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71.
A nonlinear stability method is developed for laminar two-fluid shear flows which undergo changes in the interface topology. The method is based on the nonlinear parabolized stability equations (PSE) and incorporates a scalar-based interface capturing (IC) scheme in order to track complex deformations of the fluid interface. In doing so, the formulation retains the flexibility and physical insight of instability-wave based methods, while providing hydrodynamic modeling capabilities similar to direct numerical calculations: the new formulation, referred to as the IC-PSE, can capture the nonlinear physical mechanisms responsible for generating large-scale, two-fluid structures, without incurring heavy computational costs. This approach is valid for spatially developing, laminar two-fluid shear flows which are convectively unstable, and can naturally account for the growth of finite amplitude interfacial waves, along with changes to the interfacial topology. We demonstrate the accuracy of the IC-PSE against direct Navier–Stokes calculations for two-fluid mixing layers with density and viscosity stratification. The comparisons show that the IC-PSE can predict the dynamics of the instability waves and capture the formation of Kelvin–Helmholtz vortex rolls and large scale liquid structures, at an order of magnitude less computational cost than direct calculations. The role of surface tension in the IC-PSE formulation is shown to be valid for flows in which Re/We ? 1, and the method accurately predicts the formation and non-linear evolution of flow structures in this limit. This is demonstrated for spatially developing mixing layers which lead to vortex roll-up and ligaments, prior to droplet formation. The pinch-off process itself is a high surface tension phenomenon and in not considered herein. The method also accurately captures the effect of interfacial waves on the mean flow, and the topology changes during the non-linear evolution of the two-fluid structures. 相似文献
72.
We study existence of helical solitons in the vector modified Korteweg–de Vries (mKdV) equations, one of which is integrable, whereas another one is non-integrable. The latter one describes nonlinear waves in various physical systems, including plasma and chains of particles connected by elastic springs. By using the dynamical system methods such as the blow-up near singular points and the construction of invariant manifolds, we construct helical solitons by the efficient shooting method. The helical solitons arise as the result of co-dimension one bifurcation and exist along a curve in the velocity-frequency parameter plane. Examples of helical solitons are constructed numerically for the non-integrable equation and compared with exact solutions in the integrable vector mKdV equation. The stability of helical solitons with respect to small perturbations is confirmed by direct numerical simulations. 相似文献
73.
Hani Kbashi Sergey V. Sergeyev Chengbo Mou Amos Martinez Garcia Mohammed Al Araimi Aleksei Rozhin Stanislav Kolpakov Vladimir Kalashnikov 《Annalen der Physik》2018,530(5)
During the last two decades, revealing mechanisms of origin waves with anomalous amplitude (rogue waves) have been in the focus of researchers from different fields ranging from oceanography to laser physics. Mode‐locked lasers, as a test bed system, provide a unique opportunity to collect more data on rogue waves in the form of random pulses (soliton rain) and to clarify the mechanisms of rogue‐wave emergence caused by soliton–soliton and soliton–dispersive wave interactions. Here, for the first time, for an Er‐doped mode‐locked laser, a new type of vector rogue waves is demonstrated experimentally and theoretically, which is driven by desynchronization of the orthogonal linear states of polarization, so leading to output power oscillations in the form of anomalous spikes‐dips (bright‐dark rogue waves). The results can pave the way to unlocking the universal nature of the origin of rogue waves and thus can be of interest to the broad scientific community. 相似文献
74.
Ion-acoustic waves in plasma of warm ions and isothermal electrons using time-fractional KdV equation 下载免费PDF全文
Sayed A. El-Wakil Essam M. Abulwaf Emad K. El-Shewy Abeer A. Mahmoud 《中国物理 B》2011,20(4):40508-040508
The ion-acoustic solitary wave in collisionless unmagnetized plasma consisting of warm ions-fluid and isothermal electrons is studied using the time fractional KdV equation. The reductive perturbation method has been employed to derive the Korteweg-de Vries equation for small but finite amplitude ion-acoustic wave in warm plasma. The Lagrangian of the time fractional KdV equation is used in a similar form to the Lagrangian of the regular KdV equation with fractional derivative for the time differentiation. The variation of the functional of this Lagrangian leads to the Euler-Lagrange equation that gives the time fractional KdV equation. The variational-iteration method is used to solve the derived time fractional KdV equation. The calculations of the solution are carried out for different values of the time fractional order. These calculations show that the time fractional can be used to modulate the electrostatic potential wave instead of adding a higher order dissipation term to the KdV equation. The results of the present investigation may be applicable to some plasma environments,such as the ionosphere plasma. 相似文献
75.
76.
Nuri Murat Yağmurlu Ali Sercan Karakaş 《Numerical Methods for Partial Differential Equations》2020,36(5):1170-1183
In this article, the equal width (EW) equation is going to be solved numerically. In order to show the accuracy of the presented method, six test problems namely single solitary wave, interaction of two solitary waves, interaction of three solitary waves, Maxwellian initial condition, undular bore, and soliton collision are going to be solved. For the first test problem, since it has exact solution, the error norms L2 and L∞ are going to be calculated and compared with some of the earlier studies existing in the literature. Moreover, the three invariants I1, I2, and I3 of the given problems during the simulations are calculated and tabulated. Besides those comparisons, the relative changes of the invariants are given. Finally, a comparison of those error norms and invariants has clearly shown that the present approach obtained compatible and better results than most of the earlier works by using the same parameters. 相似文献
77.
The atomic-scale structural changes in an α-Fe2O3 (hematite) (0 0 0 1) surface induced by sulfidation and subsequent oxidation processes were studied by X-ray photoemission spectroscopy, LEED, and X-ray standing wave (XSW) measurements. Annealing the α-Fe2O3(0 0 0 1) with a H2S partial pressure of 1 × 10−7 Torr produced iron sulfides on the surface as the sulfur atoms reacted with the substrate Fe ions. The oxidation state of the substrate Fe changed from 3+ to 2+ as a result of the sulfidation. The XSW measured distance of the sulfur atomic-layer from the unrelaxed substrate oxygen layer was 3.16 Å. The sulfide phase consisted of three surface domains identified by LEED. Formation of the two-dimensional FeS2 phase with structural parameters consistent with an outermost layer of (1 1 1) pyrite has been proposed. Atomic oxygen exposure oxidized the surface sulfide to a sulfate () and regenerated the α-Fe2O3(0 0 0 1) substrate, which was indicated by a (1 × 1) LEED pattern and the re-oxidization of Fe to 3+. 相似文献
78.
The goal in this work is to investigate the effectiveness of time-frequency representations for analysing dispersive waves by comparing the performance of three different methods. In particular, the smoothed pseudo-Wigner distribution, the continuous wavelet transform and the Hilbert-Huang transform are compared and evaluated in terms of their ability to analyse dispersive elastic waves. The waves under consideration are transient flexural ones generated by an impact in a beam. In view of the results of the comparative study, the advantages and shortcomings of each method are presented and discussed. 相似文献
79.
80.
Closed series solution of electromagnetic scattering by an eccentric coated cylinder is achieved in matrix form. Diffracted field patterns are examined for an incident plane transverse magnetic (TM) wave. The solution is found by the classical separation of variables technique and the translational addition theorems. Wave transformation and orthogonality of the complex exponentials are employed to produce an infinite series. Numerical results are then shown by shortening the infinite series to a limited number of terms. Solutions are discussed for a dielectric or a metamaterial coating. 相似文献