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Item type:Publication, Nonlinear wave dynamics under the presence of a strong horizontal electric field and a bathymetry(Elsevier BV, 2024-12-13)In this letter, we explore free-surface flow of an ideal dielectric liquid subjected to a strong tangential electric field in the presence of variable bottom topographies. Analytically, we demonstrate that nonlinear waves of arbitrary shape can propagate at a critical speed without distortion, provided they are in resonance with a moving localized obstacle at the bottom. Numerical solutions of the full model for various obstacle types yield two key results: (i) For localized obstacles, a wave forms above the obstacle, then splits into symmetric waves traveling in opposite directions at the same speed and a stationary disturbance formed due to electric field inhomogeneities. (ii) Periodic spatial bathymetries induce periodic motion in both space and time. Additionally, considering traveling solitary waves, we show that a small dispersive tail arises when they interact with the bathymetry.1 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Flow structure beneath periodic waves with constant vorticity under strong horizontal electric fields(Elsevier B.V., 2024-12-01)While several articles have been written on Electrohydrodynamics (EHD) flows or flows with constant vorticity separately, little is known about the extent to which the combined effects of EHD and constant vorticity affect the flow. This study aims to shed light on this topic by investigating the combined influence of a horizontal electric field and constant vorticity on the free surface and the emergence of stagnation points. Using the Euler equations framework, we employ conformal mapping and pseudo-spectral numerical methods. Our findings reveal that increasing the electric field intensity eliminates stagnation points and smoothen the wave profile. This implies that a horizontal electric field acts as a mechanism for the elimination of stagnation points within the fluid body. Besides, we have identified regimes where three stagnation points appear on the free surface — something that cannot occur in purely gravity rotational waves. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Auto-resonance process under the interaction of solitons with external force and dissipation(Elsevier Ltd, 2024-12-01)Algebraic soliton interactions with an external force in the presence of Reynolds viscosity is investigated. In the absence of an external force, the soliton amplitude decays over time. However, when an external force is introduced, it acts as a restoring force, and in some cases, the soliton's amplitude is preserved. A dynamical system that governs the soliton amplitude and its crest position is obtained assuming a weak force and weak viscosity. For an external force with a Gaussian shape, the dynamical system has two equilibrium points, namely, a saddle and a stable spiral. Asymptotic results are compared with direct numerical simulations, and a strong qualitative agreement is observed. The stable spiral predicted by the asymptotic theory is stable in the sense that soliton solutions with a chosen amplitude and crest position near the spiral point are attracted to it, preserving their amplitude and location. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Solitons in dissipative systems subjected to random force within the Benjamin–Ono type equation(Elsevier Ltd, 2024-10-01)Solitary wave dynamics is investigated under the assumption of small dissipation and an external random force. Through a change of variables, the problem becomes homogeneous, allowing for the derivation of asymptotic algebraic soliton solutions. This change of variables makes the randomness manifest primarily on the soliton phases. Consequently, the averaged soliton field and the statistical moments can be computed analytically, assuming that the phase follows a uniform distribution. In the absence of Reynolds dissipation, we show that the soliton-averaged field tends to spread and dampen as the dispersion increases. In addition, in the presence of Reynolds dissipation, we demonstrate that algebraic solitons can transition between thick and thin soliton states. Moreover, when there is viscosity in the upper moving layer, the averaged soliton field exhibits a dynamic evolution from soliton to thick soliton to soliton, contingent upon the parameter settings. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Nonlinear random wave fields within a Boussinesq system(Elsevier B.V., 2024-09-28)The dynamics of nonlinear random fields is important for understanding wave turbulence. In this work, we use a Boussinesq system to examine the distinctions between unidirectional and bidirectional waves. Our study demonstrates that in both scenarios, the wave spectra reach a stationary state. Moreover, we show that the occurrence of rogue waves is more probable in the unidirectional case. In the unidirectional case, the probability distribution of wave crests exceeds the one predicted by the Rayleigh distribution once the spectra reach the stationary state. Conversely, in the bidirectional case, the opposite trend is observed. The discovery of various types of rogue waves, including massive wave trains commonly known in the literature as “two sisters” and “three sisters” are found. