Tag: fluid mechanics

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Propulsive performance of a windsurf-inspired pitching foil

G. Bertrand, T. Aurégan, B. Thiria, R. Godoy-Diana, M. Fermigier
Physical Review Fluids 10, 074401 (2025) * Editor’s suggestion
doi: 10.1103/PhysRevFluids.10.074401
preprint: arXiv:2412.12878

The competitive practice of sailing and windsurfing has seen a recent revolution with the introduction of new appendixes of hydrofoils that generate lift and keep the board or the boat out of the water for a sufficiently high sailing speed (∼3 m/s) . This allows one to increase the speed significantly because the wave drag and the hydrodynamic drag are almost suppressed. These innovations include the new iQFOil class introduced for the 2024 Olympic Games. During race starts or in low wind conditions, particularly after maneuvers like tacking which consist of turning the bow toward and through the wind to go upwind, windsurf athletes employ a technique called pumping to initiate or maintain foiling. This involves rhythmically adjusting the sail’s angle relative to the wind through a movement where the athlete moves their center of mass up and down, causing the sail to oscillate and provide intermittent propulsion to keep the board above water (see figure). We present an experimental study with a symmetrical shape of sail where a pitching movement is applied for various frequencies and amplitudes in a wide range of mean incidence angles to mimic the behavior of a sail under real sailing conditions, especially upwind conditions. This study focuses on the coupled effect of the kinematic parameters of pumping (flapping frequency and amplitude) and the mean incidence angle between the mean chord of the sail and the direction of flow, in a context of application to competitive sailing.

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D-shaped body wake control through flexible filaments

J. C. Muñoz-Hervás, B. Semin, M. Lorite-Díez, G. J. Michon, Juan D’Adamo, J.I. Jiménez-González, R. Godoy-Diana
Physical Review Fluids 10, 063903 (2025)
doi: 10.1103/8jd7-j82q
preprint: arXiv:2411.08556

The wake flow behind blunt, D-shaped objects is an archetype to study recirculation bubbles and velocity deficits that increase drag. This has prompted interest in passive flow control methods using flexible appendages. We investigated how adding series of rigid and flexible plate-like filaments behind a D-shaped body in a water channel could modify wake dynamics and reduce drag. Using Particle Image Velocimetry to measure wake flow patterns and high-speed imaging to track filament motion, we tested various filament stiffnesses and positions across different flow velocities. The flexible filaments demonstrated passive reconfiguration in response to the flow, with tip deflection angles reaching up to 9° and vibration amplitudes of around 4° at higher flow velocities, which corresponded to reduced recirculation bubbles and decreased velocity deficits in the wake compared to cases with no filaments or rigid filaments. Interestingly, pre-curved rigid filaments matched the performance of flexible ones, suggesting that the bending motion rather than the vibration of flexible filaments drives the flow improvement, and highlighting the potential for designing effective passive flow control devices using flexible appendages in the wakes of blunt bodies.

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Water wave interactions with a submerged elastic plate

Experiments on water wave interactions with a horizontal submerged elastic plate
G. Polly, A. Mérigaud, B. Thiria, R. Godoy-Diana
Journal of Fluid Mechanics 1007, R4 (2025)
doi: 10.1017/jfm.2025.90

Submerged elastic plates have been considered as potentially effective design elements in the development of wave energy harvesters but their behavior in a wave field remains largely unexplored, especially experimentally. We discuss in this paper how a submerged elastic plate, clamped at one edge, interacts with water waves. Positioned at a fixed depth in a wave tank, the flexible plate demonstrates significant wave reflection capabilities, a characteristic absent in rigid plates of identical dimensions. The experiments thus reveal that plate motion is crucial for wave reflection. Sufficiently steep waves are shown to induce a change in the mean position of the plate, with the trailing edge reaching the free surface in some cases. This configuration change is found to be particularly efficient to break water waves. These findings contribute to understanding the potential of elastic plates for wave energy harvesting and wave attenuation scenarios.

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Form and function of anguilliform swimming: a review

V. Stin, R. Godoy-Diana, X. Bonnet, & A. Herrel
Biological Reviews (2024)
doi: 10.1111/brv.13116

Anguilliform swimmers are long and narrow animals that propel themselves by undulating their bodies. Observations in nature and recent investigations suggest that anguilliform swimming is highly efficient. However, understanding the underlying reasons for the efficiency of this type of locomotion requires interdisciplinary studies spanning from biology to hydrodynamics. Regrettably, these different fields are rarely discussed together, which hinders our ability to understand the repeated evolution of this swimming mode in vertebrates. This review compiles the current knowledge of the anatomical features that drive anguilliform swimming, compares the resulting kinematics across a wide range of anguilliform swimmers, and describes the resulting hydrodynamic interactions using data from both in vivo experiments and computational studies.

