Article
Mechanics
Xin Guan, Zhan Wang
Summary: Interfacial waves between two superimposed dielectric fluid layers under a horizontal electric field are investigated. Different models are derived from the electrified Euler equations to account for the competing forces resulting from gravity, surface tension, and electric field. Weakly and strongly nonlinear models are obtained under different scaling assumptions. It is shown that the horizontal electric field plays a significant role in the physical system, expanding the range of parameters for the existence of progressive waves and changing the qualitative characteristics of solitary waves.
JOURNAL OF FLUID MECHANICS
(2022)
Article
Mathematics, Applied
Mihaela Ifrim, Ben Pineau, Daniel Tataru, Mitchell Taylor
Summary: This study proves that the 2D finite depth capillary water wave equations do not have solitary wave solutions, under the classical assumptions of incompressibility and irrotationality and with the physical parameters being gravity, surface tension, and the fluid depth.
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
(2022)
Article
Mathematics, Applied
Marcelo V. Flamarion
Summary: In this study, we investigate trapped gravity-capillary waves generated by an accelerated submerged obstacle in a shallow water channel. Using numerical simulations and analysis, we identify different regimes where solitary waves are generated and trapped. The stability of these trapped waves is also studied.
COMPUTATIONAL & APPLIED MATHEMATICS
(2022)
Article
Mechanics
Keisuke Nakayama, Hidekazu Tsuji
Summary: Theoretical solutions show that the amplitude of soliton resonance can be four times larger than the incident solitary wave. Interaction of multiple solitary waves in shallow water results in O-type resonances. The study validates these interactions through theoretical solutions and numerical simulations.
Article
Mechanics
X. Guan, J-M Vanden-Broeck, Z. Wang
Summary: This paper investigates progressive capillary waves on the interface between two homogeneous fluids. Through numerical methods and numerical continuation, the global bifurcation of periodic travelling waves is explored, resulting in self-intersecting and boundary-touching limiting profiles. Theoretical investigation predicts the limiting configurations for most parameter sets and is in good agreement with numerical results.
JOURNAL OF FLUID MECHANICS
(2022)
Article
Geosciences, Multidisciplinary
Li-Jen Chen, Shan Wang, Jonathan Ng, Naoki Bessho, Jian-Ming Tang, Shing F. Fung, Guan Le, Daniel Gershman, Barbara Giles, Christopher T. Russell, Roy Torbert, James Burch
Summary: The study investigates the formation of solitary magnetic structures known as SLAMS using measurements from the magnetospheric multiscale mission combined with fully kinetic simulations. The results indicate that gyro-resonance between solar wind ions and electromagnetic waves leads to magnetic field amplification, while the solitary nature of SLAMS is attributed to a specific magnetic field envelope.
GEOPHYSICAL RESEARCH LETTERS
(2021)
Article
Acoustics
Marcelo V. Flamarion
Summary: This study investigates particle trajectories beneath depression solitary gravity-capillary waves in a sheared channel with finite depth and constant vorticity under the conditions of weak nonlinearity and weak dispersion. A fifth-order Korteweg-de Vries equation, which takes into account the effects of surface tension and vorticity, is derived asymptotically from the full Euler equations when the Bond number is close to a critical value determined by the vorticity. The velocity field in the bulk fluid is approximated to study submarine structures beneath depression solitary waves. The dynamical system of particle trajectories is reformulated in the moving wave frame, and the features are observed through streamlines. The presence of stagnation points in the bulk fluid for large vorticity parameter leads to the formation of cat's-eye structures, and particle trajectories can exhibit vertical excursions or purely horizontal transport. Bifurcation diagrams illustrating the number of stagnation points and complex flow structures beneath depression solitary waves are also presented. (c) 2022 Elsevier B.V. All rights reserved.
Article
Mechanics
Luke F. L. Alventosa, Radu Cimpeanu, Daniel M. Harris
Summary: This study investigates the rebound behavior of droplets impacting a deep fluid bath through experimental and theoretical research. The experiment generates millimetric drops using a piezoelectric droplet-on-demand generator and observes their impact on a bath of the same fluid. The trajectory and rebound metrics of the droplets are compared with predictions from a linear quasipotential model and direct numerical simulations of the Navier-Stokes equations. The models consider the time-dependent shapes of the bath and droplet, and the quasipotential model effectively explains historical experimental measurements of the coefficient of restitution.
JOURNAL OF FLUID MECHANICS
(2023)
Article
Mechanics
X. Guan, J. -M. Vanden-Broeck, Z. Wang, F. Dias
Summary: This study examines the limiting configuration of interfacial solitary waves between two homogeneous fluids, including a sharp angle and an enclosed bubble. By using a boundary integral equation method, the almost limiting profiles are computed, and a reduced model is proposed to further investigate the local configuration of the limiting profile. It is shown that the simplified model provides a good local approximation to the assumed limiting configuration when the angle is 2 pi/3.
