@inproceedings{Bestehorn, author = {Bestehorn, Michael}, title = {IMA8 - Interfacial Fluid Dynamics and Process}, series = {The European Physical Journal Special Topics}, volume = {26}, booktitle = {The European Physical Journal Special Topics}, number = {6}, issn = {1951-6355}, doi = {10.1140/epjst/e2017-70057-9}, pages = {1151 -- 1153}, language = {en} } @incollection{Bestehorn, author = {Bestehorn, Michael}, title = {Fluid Dynamics and Pattern Formation}, series = {Encyclopedia of Complexity and Systems Science}, booktitle = {Encyclopedia of Complexity and Systems Science}, publisher = {Springer}, address = {New York, NY}, isbn = {978-0-387-75888-6}, doi = {10.1007/978-0-387-30440-3}, abstract = {The state of a fluid is described by its velocity, density, pressure, and temperature. All these variables depend in general on space andtime. Pattern formation refers to the situation where one or more of these variables are organized within a certain spatial and/or temporalorder. This order has macroscopic length and time scales, that is, characteristic lengths and times are much larger than those of the atoms or moleculeswhich constitute the fluid. Therefore a continuous description is appropriate. Macroscopic fluid patterns may be encountered in nature as well as in technological applications for a large variety of different systems. Farfrom being complete, we mention some examples: Water waves caused by wind or by sea quakes and land slides (Tsunamis). Localized excitations of the surface of a fluid (solitons), such as that seen on shallow water channels. Shear instabilities in clouds or in multi-layer systems such as the Kelvin-Helmholtz instability or...}, language = {en} } @misc{PototskyBestehorn, author = {Pototsky, Andrey and Bestehorn, Michael}, title = {Shaping liquid drops by vibration}, series = {epl : a letters journal exploring the frontiers of physics}, volume = {121}, journal = {epl : a letters journal exploring the frontiers of physics}, number = {4}, issn = {1286-4854}, doi = {10.1209/0295-5075/121/46001}, pages = {46001-p1 -- 46001-p6}, abstract = {We present and analyze a minimal hydrodynamic model of a vertically vibrated liquid drop that undergoes dynamic shape transformations. In agreement with experiments, a circular lens-shaped drop is unstable above a critical vibration amplitude, spontaneously elongating in the horizontal direction. Smaller drops elongate into localized states that oscillate with half of the vibration frequency. Larger drops evolve by transforming into a snake-like structure with gradually increasing length. The worm state is long-lasting with a potential to fragment into smaller drops.}, language = {en} } @misc{BorciaBestehornUhligetal., author = {Borcia, Rodica and Bestehorn, Michael and Uhlig, Sebastian and Gaudet, Matthieu and Schenk, Harald}, title = {Liquid pumping induced by transverse forced vibrations of an elastic beam: A lubrication approach}, series = {Physical Review Fluids}, volume = {3}, journal = {Physical Review Fluids}, number = {8}, issn = {2469-990X}, doi = {10.1103/PhysRevFluids.3.084202}, abstract = {Two liquid pumps are investigated theoretically and numerically: a single thin liquid layer actuated by a periodic force at an elastic beam and a two-layer geometry actuated by an elastic beam. For the second geometry, the beam actuates the liquid from both sides. For both pumps, the liquid film thickness is small compared to the lateral characteristic length of the system. A lubrication theory is developed. The Euler-Bernoulli equation for transverse deformations of an elastic beam is coupled to the fundamental hydrodynamic equations: the Navier-Stokes equation and a continuity equation in the long-wave approximation. In this way, one connects the transverse displacement of the beam with the hydrodynamic quantities (pressure, velocity fields, and flow rates). Appropriate boundary conditions incorporate the function of the valves. The derivation of the theoretical model is followed by numerical simulations. We estimate flow rates (in two and three spatial dimensions) for different system parameters and we compute the efficiency of a well-designed liquid pump.}, language = {en} } @inproceedings{BorciaBorciaBestehornetal., author = {Borcia, Ion-Dan and Borcia, Rodica and Bestehorn, Michael and Xu, Wenchao and Harlander, Uwe}, title = {Surface waves generated by libration in a circular channel}, series = {The 12th European Fluid Mechanics Conference, 9 September 2018 - 13 September 2018, Vienna, Austria}, booktitle = {The 12th European Fluid Mechanics Conference, 9 September 2018 - 13 September 2018, Vienna, Austria}, pages = {1}, language = {en} } @misc{BorciaBorciaBestehornetal., author = {Borcia, Rodica and Borcia, Ion-Dan and Bestehorn, Michael and Varlamova, Olga and Hoefner, Kevin and Reif, J{\"u}rgen}, title = {Drop Behavior Influenced by the Correlation Length on Noisy Surfaces}, series = {Langmuir}, volume = {35}, journal = {Langmuir}, doi = {10.1021/acs.langmuir.8b03878}, pages = {928 -- 934}, language = {en} } @book{Bestehorn, author = {Bestehorn, Michael}, title = {Computational Physics : With Worked Out Examples in FORTRAN and MATLAB}, edition = {1. Auflage}, publisher = {De Gruyter}, address = {Berlin}, isbn = {978-3-11-051513-8}, pages = {320}, abstract = {Drawing on examples from various areas of physics, this textbook introduces the reader to computer-based physics using Fortran® and Matlab®. It elucidates a broad palette of topics, including fundamental phenomena in classical and quantum mechanics, hydrodynamics and dynamical systems, as well as effects in field theories and macroscopic pattern formation described by (nonlinear) partial differential equations. A chapter on Monte Carlo methods is devoted to problems typically occurring in statistical physics.}, language = {en} } @misc{RichterBestehorn, author = {Richter, Sebastian and Bestehorn, Michael}, title = {Direct numerical simulations of liquid films in two dimensions under horizontal and vertical external vibrations}, series = {Physical Review Fluids}, volume = {4}, journal = {Physical Review Fluids}, number = {4}, issn = {2469-990X}, doi = {10.1103/PhysRevFluids.4.044004}, pages = {044004-1 -- 044004-21}, abstract = {We consider Newtonian liquid films on a horizontal substrate with a free and deformable surface. The substrate is subjected to oscillatory accelerations in the normal or in the horizontal direction. An algorithm based on a nonlinear coordinate transformation is presented that allows for direct numerical solutions of the fully nonlinear Navier-Stokes equations and appropriate boundary conditions. No surface tracking is necessary. Normal oscillations generate the traditional subharmonic and harmonic Faraday patterns. Lateral oscillations cause a pattern formation scenario qualitatively similar to spinodal dewetting, namely the disintegration of the film into isolated drops followed by coarsening or fusion, the stabilization of a "precursor" film, and no rupture. Ratchet-like lateral excitations break the horizontal mirror symmetry x→-x and give the patterns a preferred direction. We show that drops formed due to instability of the flat film start to travel in a distinguished direction. For thin films, the results are in good agreement to those of a recently studied lubrication-based dimension-reduced model [Bestehorn et al., Phys. Rev. E 88, 023025 (2013); Bestehorn, Phys. Fluids 25, 114106 (2013)].}, language = {en} } @misc{StermanCohenBestehornOron, author = {Sterman-Cohen, Elad and Bestehorn, Michael and Oron, Alexander}, title = {Driving mechanisms of ratchet flow in thin liquid films under tangential two-frequency forcing}, series = {Physics of Fluids}, volume = {31}, journal = {Physics of Fluids}, number = {7}, doi = {10.1063/1.5098941}, pages = {14}, abstract = {In a recent paper, we demonstrated the emergence of ratchet flows in thin liquid films subjected to tangential two-frequency vibrations [E. Sterman-Cohen, M. Bestehorn, and A. Oron, "Ratchet flow of thin liquid films induced by a two-frequency tangential forcing," Phys. Fluids 30, 022101 (2018)], and asymmetric forcing was found to be a sole driving mechanism for these ratchet flows. In this paper, we consider other two-frequency excitations and reveal an additional driving mechanism of an emerging ratchet flow when the acceleration imparted by forcing is symmetric with respect to a certain moment of time within the forcing period (this type of forcing referred to as "symmetric forcing"). This driving mechanism exhibits an intricate interaction between forcing, capillarity, and gravity. We find that in contradistinction with the case of asymmetric forcing where the flow intensity reaches a constant value in the large-time limit, in the case of symmetric forcing the flow intensity exhibits oscillatory variation in time. We also discuss the flow intensity variation of the emerging ratchet flows with the fundamental wavenumber of the disturbance.}, language = {en} } @misc{BorciaBorciaBestehornetal., author = {Borcia, Ion-Dan and Borcia, Rodica and Bestehorn, Michael and Richter, Stefan and Xu, Wenchao and Harlander, Uwe}, title = {Horizontal Faraday instability and parametric excitation in a circular channel}, series = {GAMM 2019, 90th Annual Meeting of the International Assoociation of Applied Mathematics and Mechanics, February 18-22, 2019, Vienna, Austria}, journal = {GAMM 2019, 90th Annual Meeting of the International Assoociation of Applied Mathematics and Mechanics, February 18-22, 2019, Vienna, Austria}, publisher = {TU Verlag}, address = {Wien}, isbn = {978-3-903024-84-7}, pages = {338}, language = {en} } @misc{BestehornTyvandMichelitsch, author = {Bestehorn, Michael and Tyvand, Peder A. and Michelitsch, Thomas M.