arXiv subjects

Wietze Herreman

Publications and source records attributed to Wietze Herreman.

9 recordsLinked to original sources

arXiv2026

Preferential orientation of slender elastic floaters in gravity waves

Slender floaters drifting in propagating gravity waves slowly rotate towards a preferential state of orientation with respect to the angle of incidence. This angular drift arises from a wave-induced, second order mean yaw moment. We develop a diffractionless, hydro-elastic theory to compute this mean yaw moment for a thin, flexible structure whose width and thickness are small compared with the wavelength. For floater lengths smaller than half the wavelength, we derive a simple, predictive criterion for the preferred orientation: Soft, short and heavy floaters prefer the longitudinal state, while stiff, long and light floaters prefer the transverse state. For floaters longer than the wavelength, the orientational dynamics become more intricate and may exhibit multiple equilibrium states. We discuss the implications of the model for flexible floating structures such as pontoons and inflatable structures.

physics.flu-dyn↗

arXiv2026

Nonlinear synthetic Schlieren methods for free-surface topography measurement using telecentric imaging

Free-surface synthetic Schlieren (FS-SS) is a high-resolution, refraction-based optical technique for measuring the instantaneous elevation of a liquid interface. Under the assumptions of small amplitude, small slope, and small paraxial angle, the method yields a linear relationship between the gradient of the surface elevation and the apparent displacement field of a refracted pattern imaged through the surface. Here, we propose three new, nonlinear extensions of the FS-SS method that are specifically dedicated to telecentric imaging. Paraxial distortions are eliminated with a telecentric lens, thereby simplifying the optical model. This allows us to derive nonlinear surface reconstruction models that reach beyond the usual limits of small slope and small wave-magnitudes. We implement these nonlinear surface reconstruction algorithms and compare them to the original, linear reconstruction algorithm in three different experiments, using a solid glass lens, spreading oil drops and nonlinear Faraday waves. At the price of a few iterations, we can realise nonlinear surface reconstructions that are more precise, in particular when we reach high slopes or high amplitude regimes. We share a library that encodes these nonlinear surface reconstruction algorithms.

physics.flu-dyn↗

arXiv2026

Capillary effects on preferential orientation of floaters in gravity waves

We study the influence of capillary effects on the motion of thin elastic plates denser than water drifting in propagating surface gravity waves. Such floaters experience a mean angular drift that rotates them toward two preferential orientations: parallel to the direction of wave propagation (longitudinal) or parallel to the wave crests (transverse). We develop a diffractionless model (Froude-Krylov approximation) to compute the mean yaw moment acting on floaters with arbitrary bending rigidity, small relative to the wavelength. Capillary forces are incorporated through a quasi-static volume formulation based on the fluid volume displaced by the floater and its meniscus. The model predicts that the preferential orientation is governed by the non-dimensional parameter $F = kL_x^2/\overline{h}$ recently introduced in Herreman et al. (J. Fluid Mech., vol.999, 2024, A92), where $k$ is the wavenumber, $L_x$ the floater length, and $\overline{h}$ the equilibrium immersion depth, provided that $\overline{h}$ accounts for capillary effects. The orientation depends on how $F$ compares to a critical value $F_c$, which is a function of the ratio of the flexural length to the floater length. These predictions are in good agreement with experiments performed with thin metal rectangular plates of various length, width and thickness.

physics.flu-dyn↗

arXiv2025

Flexible floaters align with the direction of wave propagation

We investigate the slow, second order motion of thin flexible floating strips drifting in surface gravity waves. We introduce a diffractionless model (Froude-Krylov approximation) that neglects viscosity, surface tension, and radiation effects. This model predicts a mean yaw moment that favors a longitudinal orientation of the strip, along the direction of wave propagation. The physical mechanism for this angular drift is analog to that of the standard linear Stokes drift: it originates from a slight imbalance between the stronger acceleration on the wave crests (that favors the longitudinal orientation) and the wave troughs (that favors the transverse orientation). Laboratory experiments with thin rectangular strips of polypropylene show a systematic rotation of the strips toward the longitudinal orientation, in good agreement with our model. We finally observe that the mean angular velocity toward the stable longitudinal orientation decreases as the strip length increases, an effect likely due to dissipation, which is not accounted for in our inviscid model.

physics.flu-dyn↗

arXiv2025

Stability theory for metal pad roll with consideration of viscous and magnetic damping

We present a new theoretical model for the analytical prediction of the metal pad roll instability in idealised aluminium reduction cells consisting of two stably stratified liquid layers, which carry a vertical electric current and are exposed to a likewise vertical magnetic field. In contrast to the numerous previous models, we strive with this contribution for the most complete, and at the same time, a very approachable description of the linear metal pad roll instability. The model avoids the shallow-water approximation and incorporates some capillary effects, allowing it to be further applied to small-scale liquid metal batteries. As a major novelty the model also properly accounts for the stabilising effects of viscous and magnetic damping. To this end, we have derived explicit analytical formulae for the associated decay rates valid for arbitrary interfacial wave modes, which can also find application in other fields such as two-liquid sloshing. Our principal result is a set of explicit analytical solutions for stability thresholds and growth rates that are straightforward to implement and are intended to serve as theoretical benchmarks for multiphase magnetohydrodynamic solvers and model experiments. All of the results presented are carefully validated against five different and independent studies, with the particularity that we make use of quantitative stability threshold measurements for the first time.