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Drag-induced dissipation in wave-structure interaction

In the interaction of water waves with marine structures, the interplay between wave diffraction and drag-induced dissipation is seldom, if ever, considered. In particular, linear hydrodynamic models, and extensions thereof through the addition of a quadratic force term, do not represent the change in amplitude of the waves diffracted and radiated to the far field, which should result from local energy dissipation in the vicinity of the structure. In this work, a series of wave flume experiments is carried out, whereby waves of increasing amplitude impinge upon a vertical barrier, extending partway through the flume width. As the wave amplitude increases, the effect of drag – which is known to increase quadratically with the flow velocity – is enhanced, thus allowing the examination of the far-field effect of drag-induced dissipation, in terms of wave reflection and transmission. A potential flow model is proposed, with a simple quadratic pressure drop condition through a virtual porous surface, located on the sides of the barrier (where dissipation occurs). Experimental results confirm that drag-induced dissipation has a marked effect on the diffracted flow, i.e. on wave reflection and transmission, which is appropriately captured in the proposed model. Conversely, when diffraction becomes dominant as the barrier width becomes comparable to the incoming wavelength, the diffracted flow must be accounted for in predicting drag-induced forces and dissipation.

Modelling the far-field effect of drag-induced dissipation in wave-structure interaction: A numerical and experimental study
A. Mérigaud, B. Thiria, R. Godoy-Diana, G. Perret
Journal of Fluid Mechanics, 987, A24 (2024).
doi: 10.1017/jfm.2024.298

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Lift-up and streak waviness drive the self-sustained process in wall-bounded transition to turbulence

Flow field measurements from a Couette-Poiseuille experiment are used to examine quantitatively certain steps of the self-sustained process (SSP) of wall-bounded transition to turbulence. Although the different parts of the SSP have been discussed at large in the literature, direct measurements from experiment are scarce and the present results show, using a local analysis of the turbulent patterns, that (1) the amplitude of streamwise rolls is related to streak waviness, bringing a quantitative picture to one of the main physical mechanisms of Waleffe’s model of SSP, and (2), at low waviness, direct measurements of the correlation between the streak and roll amplitudes, respectively probed by the streamwise and wall-normal velocity perturbations, quantify the lift-up effect. This analysis method of the SSP does not rely on the specificity of Couette-Poiseuille flows and can be used to investigate this mechanism in other flows.

T. Liu, B. Semin, R. Godoy-Diana, J. E. Wesfreid
Physical Review Fluids, 9, 033901 (2024).
doi: 10.1103/PhysRevFluids.9.033901

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Far-field hydrodynamic interaction in a group of swimmers

Three-dimensional schools of hydrodynamically axisymmetric swimmers self-propelling at a constant velocity are studied. We introduce a low-order model for the induced velocity based on the far-field approximation. We inquire if, by holding suitable relative positions in the three-dimensional space, the swimmers can reduce the overall energy consumption of the school in comparison with the same number of isolated individuals at the same velocity. We find a considerable (several per cent) energy saving achievable by chain formations. The benefit increases asymptotically with the number of individuals, towards a finite limit that is a function of the minimum allowed spacing between each pair of neighbours.

G. Li, L. Duan, J. Sesterhenn, R. Godoy-Diana, B. Thiria, & D. Kolomenskiy
Journal of Fluid Mechanics, 974, A34 (2023).
doi: 10.1017/jfm.2023.802

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Volumetric velocimetry of the wake of a swimming snake

We describe a method for measuring the 3D vortical structures produced by an anguilliform swimmer using volumetric velocimetry. The wake of freely swimming dice snakes (Natrix tessellata) was quantified, revealing the creation of multiple vortices along the body of the snake due to its undulation. The 3D structure of the vortices generally consisted of paired vortex tubes, some of which were linked together to form a hairpin structure. The observations match predictions from computational fluid dynamic studies of other anguilliform swimmers. Quantitative measurements allowed us to study vortex circulation and size, and global kinetic energy of the flow, which varied with swimming speed, vortex topology and individual characteristics. Our findings provide a baseline for comparing wake structures of snakes with different morphologies and ecologies and investigating the energetic efficiency of anguilliform swimming.