}, title = {Dimension-Reduced Model for Deep-Water Waves}, series = {Journal of Applied Mathematics and Physics}, volume = {7}, journal = {Journal of Applied Mathematics and Physics}, number = {1}, issn = {2327-4379}, doi = {10.4236/jamp.2019.71007}, pages = {72 -- 92}, abstract = {Starting from the 2D Euler equations for an incompressible potential flow, a dimension-reduced model describing deep-water surface waves is derived. Similar to the Shallow-Water case, the z-dependence of the dependent variables is found explicitly from the Laplace equation and a set of two one- dimensional equations in x for the surface velocity and the surface elevation remains. The model is nonlocal and can be formulated in conservative form, describing waves over an infinitely deep layer. Finally, numerical solutions are presented for several initial conditions. The side-band instability of Stokes waves and stable envelope solitons are obtained in agreement with other work. The conservation of the total energy is checked.}, language = {en} } @misc{BorciaBorciaRichteretal., author = {Borcia, Ion-Dan and Borcia, Rodica and Richter, Sebastian and Xu, Wenchao and Bestehorn, Michael and Harlander, Uwe}, title = {Horizontal Faraday instability in a circular channel}, series = {Proceedings in Applied Mathematics and Mechanics (PAMM)}, volume = {19}, journal = {Proceedings in Applied Mathematics and Mechanics (PAMM)}, number = {1}, issn = {1617-7061}, doi = {10.1002/pamm.201900242}, pages = {2}, abstract = {We study surface waves in a circular channel placed on a rotating table. The tank can rotate with constant velocity and/or can oscillate. For a glycerin-water-solution with high viscosity, oscillation amplitudes about 20 cm and frequencies of 0.5 Hz, we observe surface patterns generated by a parametric instability. The circular geometry of the channel assures in a natural way the periodic lateral boundary conditions often used in the numerical simulations. Up to our knowledge this is the first experiment which evidences the horizontal Faraday instability in a container without walls blocking the flow in the oscillation direction. Experimental and numerical results are compared and discussed.}, language = {en} } @misc{BorciaBorciaXuetal., author = {Borcia, Ion-Dan and Borcia, Rodica and Xu, Wenchao and Bestehorn, Michael and Richter, Sebastian and Harlander, Uwe}, title = {Undular bores in a large circular channel}, series = {European Journal of Mechanics - B/Fluids}, volume = {79}, journal = {European Journal of Mechanics - B/Fluids}, issn = {0997-7546}, doi = {10.1016/j.euromechflu.2019.09.003}, pages = {67 -- 73}, abstract = {An experimental device previously developed for studying rotating baroclinic flows has been used to investigate undular bores formation, propagation and collision. Up to our knowledge this is the first experimental study of undular bores in a circular channel. For a setup without barriers, this geometry accomplishes in a natural way the periodic lateral boundary conditions, very often used in numerical simulations. An excellent agreement between the experiment and simulation has been achieved. The spatio-temporal structure of bores is well reproduced for the first few reflections or collisions.}, language = {en} } @misc{GrangerMichelitschBestehornetal., author = {Granger, T{\´e}o and Michelitsch, Thomas M. and Bestehorn, Michael and Riascos, Alejandro P. and Collet, Bernard A.}, title = {Stochastic Compartment Model with Mortality and Its Application to Epidemic Spreading in Complex Networks}, series = {Entropy}, volume = {26}, journal = {Entropy}, number = {5}, issn = {1099-4300}, doi = {10.3390/e26050362}, abstract = {We study epidemic spreading in complex networks by a multiple random walker approach. Each walker performs an independent simple Markovian random walk on a complex undirected (ergodic) random graph where we focus on the Barab{\´a}si-Albert (BA), Erd{\"o}s-R{\´e}nyi (ER), and Watts-Strogatz (WS) types. Both walkers and nodes can be either susceptible (S) or infected and infectious (I), representing their state of health. Susceptible nodes may be infected by visits of infected walkers, and susceptible walkers may be infected by visiting infected nodes. No direct transmission of the disease among walkers (or among nodes) is possible. This model mimics a large class of diseases such as Dengue and Malaria with the transmission of the disease via vectors (mosquitoes). Infected walkers may die during the time span of their infection, introducing an additional compartment D of dead walkers. Contrary to the walkers, there is no mortality of infected nodes. Infected nodes always recover from their infection after a random finite time span. This assumption is based on the observation that infectious vectors (mosquitoes) are not ill and do not die from the infection. The infectious time spans of nodes and walkers, and the survival times of infected walkers, are represented by independent random variables. We derive stochastic evolution equations for the mean-field compartmental populations with the mortality of