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arXiv2018

Rogue Waves and Large Deviations in Deep Sea

The appearance of rogue waves in deep sea is investigated using the modified nonlinear Schrödinger (MNLS) equation in one spatial-dimension with random initial conditions that are assumed to be normally distributed, with a spectrum approximating realistic conditions of a uni-directional sea state. It is shown that one can use the incomplete information contained in this spectrum as prior and supplement this information with the MNLS dynamics to reliably estimate the probability distribution of the sea surface elevation far in the tail at later times. Our results indicate that rogue waves occur when the system hits unlikely pockets of wave configurations that trigger large disturbances of the surface height. The rogue wave precursors in these pockets are wave patterns of regular height but with a very specific shape that is identified explicitly, thereby allowing for early detection. The method proposed here combines Monte Carlo sampling with tools from large deviations theory that reduce the calculation of the most likely rogue wave precursors to an optimization problem that can be solved efficiently. This approach is transferable to other problems in which the system's governing equations contain random initial conditions and/or parameters.

physics.flu-dyn↗
arXiv2017

Physical and geometric constraints explain the labyrinth-like shape of the nasal cavity

The nasal cavity is a vital component of the respiratory system that heats and humidifies inhaled air in all vertebrates. Despite this common function, the shapes of nasal cavities vary widely across animals. To understand this variability, we here connect nasal geometry to its function by theoretically studying the airflow and the associated scalar exchange that describes heating and humidification. We find that optimal geometries, which have minimal resistance for a given exchange efficiency, have a constant gap width between their side walls, but their overall shape is restricted only by the geometry of the head. Our theory explains the geometric variations of natural nasal cavities quantitatively and we hypothesize that the trade-off between high exchange efficiency and low resistance to airflow is the main driving force shaping the nasal cavity. Our model further explains why humans, whose nasal cavities evolved to be smaller than expected for their size, become obligate oral breathers in aerobically challenging situations.

physics.bio-ph↗
arXiv2025

Creases as elastocapillary gates for autonomous droplet control

Droplets are the core functional units in microfluidic technologies that aim to integrate computation and reaction on a single platform. Achieving directed transport and control of these droplets typically demands elaborate substrate patterning, modulation of external fields, and real-time feedback. Here we reveal that an engineered pattern of creases on a soft interface autonomously gate and steer droplets through a long-range elastocapillary repulsion, allowing programmable flow of information. Acting as an energy barrier, the crease bars incoming droplets below a critical size, without making contact. We uncover the multi-scale, repulsive force-distance law describing interactions between a drop and a singular crease. Leveraging this mechanism, we demonstrate passive and active filtration based on droplet size and surface tension, and implement functionalities such as path guidance, tunable hysterons, pulse modulators, and elementary logic operations like adders. This crease-based gating approach thus demonstrates complex in-unit processing capabilities - typically accessible only through sophisticated surface and fluidic modifications - offering a multimodal, potentially rewritable strategy for droplet control in interfacial assembly and biochemical assays.

cond-mat.soft↗
arXiv2026

Dynamic multiphase flow triggers chaotic mixing in porous media

Solute mixing plays a pivotal role in a broad spectrum of chemical and biological processes across natural and engineered porous media. However, current understanding of mixing dynamics remains largely constrained to steady flows in fully or partially water-saturated environments. Multiphase flow systems are generally unsteady, with moving fluid interfaces and flow paths that change in time. Despite the widespread occurrence of dynamic multiphase flows, their impacts on solute mixing are largely unknown. Here, we use experiments and numerical simulations to investigate the effect of dynamic two-phase flow on the stretching and folding of fluid elements, a fundamental mechanism driving solute mixing and reactions in porous media. We find that dynamic two-phase flows induce chaotic mixing, characterized by exponential stretching of fluid elements, leading to strongly enhanced mixing compared to steady single phase flows. By extensive numerical multiphase flow simulations, we establish dynamic steady states where we reliably measure the mean fluid stretching rate as a function of flow rate. We show that stretching is maximized at an optimum flow rate which balances fluid shear deformation against the frequency of flow reorientation by the intermittent motion of the fluid interface. The findings are rationalized by a mechanistic model linking basic multiphase flow characteristics to the stretching rate, opening new perspectives to understand and control mixing and reactions in a wide range of multiphase flow systems.

