multi-point statistics is often an essential step towards better understanding of the measured flow fields. Increasingly there is a focus towards uncertainty quantification of the measurement system however these evaluations are seldom used to directly improve the statistics by directly involving them into the calculation. We present our Functional Binning approach which makes use of such uncertainty information as a core component for the calculation of improved statistics. The improvements towards prior approaches are shown utilizing synthetic data as well as data from a real-world subsonic jet experiment. Beyond the initial formulation for one-point statistics, we show that this approach is readily extended towards two-point statistics and explore more advanced utilizations of uncertainty information for the optimal selection of particle pairs. Furthermore, the benefits of more individualized particle error estimations are investigated and some strategies for archiving such information are investigated.

Over a thousand animal species are capable of walking on the interface between air and water. These speciesinclude water striders, a family of insects from the order Hemiptera that has an almost unique ability to walk on the surface of the water without penetrating it. They achieve this outstanding feat by making use of the surface tension and their long hydrophobic legs. Experiments have revealed that water striders transfer some momentum to the underlying fluid through capillary waves and hemi-spherical vortices and that both waves and vortices contribute to the mechanism of propulsion. However, the exact momentum and energy carried by waves and vortices have never been quantified together, and only the energy of the surface waves has been quantified to date. An analysis of the complete energy balance between the interface and the body of the water requires measurement of the free surface topography, together with the three-dimensional (3D) flow field in the water under the surface. The ultimate aim of this work was to develop a method capable of doing this.