physics.flu-dyn↗

arXiv2017

Mean mass transport in an orbitally shaken cylindrical container

A cylindrical container partially filled with a liquid in orbital shaking motion, i.e. in circular translation with fixed orientation with respect to an inertial frame of reference, generates, along with a rotating sloshing wave, a mean flow rotating in the same direction as the wave. Here we investigate experimentally the structure and the scaling of the wave flow and the Lagrangian mean flow in the weakly nonlinear regime, for small forcing amplitude and for forcing frequency far from the resonance, using conventional and stroboscopic particle image velocimetry. The Lagrangian mean flow is composed of a strong global rotation near the center and a non trivial pattern of poloidal recirculation vortices of weaker amplitude, mostly active near the contact line. The global rotation near the center is robust with respect to changes in viscosity and forcing frequency, and its amplitude compares well with the predicted Stokes drift for an inviscid rotating sloshing wave. On the other hand, the spatial structure of the poloidal vortices show strong variation with viscosity and forcing frequency, suggesting that it results from the streaming flow driven by the complex oscillatory boundary layers near the contact line.

physics.flu-dyn↗

arXiv2016

Metal pad roll instability in liquid metal batteries

The increasing deployment of renewable energies requires three fundamental changes to the electric grid: more transmission lines, a flexibilisation of the demand and grid scale energy storage. Liquid metal batteries (LMBs) are considered these days as a promising means of stationary energy storage. Built as a stable density stratification of two liquid metals separated by a liquid salt, LMBs have three main advantages: a low price, a long life-time and extremely high current densities. In order to be cheap, LMBs have to be built large. However, battery currents in the order of kilo-amperes may lead to magnetohydrodynamic (MHD) instabilities, which - in the worst case - may short-circuit the thin electrolyte layer. The metal pad roll instability, as known from aluminium reduction cells, is considered as one of the most dangerous phenomena for LMBs. We develop a numerical model, combining fluid- and electrodynamics with the volume-of-fluid method, to simulate this instability in cylindrical LMBs. We explain the instability mechanism similar to that in aluminium reduction cells and give some first results, including growth rates and oscillation periods of the instability.

physics.flu-dyn↗

arXiv2016

Sloshing instability and electrolyte layer rupture in liquid metal batteries

Liquid metal batteries (LMBs) are discussed today as a cheap grid scale energy storage, as required for the deployment of fluctuating renewable energies. Built as a stable density stratification of two liquid metals separated by a thin molten salt layer, LMBs are susceptible to short-circuit by fluid flows. Using direct numerical simulation, we study a sloshing long wave interface instability in cylindrical cells, which is already known from aluminium reduction cells. After characterising the instability mechanism, we investigate the influence of cell current, layer thickness, density, viscosity, conductivity and magnetic background field. Finally we study the shape of the interface and give a dimensionless parameter for the onset of sloshing as well as for the short-circuit.

physics.flu-dyn↗

arXiv2014

Libration driven multipolar instabilities

We consider rotating flows in non-axisymmetric enclosures that are driven by libration, i.e. by a small periodic modulation of the rotation rate. Thanks to its simplicity, this model is relevant to various contexts, from industrial containers (with small oscillations of the rotation rate) to fluid layers of terrestial planets (with length-of-day variations). Assuming a multipolar $n$-fold boundary deformation, we first obtain the two-dimensional basic flow. We then perform a short-wavelength local stability analysis of the basic flow, showing that an instability may occur in three dimensions. We christen it the Libration Driven Multipolar Instability (LDMI). The growth rates of the LDMI are computed by a Floquet analysis in a systematic way, and compared to analytical expressions obtained by perturbation methods. We then focus on the simplest geometry allowing the LDMI, a librating deformed cylinder. To take into account viscous and confinement effects, we perform a global stability analysis, which shows that the LDMI results from a parametric resonance of inertial modes. Performing numerical simulations of this librating cylinder, we confirm that the basic flow is indeed established and report the first numerical evidence of the LDMI. Numerical results, in excellent agreement with the stability results, are used to explore the non-linear regime of the instability (amplitude and viscous dissipation of the driven flow). We finally provide an example of LDMI in a deformed spherical container to show that the instability mechanism is generic. Our results show that the previously studied libration driven elliptical instability simply corresponds to the particular case $n=2$ of a wider class of instabilities. Summarizing, this work shows that any oscillating non-axisymmetric container in rotation may excite intermittent, space-filling LDMI flows, and this instability should thus be easy to observe experimentally.

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