walkers and delayed transitions among the compartments. From linear stability analysis, we derive the basic reproduction numbers RM,R0with and without mortality, respectively, and prove that RM1, the healthy state is unstable, whereas for zero mortality, a stable endemic equilibrium exists (independent of the initial conditions), which we obtained explicitly. We observed that the solutions of the random walk simulations in the considered networks agree well with the mean-field solutions for strongly connected graph topologies, whereas less well for weakly connected structures and for diseases with high mortality. Our model has applications beyond epidemic dynamics, for instance in the kinetics of chemical reactions, the propagation of contaminants, wood fires, and others.}, language = {en} } @misc{BorciaRichterBorciaetal., author = {Borcia, Ion-Dan and Richter, Sebastian and Borcia, Rodica and Sch{\"o}n, Franz-Theo and Harlander, Uwe and Bestehorn, Michael}, title = {Wave propagation in a circular channel: sloshing and resonance}, series = {The European Physical Journal Special Topics}, volume = {Vol. 232}, journal = {The European Physical Journal Special Topics}, number = {4}, issn = {1951-6401}, doi = {10.1140/epjs/s11734-023-00790-z}, pages = {461 -- 468}, abstract = {Surface wave resonance of a liquid (water) layer confined in a circular channel is studied both experimentally and numerically. For the experiment, eight unevenly distributed ultrasonic distance sensors measure the local height of the wave surface. The resonance curves show maxima only for odd multiples of the fundamental resonance frequency . We explained this behavior using a simple intuitive "ping-pong" like model. Collision of wave fronts can be observed for higher frequencies. Also, the wave reflection on the walls can be treated as wave collision with itself. The non-linearity seems to be weak in our study so the delay in the wave propagation before and after the collision is small. Time-space plots show localized propagating waves with high amplitudes for frequencies near resonance. Between the peaks low amplitude and harmonic patterns are observed. However, for higher frequencies, the frequency band for localized waves becomes wider. In the Fourier space-time plane, this can be observed as a point for the harmonic patterns or a superposition of two lines: one line parallel to wave-vector k axis corresponding to the excitation frequency and a second line with inclination given by wave propagation velocity . For planned future work, this result will help us to reconstruct the whole water surface elevation using time-series from only a few measurement points}, language = {en} } @misc{SchoenBestehorn, author = {Sch{\"o}n, Franz-Theo and Bestehorn, Michael}, title = {Instabilities and pattern formation in viscoelastic fluids}, series = {The European Physical Journal Special Topics}, volume = {Vol. 232}, journal = {The European Physical Journal Special Topics}, number = {4}, issn = {1951-6401}, doi = {10.1140/epjs/s11734-023-00792-x}, pages = {375 -- 383}, language = {en} } @misc{GrangerMichelitschBestehornetal., author = {Granger, T{\´e}o and Michelitsch, Thomas M. and Bestehorn, Michael and Riascos, Alejandro P. and Collet, Bernard A.}, title = {Four-compartment epidemic model with retarded transition rates}, series = {Physical Review E}, volume = {107}, journal = {Physical Review E}, number = {4}, issn = {2470-0045}, doi = {10.1103/PhysRevE.107.044207}, pages = {044207-1 -- 044207-15}, abstract = {We study an epidemic model for a constant population by taking into account four compartments of the individuals characterizing their states of health. Each individual is in one of the following compartments: susceptible S; incubated, i.e., infected yet not infectious, C; infected and infectious I; and recovered, i.e., immune, R. An infection is visible only when an individual is in state I. Upon infection, an individual performs the transition pathway S→C→I→R→S, remaining in compartments C, I, and R for a certain random waiting time tC, tI, and tR, respectively. The waiting times for each compartment are independent and drawn from specific probability density functions (PDFs) introducing memory into the model. The first part of the paper is devoted to the macroscopic S-C-I-R-S model. We derive memory evolution equations involving convolutions (time derivatives of general fractional type). We consider several cases. The memoryless case is represented by exponentially distributed waiting times. Cases of long waiting times with fat-tailed waiting-time distributions are considered as well where the S-C-I-R-S evolution equations take the form of time-fractional ordinary differential equations. We obtain formulas for the endemic equilibrium and a condition of its existence for cases when the waiting-time PDFs have existing means. We analyze the stability of healthy and endemic equilibria and derive conditions for which the