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Wave fields under the influence of a random-driven force: The Burgers equation(Elsevier B.V., 2024-12-15)In this work, we examine the classical Burgers equation and investigate the effects of a random force on the wave field. Two scenarios are considered: the impact of a random force on different wave fields within the viscous Burgers equation and the effect of a periodic random force in the inviscid Burgers equation. For the first case, we demonstrate that the random force primarily causes wave fronts to increase or decrease depending on the dispersion parameter. For an initially deformed sinusoidal wave, the external force causes the mean wave field to spread out and dampen over time. The Cole-Hopf transformation is also used to obtain asymptotically the averaged wave field in certain regimes. For the inviscid problem, we assume the random force to be periodic with random phase to show that the mean wave field corresponds to the solution of the classical inviscid Burgers equation without external forces. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Flow patterns induced by a moving disturbance in rotational flows within the forced Korteweg–de Vries equation(Springer Nature, 2024-12-01)Flow structures beneath a moving disturbance along a water free surface in the weakly nonlinear weakly dispersive regime in a sheared channel with finite depth and constant vorticity are investigated. We compute the exact two branches of steady solutions in the disturbance moving frame. The velocity field in the bulk fluid is approximated which allows us to compute the flow structures beneath the free surface including stagnation points and Kelvin cat-eyes structures. We show that stagnation points exist only in one branch of solutions. The bifurcation of the flow is analyzed according to the intensity of the vorticity and the speed of the moving disturbance. Differently from the unforced problem, stagnation points can arise for small values of the vorticity as long as the moving disturbance travels sufficiently fast. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Wave evolution within the cubic vortical Whitham equation(Elsevier BV, 2024-12-26)In this work, we study the evolution of disturbances within the framework of the Cubic Vortical Whitham (CV-Whitham) equation, considering both positive and negative cubic nonlinearities. This equation plays important role for description of the wave processes in the presence of shear flows. We find well-formed breather-type structures arising from the evolution of depression disturbances with positive cubic nonlinearity. For elevation disturbances, the results are two-fold. When the cubic nonlinearity is negative, we show that the CV-Whitham equation and the Gardner equation are qualitatively similar, differing only by a small phase lag due to differences in the dispersion term. However, with positive cubic nonlinearity, the differences between the solutions become more pronounced, with the CV-Whitham equation producing sharper waves that suggest the onset of wave breaking. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Wave packet dynamics within the modular Schamel equation(Elsevier BV, 2026-04-01)In this article, we investigate the evolution of long waves and the dynamics of wave packets governed by the modular Schamel equation. We show that the wave field disintegrates into solitary waves of both polarities and recurrence is not observed. Their interactions substantially amplify the wave field and, over long times and large domains, can trigger the formation of freak waves. Furthermore, under the assumption of weak nonlinearity, we seek wave packet solutions of the Schamel equation and derive a generalized nonlinear Schrödinger (gNLS) envelope equation, which inherits the same nonlinearity as the Schamel equation. In the parameter regime of interest, the gNLS supports only bright solitons, which inherit the Schamel solitary-wave profile (up to scaling). Additionally, the derived bright soliton was examined as an initial-value problem for the modular Schamel equation, where its numerical stability was confirmed, showing good agreement with the theoretical predictions.Scopus© Citations 1 1 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Wave dynamics within the Whitham-Ostrovsky equation(Springer Science+Business Media, 2026-06-01)In this article, we investigate wave packet and solitary wave dynamics in the Whitham–Ostrovsky (WO) equation. By means of a multiple-scales expansion, we formally derive a nonlinear Schrödinger (NLS) equation governing the envelope evolution. The corresponding modulational stability diagram is then obtained using the Lighthill criterion. We show that sufficiently large values of the low-frequency dispersive term render plane-wave solutions modulationally unstable. Direct numerical simulations confirm that, within the unstable region, wave packets undergo a pronounced compression, consistent with the self-focusing mechanism of the focusing NLS equation. In contrast, in the modulationally stable region, the wave packet progressively broadens in space while its peak amplitude decreases, as the wave energy is redistributed over an increasingly wider spatial interval. We further examine how solitary-wave solutions of the Whitham equation are modified within the WO framework, where they evolve into localized wave packets due to the presence of the rotating term. In addition, we investigate the dynamics of solitary waves in the anomalous dispersion regime. These solutions are computed numerically and evolved under the full time-dependent equation, revealing that their interactions are inelastic, with noticeable generation of dispersive radiation and an increase in the amplitude of the larger solitary wave. Although such interactions could, in principle, promote the emergence of a “soliton champion” or even a freak-wave–type structure after repeated collisions, the progressive steepening of the solitary waves alters this scenario. Numerical simulations indicate that, instead of forming a persistent dominant soliton, the wave profile continues to sharpen until the onset of wave breaking occurs.
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