Wave Motion最新文献

By means of the Hirota’s bilinear method and special multi-linear variable separation ansatz, new exact solutions with low dimensional arbitrary functions of some (2+1)-dimensional nonlinear evolution equations are constructed. That is, we propose a unified method for solving the mNNV-type equations and the Burger-type equations. The key factor to the success of this method is that we have constructed some simplified Hirota’s bilinear calculation formulas in the form of variable separation of arbitrary order. Appropriate multi-valued functions are used to construct coherent structures such as the bell-type, peak-type and loop-type folding waves.

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.

The interconnection of time and frequency domains for capillary gravity wave motion in the presence of current is discussed in this article. The general time-dependent problem is solved using Green’s function technique, and the asymptotic solution is derived using the method of stationary phase for large time and space. Also, the frequency domain solution is derived as a special case using the Cauchy Residue theorem. Different types of wave resonances like Trapping, Blocking and Bragg resonances are discussed. The existence of the trapped mode below the cutoff frequency is justified theoretically, and numerical results are obtained using the multipole expansion method. The blocking and Bragg resonances are analyzed above the cutoff frequency. It is found that in the presence of current, when the ripple wavenumber of the bottom undulation equals twice the cosine angle of incidence of wave times the wavenumber of the wave, Bragg resonance occurs. It is found that three propagating modes exist in the case of wave blocking, and the trapped modes exist only for the first propagating mode. Furthermore, because of the negative group velocity inside the blocking zone, the Bragg reflection increases while decreasing outside. The effect of current on the wave energy propagation in the form of group velocity is analyzed and the same is verified in the case of time-dependent problem.

The purpose of this work is to propose a new composite scheme based on differential quadrature method (DQM) and modified cubic unified and extended trigonometric B-spline (CUETB-spline) functions to numerically approximate one-dimensional (1D) and two-dimensional (2D) Sine-Gordon Eqs. (SGEs). These functions are modified and then applied in DQM to determine the weighting coefficients (WCs) of spatial derivatives. Using the WCs in SGEs, we obtain systems of ordinary differential equations (ODEs) which is resolved by the five-stage and order four strong stability-preserving time-stepping Runge–Kutta (SSP-RK_5,4) scheme. This method's precision and consistency are validated through numerical approximations of the one-and two-dimensional problems, showing that the projected method outcomes are more accurate than existing ones as well as an incomparable agreement with the exact solutions is found. Besides, the rate of convergence (ROC) is performed numerically, which shows that the method is second-order convergent with respect to the space variable. The proposed method is straightforward and can effectively handle diverse problems. Dev-C++ 6.3 version is used for all calculations while Figs. are drawn by MATLAB 2015b.