endemic state becomes oscillatory (Hopf) unstable. In the second part, we implement a simple multiple-random-walker approach (microscopic model of Brownian motion of Z independent walkers) with random S-C-I-R-S waiting times in computer simulations. Infections occur with a certain probability by collisions of walkers in compartments I and S. We compare the endemic states predicted in the macroscopic model with the numerical results of the simulations and find accordance of high accuracy. We conclude that a simple random-walker approach offers an appropriate microscopic description for the macroscopic model. The S-C-I-R-S-type models open a wide field of applications allowing the identification of pertinent parameters governing the phenomenology of epidemic dynamics such as extinction, convergence to a stable endemic equilibrium, or persistent oscillatory behavior.}, language = {en} } @misc{BestehornRiascosMichelitschetal., author = {Bestehorn, Michael and Riascos, Alejandro P. and Michelitsch, Thomas M. and Collet, Bernard A.}, title = {A Markovian random walk model of epidemic spreading}, series = {Continuum Mechanics and Thermodynamics}, volume = {33}, journal = {Continuum Mechanics and Thermodynamics}, number = {4}, issn = {1432-0959}, doi = {10.1007/s00161-021-00970-z}, pages = {1207 -- 1221}, abstract = {We analyze the dynamics of a population of independent random walkers on a graph and develop a simple model of epidemic spreading. We assume that each walker visits independently the nodes of a finite ergodic graph in a discrete-time Markovian walk governed by his specific transition matrix. With this assumption, we first derive an upper bound for the reproduction numbers. Then, we assume that a walker is in one of the states: susceptible, infectious, or recovered. An infectious walker remains infectious during a certain characteristic time. If an infectious walker meets a susceptible one on the same node, there is a certain probability for the susceptible walker to get infected. By implementing this hypothesis in computer simulations, we study the space-time evolution of the emerging infection patterns. Generally, random walk approaches seem to have a large potential to study epidemic spreading and to identify the pertinent parameters in epidemic dynamics.}, language = {en} } @misc{PototskyOronBestehorn, author = {Pototsky, Andrey and Oron, Alexander and Bestehorn, Michael}, title = {Equilibrium shapes and floatability of static and vertically vibrated heavy liquid drops on the surface of a lighter fluid}, series = {Journal of Fluid Mechanics}, volume = {922}, journal = {Journal of Fluid Mechanics}, issn = {1469-7645}, doi = {10.1017/jfm.2021.546}, pages = {A31-1 -- A31-21}, abstract = {A small drop of a heavier fluid may float on the surface of a lighter fluid supported by surface tension forces. In equilibrium, the drop assumes a radially symmetric shape with a circular triple-phase contact line. We show that such a floating liquid drop with a sufficiently small volume has two distinct equilibrium shapes at terrestrial gravity: one with a larger and one with a smaller radius of the triple-phase contact line. Static stability analysis reveals that both shapes could be stable if the drop volume is below a certain critical value. Experiments conducted with μL-sized water drops floating on commercial oil support the existence of multiple contact line radii for a drop with fixed volume. Next, we experimentally study the floatability of a less viscous water drop on the surface of a more viscous and less dense oil, subjected to a low-frequency (Hz-order) vertical vibration. We find that in a certain range of amplitudes, vibration helps heavy liquid drops to stay afloat. The physical mechanism of the increased floatability is explained by the horizontal elongation of the drop driven by subharmonic Faraday waves. The average length of the triple-phase contact line increases as the drop elongates that leads to a larger average lifting force produced by the surface tension.}, language = {en} } @misc{PirizPirizTahiretal., author = {Piriz, S. A. and Piriz, Antonio R. and Tahir, Naeem A. and Richter, Sebastian and Bestehorn, Michael}, title = {Rayleigh-Taylor instability in elastic-plastic solid slabs bounded by a rigid wall}, series = {Physical Review E}, volume = {103}, journal = {Physical Review E}, number = {2}, issn = {2470-0045}, doi = {10.1103/PhysRevE.103.023105}, pages = {023105-1 -- 023105-12}, abstract = {The linear evolution of the incompressible Rayleigh-Taylor instability for the interface between an elastic-plastic slab medium and a lighter semi-infinite ideal fluid beneath the slab is developed for the case in which slab is attached to a rigid wall at the top surface. The theory yields the maps for the stability in the space determined by the initial perturbation amplitude and wavelength, as well as for the transition boundary from the elastic to the plastic regimes for arbitrary thicknesses of the slab and density contrasts between the media. In particular, an approximate but very accurate scaling law is found for the minimum initial perturbation amplitude required for instability and for the corresponding perturbation wavelength at which it occurs. These results allows for an interpretation of the recent experiments by Maimouni et al. [Phys. Rev. Lett. 116, 154502 (2016)].