JOURNAL OF FLUID MECHANICS
(2021)
Article
Mechanics
Binbin Zhao, Tianyu Zhang, Wenyang Duan, Zhan Wang, Xinyu Guo, Masoud Hayatdavoodi, R. Cengiz Ertekin
Summary: The paper applies the MCC-RL model to investigate internal waves generated by a moving body on the bottom. Comparison with Euler's solutions shows good agreement and accuracy of the MCC-RL results. It is found that the amplitudes of the generated internal solitary waves in front of the moving body increase as the body speed exceeds a critical value, and decrease when the speed further increases.
JOURNAL OF FLUID MECHANICS
(2023)
Article
Multidisciplinary Sciences
Keisuke Nakayama, Kojiro Tani, Hideto Yoshimura, Ichiro Fujita
Summary: This study investigates the vorticity effect on solitary wave profiles through laboratory experiments and numerical simulations, revealing that solitary waves with positive vorticity have an extended effective wavelength, less attenuation, and longer duration compared to solitary waves without vorticity.
SCIENTIFIC REPORTS
(2022)
Article
Mechanics
Chunxin Yuan, Zhan Wang
Summary: In the context of three-dimensional oceanic internal waves with topographic effects, a modified Berney-Luke equation is proposed to describe the interactions between internal waves on a sloping bottom. Numerical results show good agreement between the modified equation and the primitive equations, validating the simplified model. Additionally, a layering scheme is proposed to deal with continuous stratification in realistic ocean environments.
JOURNAL OF FLUID MECHANICS
(2022)
Article
Mechanics
Josh Shelton, Paul Milewski, Philippe H. Trinh
Summary: This study presents new numerical solutions for nonlinear standing water waves, taking into account the effects of gravity and surface tension. The numerical scheme used captures the phenomenon of small-scale parasitic ripples, showing that their amplitude is exponentially small in the limit of zero surface tension. The behavior of these ripples is linked to the generation of a complex bifurcation structure.
JOURNAL OF FLUID MECHANICS
(2023)
Article
Mechanics
Josh Shelton, Paul Milewski, Philippe H. Trinh
Summary: This paper numerically explores the low surface tension limit of the steep gravity-capillary travelling-wave problem, classifying the bifurcation structure that arises and unifying previous numerical studies. The results demonstrate that different choices of solution amplitude can lead to subtle restrictions on the continuation procedure, with wave energy as a continuation parameter allowing solution branches to be continuously deformed to the zero surface tension limit of a travelling Stokes wave.
JOURNAL OF FLUID MECHANICS
(2021)
Article
Mechanics
Wooyoung Choi
Summary: This paper investigates high-order strongly nonlinear long wave models and finds that the system for the bottom velocity is stable to all disturbances at any order of approximation. However, systems for other velocities can be unstable or even ill-posed. A new third-order solitary wave solution of the Euler equations is obtained using the high-order strongly nonlinear system and is expanded in an amplitude parameter. The paper shows the importance of using a more accurate spatial discretization scheme for numerical computations and successfully solves the strongly nonlinear systems for the propagation of solitary waves and their collision.
JOURNAL OF FLUID MECHANICS
(2022)
Article
Mathematics, Applied
Abdullah Madhi Alsharif, Stephen P. Decent, Emilian I. Parau, Mark J. H. Simmons, Jamal Uddin
IMA JOURNAL OF APPLIED MATHEMATICS
(2019)
Article
Mathematics, Applied
Adam A. Yorkston, Mark G. Blyth, Emilian Parau
SIAM JOURNAL ON APPLIED MATHEMATICS
(2020)
Article
Biochemistry & Molecular Biology
Minglei Yang, Hugh C. Woolfenden, Yueying Zhang, Xiaofeng Fang, Qi Liu, Maria L. Vigh, Jitender Cheema, Xiaofei Yang, Matthew Norris, Sha Yu, Alberto Carbonell, Peter Brodersen, Jiawei Wang, Yiliang Ding
NUCLEIC ACIDS RESEARCH
(2020)
Article
Engineering, Multidisciplinary
A. A. Yorkston, M. G. Blyth, E. I. Parau
Summary: This paper presents a novel method to calculate the deformation of a simple elastic aerofoil and determine its aerodynamic viability. It is found that as the flow speed increases, the aerofoil deforms significantly around its trailing edge, resulting in a loss of lift and an increase in drag. By adjusting the internal support, viscous boundary layer separation can be delayed, leading to a substantial increase in the lift-to-drag ratio of the aerofoil.
JOURNAL OF ENGINEERING MATHEMATICS
(2021)
Article
Mechanics
M. G. Blyth, E. Parau
Summary: The stability of periodic travelling waves on fluid of infinite depth is examined in the presence of a constant background shear field, showing that instability occurs for any non-zero amplitude wave.