physics.flu-dyn↗
arXiv2018

New smoothed particle hydrodynamics (SPH) formulation for modeling heat conduction with solidification and melting

When modelling phase change, the latent heat released (absorbed) during solidification (melting) must be included in the heat transfer equation. In this paper, different SPH methods for the implementation of latent heat, in the context of transient heat conduction, are derived and tested. First, SPH discretizations of two finite element methods are presented, but these prove to be computationally expensive. Then, by starting from a simple approximation and enhancing accuracy using different numerical treatments, a new SPH method is introduced, that is fast and easy to implement. An evaluation of this new method on various analytical and numerical results confirms its accuracy and robustness.

physics.flu-dyn↗
arXiv2013

Lagrangian Markovianized Field Approximation for turbulence

In a previous communication (W.J.T. Bos and J.-P. Bertoglio 2006, Phys. Fluids, 18, 031706), a self-consistent Markovian triadic closure was presented. The detailed derivation of this closure is given here, relating it to the Direct Interaction Approximation and Quasi-Normal types of closure. The time-scale needed to obtain a self-consistent closure for both the energy spectrum and the scalar variance spectrum is determined by evaluating the correlation between the velocity and an advected displacement vector-field. The relation between this latter correlation and the velocity-scalar correlation is stressed, suggesting a simplified model of the latter. The resulting closed equations are numerically integrated and results for the energy spectrum, scalar fluctuation spectrum and velocity-displacement correlation spectrum are presented for low, unity and high values of the Schmidt number.

physics.flu-dyn↗
arXiv2014

A new assessment of the second order moment of Lagrangian velocity increments in turbulence

The behavior of the second-order Lagrangian structure functions on state-of-the-art numerical data both in two and three dimensions is studied. On the basis of a phenomenological connection between Eulerian space-fluctuations and the Lagrangian time-fluctuations, it is possible to rephrase the Kolmogorov $4/5$-law into a relation predicting the linear (in time) scaling for the second order Lagrangian structure function. When such a function is directly observed on current experimental or numerical data, it does not clearly display a scaling regime. A parameterization of the Lagrangian structure functions based on Batchelor model is introduced and tested on data for $3d$ turbulence, and for $2d$ turbulence in the inverse cascade regime. Such parameterization supports the idea, previously suggested, that both Eulerian and Lagrangian data are consistent with a linear scaling plus finite-Reynolds number effects affecting the small- and large-time scales. When large-time saturation effects are properly accounted for, compensated plots show a detectable plateau already at the available Reynolds number. Furthermore, this parameterization allows us to make quantitative predictions on the Reynolds number value for which Lagrangian structure functions are expected to display a scaling region. Finally, we show that this is also sufficient to predict the anomalous dependency of the normalized root mean squared acceleration as a function of the Reynolds number, without fitting parameters.

physics.flu-dyn↗
arXiv2013

Geometrical statistics of the vorticity vector and the strain rate tensor in rotating turbulence

We report results on the geometrical statistics of the vorticity vector obtained from experiments in electromagnetically forced rotating turbulence. A range of rotation rates $Ω$ is considered, from non-rotating to rapidly rotating turbulence with a maximum background rotation rate of $Ω=5$ rad/s (with Rossby number much smaller than unity). Typically, in our experiments ${\rm{Re}}_λ\approx 100$. The measurement volume is located in the centre of the fluid container above the bottom boundary layer, where the turbulent flow can be considered locally statistically isotropic and horizontally homogeneous for the non-rotating case, see van Bokhoven et al., Phys. Fluids 21, 096601 (2009). Based on the full set of velocity derivatives, measured in a Lagrangian way by 3D Particle Tracking Velocimetry, we have been able to quantify statistically the effect of system rotation on several flow properties. The experimental results show how the turbulence evolves from almost isotropic 3D turbulence ($Ω\lesssim 0.2$ rad/s) to quasi-2D turbulence ($Ω\approx 5.0$ rad/s) and how this is reflected by several statistical quantities. In particular, we have studied the orientation of the vorticity vector with respect to the three eigenvectors of the local strain rate tensor and with respect to the vortex stretching vector. Additionally, we have quantified the role of system rotation on the self-amplification terms of the enstrophy and strain rate equations and the direct contribution of the background rotation on these evolution equations. The main effect is the strong reduction of extreme events and related (strong) reduction of the skewness of PDFs of several quantities such as, for example, the intermediate eigenvalue of the strain rate tensor and the enstrophy self-amplification term.