}, language = {en} } @misc{TyvandMulstadBestehorn, author = {Tyvand, Peder A. and Mulstad, Camilla and Bestehorn, Michael}, title = {A nonlinear impulsive Cauchy-Poisson problem. Part 1. Eulerian description}, series = {Journal of Fluid Mechanics}, volume = {906}, journal = {Journal of Fluid Mechanics}, issn = {1469-7645}, doi = {10.1017/jfm.2020.787}, pages = {A24-1 -- A24-32}, abstract = {A nonlinear Cauchy-Poisson problem with impulsive surface forcing is investigated analytically and numerically. An incompressible liquid with an initially horizontal surface is instantaneously put into motion by an impulsive surface pressure distribution turned on and off during an infinitesimal time interval. We consider symmetric, antisymmetric and asymmetric pressure impulses based on dipoles and quadrupoles. The subsequent inviscid free-surface flow is governed by fully nonlinear surface conditions, which are solved exactly to third order in a small-time expansion. The small-time expansion applies to flows dominated by inertia. Such flows are generated by relatively strong pressure impulses, measured in gravitational units. We solve the problem numerically and find that only relatively weak pressure impulses will lead to oscillatory waves. The free surface will break before a full gravitational oscillation is completed when the amplitude of the pressure impulse exceeds one gravitational unit.}, language = {en} } @misc{TyvandMulstadBestehorn, author = {Tyvand, Peder A. and Mulstad, Camilla and Bestehorn, Michael}, title = {A nonlinear impulsive Cauchy-Poisson problem. Part 2. Lagrangian description}, series = {Journal of Fluid Mechanics}, volume = {906}, journal = {Journal of Fluid Mechanics}, issn = {1469-7645}, doi = {10.1017/jfm.2020.788}, pages = {A25-1 -- A25-19}, abstract = {A fully nonlinear Cauchy-Poisson problem is investigated analytically by a small-time expansion. The inviscid incompressible fluid layer has an initially horizontal surface. The fluid is forced into motion by an impulsive surface pressure. The early nonlinear free-surface problem is solved to second order in a small-time expansion by the Lagrangian description of motion. Comparisons are made with two other solution procedures for the same nonlinear problem in the absence of gravity: a third-order small-time expansion and a numerical solution, based on full nonlinearity according to the standard Eulerian description. Good agreement is found between the present second-order Lagrangian solution and the previous third-order Eulerian solution, until both these asymptotic expansions diverge rather abruptly at the same time.}, language = {en} } @misc{Bestehorn, author = {Bestehorn, Michael}, title = {Rayleigh-Taylor and Kelvin-Helmholtz instability studied in the frame of a dimension-reduced model}, series = {Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences}, volume = {378}, journal = {Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences}, issn = {1471-2962}, doi = {10.1098/rsta.2019.0508}, pages = {1 -- 10}, abstract = {Introducing an extension of a recently derived dimension-reduced model for an infinitely deep inviscid and irrotational layer, a two-layer system is examined in the present paper. A second thin viscous layer is added on top of the original one-layer system. The set-up is a combination of a long-wave approximation (upper layer) and a deep-water approximation (lower layer). Linear stability analysis shows the emergency of Rayleigh-Taylor and Kelvin-Helmholtz instabilities. Finally, numerical solutions of the model reveal spatial and temporal pattern formation in the weakly nonlinear regime of both instabilities. This article is part of the theme issue 'Stokes at 200 (Part 1)'.}, language = {en} } @misc{TyvandBestehorn, author = {Tyvand, Peder A. and Bestehorn, Michael}, title = {Nonlinear wave resonance from bottom vibrations in uniform open-channel flow}, series = {European Journal of Mechanics. B, Fluids}, volume = {79}, journal = {European Journal of Mechanics. B, Fluids}, issn = {1873-7390}, doi = {10.1016/j.euromechflu.2019.07.004}, pages = {74 -- 86}, abstract = {It is known from linear theory that bottom oscillations in uniform open-channel flow can produce resonant surface waves with zero group velocity and diverging amplitude (Tyvand and Torheim 2012). This resonance exists for Froude numbers smaller than one, at a critical frequency dependent on the Froude number. This resonance phenomenon is studied numerically in the time domain, with fully nonlinear free-surface conditions. An oscillatory 2D bottom source is started, and the local elevation at resonance grows until it may reach a saturation amplitude. Four waves exist at subcritical Froude numbers, where resonance represents the third and the fourth wave merging. In the zero-frequency limit, the dispersive second and fourth wave merge into a steady wave with finite group velocity and amplitude, and no other periodic waves exist. In the time-dependent nonlinear analysis at zero frequency, a transient undular bore may emerge as the dominating phenomenon.