JOURNAL OF FLUID MECHANICS
(2022)
Article
Mathematics, Applied
Abdullah M. Alsharif, Emilian Parau
Summary: This paper derives one-dimensional equations for a rotating viscous slender liquid jet in a radial electric field using asymptotic methods, and solves these equations to study the trajectory of curved Newtonian liquid jets and the temporal instability of steady solutions. It is found that the electric force enhances the growth rate and increases the corresponding maximum wavenumber.
IMA JOURNAL OF APPLIED MATHEMATICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Claudia Tugulan, Olga Trichtchenko, Emilian Parau
Summary: This work presents three-dimensional, nonlinear traveling wave solutions for water waves under a sheet of ice, specifically flexural-gravity waves. The ice is modeled as a thin elastic plate on top of water with infinite depth, and the equations are formulated using a boundary integral method. Depending on the velocity of the moving disturbance generating the flow, different deflection patterns of the floating ice sheet are observed. A novel hybrid preconditioning technique is introduced to efficiently compute solutions, which significantly increases grid refinement and decreases computational time compared to existing methods. The approach is demonstrated to be applicable to three-dimensional ice wave patterns in different velocity regimes.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Mechanics
A. Alberello, E. I. Parau
Summary: Sea ice attenuates waves from the open ocean. In this study, a nonlinear Schrodinger equation is used to model the evolution of energetic random waves in the marginal ice zone, showing that preferential dissipation of high frequency components leads to a downshift of the spectral peak and a slower energy decay rate compared to a linear model.
Article
Acoustics
A. A. Yorkston, M. G. Blyth, E. I. Parau
Summary: This paper investigates the deformation of a two-dimensional inextensible elastic cell in an inviscid uniform stream with circulation. Equilibria for low far-field flow speeds are obtained based on an asymptotic expansion using conformal mapping, and fully nonlinear solutions are obtained numerically. The study shows that the nature of cell deformation in response to circulation depends on the transmural pressure relative to critical values.
Article
Physics, Fluids & Plasmas
Z. Wang, J. Chai, E. Parau, C. Page, M. Wang
Summary: This paper considers hydraulic falls on the interface of a two-layer density stratified fluid flow in the presence of bottom topography. By deriving the forced Korteweg-de Vries and modified Korteweg-de Vries equations in different asymptotic limits, the existence and classification of fall solutions are understood. The full Euler equations are then numerically solved using a boundary integral equation method. New solutions characterized by a train of trapped waves are found for interfacial flows past two obstacles. The effects of the relative location, aspect ratio, and convexity-concavity property of the obstacles on interface profiles are also investigated.
PHYSICAL REVIEW FLUIDS
(2022)
Article
Acoustics
Evgueni Dinvay, Henrik Kalisch, Emilian Parau
Summary: This paper investigates the waves generated by moving loads on ice plates floating on an incompressible fluid. Two different viscoelastic approximations are considered for the ice cover. The problem is formulated in terms of the exact dispersion relation and the Dirichlet-Neumann operator. Weakly nonlinear and linear approximations are derived, and the Laplace transform is used to find the exact solutions of the linearized problems for the two viscoelastic models considered.
Article
Engineering, Mechanical
Jin Chai, Zhan Wang, Emilian I. Parau
Summary: This article considers steady nonlinear flexural-gravity hydraulic falls on the interface of a two-layer density stratified flow past a submerged obstruction on the bottom of a channel. The fluid is assumed to be ideal, and the flow is irrotational. The effect of hydroelasticity is included by modeling the interface as a thin elastic shell with the Cosserat theory. The full Euler equations are numerically solved using boundary integral equation techniques to find steady solutions. New solutions characterized by subcritical flow upstream and different depth ratios are found, and the effects of the aspect ratio of obstruction are investigated. Moreover, solutions with trapped waves and soliton-like forms are sought by introducing a second obstruction downstream and considering small sheet rigidity.
JOURNAL OF FLUIDS AND STRUCTURES
(2023)
Article
Multidisciplinary Sciences
Kristoffer Johnsen, Henrik Kalisch, Emilian Parau
Summary: This paper investigates the response of a floating ice sheet to a load moving in a curved path. It focuses on the effect of turning on wave patterns and strain distribution, and identifies scenarios where turning can increase wave amplitude and strain in the ice, potentially leading to crack formation and ice failure. The paper uses a mathematical model based on linearized differential equations and solves them using Fourier and Laplace transforms. The model is validated against existing results and tested for various load trajectories involving turning and decelerating.
SCIENTIFIC REPORTS
(2022)
Article
Multidisciplinary Sciences
Alberto Alberello, Emilian Parau, Amin Chabchoub
Summary: Studying wave propagation in the Arctic and Southern Oceans is crucial for modeling the Earth climate system, and a dissipative NLS model was used to simulate the evolution of unstable waves, revealing that modulational instability in sea ice exists in a phase-shifted form.
SCIENTIFIC REPORTS
(2023)
Article
Mathematics, Applied
M. G. Blyth, E. Parau
SIAM JOURNAL ON APPLIED MATHEMATICS
(2019)