physics.flu-dyn↗
arXiv2013

Global drag-induced instabilities in protoplanetary disks

We use the Fokker-Planck equation and model the dispersive dynamics of solid particles in annular protoplanetary disks whose gas component is more massive than the particle phase. We model particle--gas interactions as hard sphere collisions, determine the functional form of diffusion coefficients, and show the existence of two global unstable modes in the particle phase. These modes have spiral patterns with the azimuthal wavenumber $m=1$ and rotate slowly. We show that in ring-shaped disks, the phase space density of solid particles increases linearly in time towards an accumulation point near the location of pressure maximum, while instabilities grow exponentially. Therefore, planetesimals and planetary cores can be efficiently produced near the peaks of unstable density waves. In this mechanism, particles migrating towards the accumulation point will not participate in the formation of planets, and should eventually form a debris ring like the main asteroid belt or classical Kuiper belt objects. We present the implications of global instabilities to the formation of ice giants and terrestrial planets in the solar system.

astro-ph.EP↗
arXiv2013

Can planetesimals form by collisional fusion?

As a test bed for the growth of protoplanetary bodies in a turbulent circumstellar disk we examine the fate of a boulder using direct numerical simulations of particle seeded gas flowing around it. We provide an accurate description of the flow by imposing no-slip and non-penetrating boundary conditions on the boulder surface using the immersed boundary method pioneered by Peskin (2002). Advected by the turbulent disk flow, the dust grains collide with the boulder and we compute the probability density function (PDF) of the normal component of the collisional velocity. Through this examination of the statistics of collisional velocities we test the recently developed concept of collisional fusion which provides a physical basis for a range of collisional velocities exhibiting perfect sticking. A boulder can then grow sufficiently rapidly to settle into a Keplerian orbit on disk evolution time scales.

astro-ph.EP↗
arXiv2014

Modeling jet and outflow feedback during star cluster formation

Powerful jets and outflows are launched from the protostellar disks around newborn stars. These outflows carry enough mass and momentum to transform the structure of their parent molecular cloud and to potentially control star formation itself. Despite their importance, we have not been able to fully quantify the impact of jets and outflows during the formation of a star cluster. The main problem lies in limited computing power. We would have to resolve the magnetic jet-launching mechanism close to the protostar and at the same time follow the evolution of a parsec-size cloud for a million years. Current computer power and codes fall orders of magnitude short of achieving this. In order to overcome this problem, we implement a subgrid-scale (SGS) model for launching jets and outflows, which demonstrably converges and reproduces the mass, linear and angular momentum transfer, and the speed of real jets, with ~ 1000 times lower resolution than would be required without SGS model. We apply the new SGS model to turbulent, magnetized star cluster formation and show that jets and outflows (1) eject about 1/4 of their parent molecular clump in high-speed jets, quickly reaching distances of more than a parsec, (2) reduce the star formation rate by about a factor of two, and (3) lead to the formation of ~ 1.5 times as many stars compared to the no-outflow case. Most importantly, we find that jets and outflows reduce the average star mass by a factor of ~ 3 and may thus be essential for understanding the characteristic mass of the stellar initial mass function.

astro-ph.SR↗
arXiv2014

Magnetic Prandtl number dependence of kinetic to magnetic dissipation ratio

Using direct numerical simulations of three-dimensional hydromagnetic turbulence, either with helical or non-helical forcing, we show that the ratio of kinetic-to-magnetic energy dissipation always increases with the magnetic Prandtl number, i.e., the ratio of kinematic viscosity to magnetic diffusivity. This dependence can always be approximated by a power law, but the exponent is not the same in all cases. For non-helical turbulence, the exponent is around 1/3, while for helical turbulence it is between 0.6 and 2/3. In the statistically steady state, the rate of the energy conversion from kinetic into magnetic by the dynamo must be equal to the Joule dissipation rate. We emphasize that for both small-scale and large-scale dynamos, the efficiency of energy conversion depends sensitively on the magnetic Prandtl number, and thus on the microphysical dissipation process. To understand this behavior, we also study shell models of turbulence and one-dimensional passive and active scalar models. We conclude that the magnetic Prandtl number dependence is qualitatively best reproduced in the one-dimensional model as a result of dissipation via localized Alfven kinks.