}, language = {en} } @misc{PototskyOronBestehorn, author = {Pototsky, Andrey and Oron, Alexander and Bestehorn, Michael}, title = {Vibration-induced floatation of a heavy liquid drop on a lighter liquid film}, series = {Physic of Fluids}, volume = {31}, journal = {Physic of Fluids}, number = {8}, issn = {1089-7666}, doi = {10.1063/1.5099661}, pages = {087101-1 -- 087101-13}, abstract = {We carry out a theoretical study of vibration-induced saturation of the Rayleigh-Taylor instability for an isolated liquid drop on the surface of a less dense finite-thickness carrier film. Without vibration, a heavy drop falls through the carrier film by forming a stretching liquid column until the bottom tip of the column reaches the solid substrate and the carrier film ruptures. We show that an externally applied vertical vibration prevents the rupture of the film and enables stable flotation of the drop. A hydrodynamic model is used to study the effect of inertia on the long-time dynamics of the drop. It is shown that rupture can only be prevented when the Reynolds number is nonzero.}, language = {en} } @misc{BestehornMichelitsch, author = {Bestehorn, Michael and Michelitsch, Thomas M.}, title = {Oscillating Behavior of a Compartmental Model with Retarded Noisy Dynamic Infection Rate}, series = {International Journal of Bifurcation and Chaos}, volume = {33}, journal = {International Journal of Bifurcation and Chaos}, number = {5}, issn = {1793-6551}, doi = {10.1142/S0218127423500566}, abstract = {Our study is based on an epidemiological compartmental model, the SIRS model. In the SIRS model, each individual is in one of the states susceptible (S), infected (I) or recovered (R), depending on its state of health. In compartment R, an individual is assumed to stay immune within a finite time interval only and then transfers back to the S compartment. We extend the model and allow for a feedback control of the infection rate by mitigation measures which are related to the number of infections. A finite response time of the feedback mechanism is supposed that changes the low-dimensional SIRS model into an infinite-dimensional set of integro-differential (delay-differential) equations. It turns out that the retarded feedback renders the originally stable endemic equilibrium of SIRS (stable focus) to an unstable focus if the delay exceeds a certain critical value. Nonlinear solutions show persistent regular oscillations of the number of infected and susceptible individuals. In the last part we include noise effects from the environment and allow for a fluctuating infection rate. This results in multiplicative noise terms and our model turns into a set of stochastic nonlinear integro-differential equations. Numerical solutions reveal an irregular behavior of repeated disease outbreaks in the form of infection waves with a variety of frequencies and amplitudes.}, language = {en} } @misc{BestehornSharmaBorciaetal., author = {Bestehorn, Michael and Sharma, Deewakar and Borcia, Rodica and Amiroudine, Sakir}, title = {Faraday instability of binary miscible/immiscible fluids with phase field approach}, series = {Physical Review Fluids}, volume = {6}, journal = {Physical Review Fluids}, number = {6}, issn = {2469-990X}, doi = {10.1103/PhysRevFluids.6.064002}, pages = {1 -- 26}, abstract = {The objective in the present paper is to study binary fluids with phase field modeling coupled with Navier-Stokes equations. An extended free energy is proposed to account for the continuous path from immiscible to miscible states. We consider fluid pairs that are immiscible for temperatures below the critical one (consolute temperature) and miscible above it. Our extended phase field equation permits us to move from the immiscible state (governed by the Cahn-Hilliard equation) to the miscible state (defined by the species diffusion equation). The scaling of interface tension and interface width with the distance to the critical point is highlighted. The whole system is mechanically excited showing Faraday instability of a flat interface. A linear stability analysis is performed for the stable case (interface waves) as well as for the unstable Faraday one. For the latter, a Floquet analysis shows the well-known Arnold's tongues as a function of the consolute temperature and depth layer. Moreover, two-dimensional finite difference simulations have been performed allowing us to model nonlinear flow patterns both in miscible and immiscible phases. Linear theory and nonlinear simulations show interesting results such as the diminishing of the wavelength of Faraday waves or a shift of the critical vibration amplitude when the consolute temperature is approached.