V. Stin, R. Godoy-Diana, X. Bonnet, & A. Herrel. Measuring the 3D wake of swimming snakes (Natrix tessellata) using volumetric velocimetry.
Journal of Experimental Biology, 226, jeb245929 (2023)
doi: 10.1242/jeb.245929

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Geometrical framework for hydrodynamics and control of wave energy converters

A. Mérigaud, B. Thiria, & R. Godoy-Diana
PRX Energy 2, 023003 (2023)
doi: 10.1103/PRXEnergy.2.023003

Approaches for converting the energy of sea-surface waves into useful power remain on the fringe of renewable energy solutions despite years of research. Among the hundreds of proposed wave-energy converters, no single wave-energy device provides sufficient power to be an attractive practical solution. Therefore, considering an integrated farm of many devices is an intrinsic part of the problem. Models need to consider the dynamics of many devices simultaneously, and the devices’ interaction with each other and the environment introduces additional complexity. In this work, we propose a conceptually simple analysis framework that uses geometry in the complex plane to understand the basic relations underlying wave-energy conversion in a model farm. Under this framework, a single complex variable encapsulates wave reflection, transmission, and absorption by a row of wave-energy converters and provides guidance for achieving maximal power output under impedance-matching conditions.

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Decay of streaks and rolls in plane Couette–Poiseuille flow

We report the results of an experimental investigation into the decay of turbulence in plane Couette–Poiseuille flow using ‘quench’ experiments where the flow laminarises after a sudden reduction in Reynolds number 𝑅𝑒. Specifically, we study the velocity field in the streamwise–spanwise plane. We show that the spanwise velocity containing rolls decays faster than the streamwise velocity, which displays elongated regions of higher or lower velocity called streaks. At final Reynolds numbers above 425, the decay of streaks displays two stages: first a slow decay when rolls are present and secondly a more rapid decay of streaks alone. The difference in behaviour results from the regeneration of streaks by rolls, called the lift-up effect. We define the turbulent fraction as the portion of the flow containing turbulence and this is estimated by thresholding the spanwise velocity component. It decreases linearly with time in the whole range of final 𝑅𝑒. The corresponding decay slope increases linearly with final 𝑅𝑒. The extrapolated value at which this decay slope vanishes is 𝑅𝑒𝑎𝑧≈656±10, close to 𝑅𝑒𝑔≈670 at which turbulence is self-sustained. The decay of the energy computed from the spanwise velocity component is found to be exponential. The corresponding decay rate increases linearly with 𝑅𝑒, with an extrapolated vanishing value at 𝑅𝑒𝐴𝑧≈688±10. This value is also close to the value at which the turbulence is self-sustained, showing that valuable information on the transition can be obtained over a wide range of 𝑅𝑒.

Decay of streaks and rolls in plane Couette-Poiseuille flow
T. Liu, B. Semin, L. Klotz, R. Godoy-Diana, J. E. Wesfreid & T. Mullin
Journal of Fluid Mechanics 915, A65 (2021)
doi:10.1017/jfm.2021.89

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On the energetics and stability of a minimal fish school

On the energetics and stability of a minimal fish school
G. Li, D. Kolomenskiy, H. Liu, B. Thiria & R. Godoy-Diana
PLoS ONE 14(8): e0215265 (2019)
https://doi.org/10.1371/journal.pone.0215265

See also:
On the interference of vorticity and pressure fields of a minimal fish school
G. Li, D. Kolomenskiy, H. Liu, B. Thiria & R. Godoy-Diana
Journal of Aero Aqua Bio-mechanisms 8 (1), 27-33 (2019)
[doi:10.5226/jabmech.8.27]

The physical basis for fish schooling is examined using three-dimensional numerical simulations of a pair of swimming fish, with kinematics and geometry obtained from experimental data. Energy expenditure and efficiency are evaluated using a cost of transport function, while the effect of schooling on the stability of each swimmer is examined by probing the lateral force and the lateral and longitudinal force fluctuations. We construct full maps of the aforementioned quantities as functions of the spatial pattern of the swimming fish pair and show that both energy expenditure and stability can be invoked as possible reasons for the swimming patterns and tail-beat synchronization observed in real fish. Our results suggest that high cost of transport zones should be avoided by the fish. Wake capture may be energetically unfavorable in the absence of kinematic adjustment. We hereby hypothesize that fish may restrain from wake capturing and, instead, adopt side-to-side configuration as a conservative strategy, when the conditions of wake energy harvesting are not satisfied. To maintain a stable school configuration, compromise between propulsive efficiency and stability, as well as between school members, ought to be considered.