astro-ph.SR↗
arXiv2014

An optimisation approach for analysing nonlinear stability with transition to turbulence in fluids as an exemplar

This article introduces, and reviews recent work using, a simple optimisation technique for analysing the nonlinear stability of a state in a dynamical system. The technique can be used to identify the most efficient way to disturb a system such that it transits from one stable state to another. The key idea is introduced within the framework of a finite-dimensional set of ordinary differential equations (ODEs) and then illustrated for a very simple system of 2 ODEs which possesses bistability. Then the transition to turbulence problem in fluid mechanics is used to show how the technique can be formulated for a spatially-extended system described by a partial differential equation (the well-known Navier-Stokes equation). Within that context, the optimisation technique bridges the gap between (linear) optimal perturbation theory and the (nonlinear) dynamical systems approach to fluid flows. The fact that the technique has now been recently shown to work in this very high dimensional setting augurs well for its utility in other physical systems.

physics.flu-dyn↗
arXiv2013

Convective overshoot mixing in stellar interior models

The convective overshoot mixing plays an important role in stellar structure and evolution. However, the overshoot mixing is a long standing problem. The uncertainty of the overshoot mixing is one of the most uncertain factors in stellar physics. As it is well known, the convective and overshoot mixing is determined by the radial chemical component flux. In this paper, a local model of the radial chemical component flux is established based on the hydrodynamic equations and some model assumptions. The model is tested in stellar models. The main conclusions are as follows. (i) The local model shows that the convective and overshoot mixing could be regarded as a diffusion process, and the diffusion coefficient for different chemical element is the same. However, if the non-local terms, i.e., the turbulent convective transport of radial chemical component flux, are taken into account, the diffusion coefficient for each chemical element should be in general different. (ii) The diffusion coefficient of convective / overshoot mixing shows different behaviors in convection zone and in overshoot region because the characteristic length scale of the mixing is large in the convection zone and small in the overshoot region. The overshoot mixing should be regarded as a weak mixing process. (iii) The result of the diffusion coefficient of mixing is tested in stellar models. It is found that a single choice of our central mixing parameter leads to consistent results for a solar convective envelope model as well as for core convection models of stars with mass from 2M to 10M.

astro-ph.SR↗
arXiv2014

Modeling the dynamics of single-bubble sonoluminescence

Sonoluminescence (SL) is the phenomenon in which acoustic energy is (partially) transformed into light. It may occur by means of many or just one bubble of gas inside a liquid medium, giving rise to the terms multi-bubble- and single-bubble sonoluminescence (MBSL and SBSL). In the last years some models have been proposed to explain this phenomenon, but there is still no complete theory for the light emission mechanism (especially in the case of SBSL). In this work, we will not address this more complicated particular issue, but only present a simple model describing the dynamical behaviour of the sonoluminescent bubble, in the SBSL case. Using simple numerical techniques within the software Matlab, we discuss solutions considering various possibilities for some of the parameters involved: liquid compressibility, superficial tension, viscosity, and type of gas. The model may be used as an introductory study of sonoluminescence in physics courses at undergraduate or graduate levels, as well as a quite clarifying example of a physical system exhibiting large nonlinearity.

physics.ed-ph↗
arXiv2014

How linear surface waves are affected by a current with constant vorticity

The interaction of surface waves with Couette-type current with uniform vorticity is a well suited problem for students approaching the theory of surface waves. The problem, although mathematically simple, contains rich physics, and is moreover important in several situations from oceanography and marine technology to microfluidics. We here lay out a simple two-dimensional theory of waves propagating upon a basic flow of uniform vorticity of constant depth. The dispersion relation is found, showing how the shearing current introduces different phase velocities for upstream and downstream propagating waves. The role of surface tension is discussed and applied to the case of a wave pattern created by a moving source, stationary as seen by the source. We conclude by discussing how the average potential and kinetic energies are no longer equal in the presence of shear.

physics.flu-dyn↗