}, language = {en} } @misc{BorciaBorciaBestehornetal., author = {Borcia, Rodica and Borcia, Ion-Dan and Bestehorn, Michael and Sharma, Deewakar and Amiroudine, Sakir}, title = {Phase field modeling in liquid binary mixtures: isothermal and non-isothermal problems}, series = {Physical Review Fluids}, volume = {7}, journal = {Physical Review Fluids}, number = {6}, issn = {2469-990X}, doi = {10.1103/PhysRevFluids.7.064005}, pages = {1 -- 19}, abstract = {The objective in the present paper is to study binary fluids with phase field modeling coupled with Navier-Stokes equations. An extended free energy is proposed to account for the continuous path from immiscible to miscible states. We consider fluid pairs that are immiscible for temperatures below the critical one (consolute temperature) and miscible above it. Our extended phase field equation permits us to move from the immiscible state (governed by the Cahn-Hilliard equation) to the miscible state (defined by the species diffusion equation). The scaling of interface tension and interface width with the distance to the critical point is highlighted. The whole system is mechanically excited showing Faraday instability of a flat interface. A linear stability analysis is performed for the stable case (interface waves) as well as for the unstable Faraday one. For the latter, a Floquet analysis shows the well-known Arnold's tongues as a function of the consolute temperature and depth layer. Moreover, two-dimensional finite difference simulations have been performed allowing us to model nonlinear flow patterns both in miscible and immiscible phases. Linear theory and nonlinear simulations show interesting results such as the diminishing of the wavelength of Faraday waves or a shift of the critical vibration amplitude when the consolute temperature is approached.}, language = {en} } @misc{BestehornOron, author = {Bestehorn, Michael and Oron, Alexander}, title = {Hopf instability of a Rayleigh-Taylor unstable thin film heated from the gas side}, series = {European Physical Journal Special Topics}, volume = {232}, journal = {European Physical Journal Special Topics}, number = {4}, issn = {1951-6401}, doi = {10.1140/epjs/s11734-023-00782-z}, pages = {367 -- 374}, abstract = {A thin liquid film located on the underside of a horizontal solid substrate can be stabilized by the Marangoni effect if the liquid is heated at its free surface. Applying long-wave approximation and projecting the velocity and temperature fields onto a basis of low-order polynomials, we derive a dimension-reduced set of three coupled evolution equations where nonlinearities of both the Navier-Stokes and the heat equation are included. We find that in a certain range of fluid parameters and layer depth, the first bifurcation from the motionless state is oscillatory which sets in with a finite but small wave number. The oscillatory branch is determined using a linear stability analysis of the long-wave model, but also by solving the linearized original hydrodynamic equations. Finally, numerical solutions of the reduced nonlinear model equations in three spatial dimensions are presented.}, language = {en} } @misc{SchoenHarlanderBorciaetal., author = {Sch{\"o}n, Franz-Theo and Harlander, Uwe and Borcia, Ion Dan and Borcia, Rodica and Bestehorn, Michael}, title = {Mean fluid transport in an oscillating circular channel with asymmetric forcing}, series = {Water waves : an interdisciplinary journal}, volume = {2025}, journal = {Water waves : an interdisciplinary journal}, publisher = {Birkh{\"a}user, part of Springer Nature}, address = {Basel}, issn = {2523-3688}, doi = {10.1007/s42286-025-00121-w}, pages = {1 -- 21}, abstract = {We investigate surface waves in an oscillating circular channel with local topography. The focus is on spatially or temporally breaking this dynamic system's symmetry. Asymmetrical wave dynamics and a mean flux excitation are detected to varying degrees, depending on the two input parameters, fluid depth and the tank's oscillation frequency. The fluid resonates around multiples of the fundamental eigenfrequency of the channel. The development of solitary wave-trains (undular bores) is observed in these resonance bands. A particle image velocimetry system measures the velocity field in the vertical plane of the free surface flow. Moreover, we are using 17 evenly distributed ultrasonic sensors to measure the surface displacement. This makes it possible to find out how strongly the mean flux depends on the resonance frequencies and to study the influence of the surface waves on the symmetry breaking. A numerical long-wave model helps to isolate the various factors influencing the mean flux.}, language = {en} }