Narrow Results

In this paper, we are planning to consider the fluctuations of two nonlinear equations which govern the dynamics of water waves named Camassa–Holm and KdV. We consider the total number of positive slopes produced when the fluctuations of the wave velocity u(x) of a surface wave of a fluid, for example water, is crossed by the level in the Camassa–Holm and KdV equations. Here, we just concentrate on the high Reynolds number limit and do the level crossing analysis where υ → 0. In our desired limit, the dissipative term becomes absent or very weak compared to the nonlinear term which is responsible for increasing the amplitude and creating wave steepening, which results in the appearance of shocks. Thus, our analysis works at the times before the appearance of shocks. Our aim in this paper is to show how the quantity, , counts the fluctuations of the wave velocity in the surface water wave fluctuations which are governed by the KdV and Camassa–Holm (CH) equations.

Self-phase modulation (SPM) induces a varying refractive index of the medium due to the optical Kerr effect. The optical waves propagation (OWP) in a medium with SPM occupied a remarkable area of research in the literature. A model equation to describe OWP in the absence of SPM was proposed very recently by Biswas–Arshed equation (BAE). This work is based on constructing the solutions that describe the waves which arise from soliton-periodic wave collisions. A variety of geometric optical wave structures are observed. Here, a transformation that allows to investigate the multi-geometric structures of OW’s result from soliton-periodic wave collisions is introduced. Chirped, conoidal, breathers, diamond and W-shaped optical waves are shown to propagate in the medium in the absence of SPM. The exact solutions of BAE are obtained by using the unified method, which was presented recently. We mention that the results found here, are completely new.

We analyze guided waves in the linear media separated nonlinear interface. The mathematical formulation of the model is a one-dimensional boundary value problem for the nonlinear Schrödinger equation. The Kerr type nonlinearity in the equation is taken into account only inside the waveguide. We show that the existence of nonlinear stationary waves of three types is possible in defined frequency ranges. We derive the frequency of obtained stationary states in explicit form and find the conditions of its existence. We show that it is possible to obtain the total wave transition through a plane defect. We determine the condition for realizing of such a resonance. We obtain the reflection and transition coefficients in the vicinity of the resonance. We establish that complete wave propagation with nonzero defect parameters can occur only when the nonlinear properties of the defect are taken into account.

Tidal turbine arrays have undergone extensive research to determine the optimal spacing for efficient performance and reduced wake generation. Small-scale laboratory tests are typically conducted to analyze wake structures prior to deployment. These tests often result in conditions of extreme blockage due to channel narrowing in comparison to turbine size. The primary objective of this study is to investigate flow behavior around turbines under blockage conditions and their performance close to the free surface, both in current-only and wave-and-current scenarios. The methodology employed a combination of blade element momentum theory and computational fluid dynamics (CFD) integrating a virtual blade model (VBM) code. The findings of this study indicate potential enhancements in tidal turbine array performance of up to 7% in lateral arrangements and 11% in streamwise arrangements under blockage conditions. The wake is significantly influenced by surface waves, which also contribute to increased downstream turbine performance.

We refute a physical model, recently proposed by Gunn, Allison and Abbott (GAA) [http://arxiv.org/pdf/1402.2709v2.pdf], to utilize electromagnetic waves for eavesdropping on the Kirchhoff-law–Johnson-noise (KLJN) secure key distribution. Their model, and its theoretical underpinnings, is found to be fundamentally flawed because their assumption of electromagnetic waves violates not only the wave equation but also the second law of thermodynamics, the principle of detailed balance, Boltzmann's energy equipartition theorem, and Planck's formula by implying infinitely strong blackbody radiation. We deduce the correct mathematical model of the GAA scheme, which is based on impedances at the quasi-static limit. Mathematical analysis and simulation results confirm our approach and prove that GAA's experimental interpretation is incorrect too.

Pulsar winds are the ideal environment for the study of non-linear electromagnetic waves. It is generally thought that a pulsar launches a striped wind, a magnetohydrodynamic entropy wave, where plasma sheets carried along with the flow separate regions of alternating magnetic field. But when the density drops below a critical value, or equivalently for distances from the pulsar greater than a critical radius, a strong superluminal wave can also propagate. In this contribution we discuss the conversion of the equatorial striped wind into a linearly polarized superluminal wave, and we argue that this mode is important for the conversion of Poynting flux to kinetic energy flux before the outflow reaches the termination shock.

Predicting trajectories of fluid parcels on the water surface perturbed by waves is a difficult mathematical and theoretical problem. It is even harder to model flows generated on the water surface due to complex three-dimensional wave fields, which commonly result from the modulation instability of planar waves. We have recently shown that quasi-standing, or Faraday, waves are capable of generating horizontal fluid motions on the water surface whose statistical properties are very close to those in two-dimensional turbulence. This occurs due to the generation of horizontal vortices. Here we show that progressing waves generated by a localized source are also capable of creating horizontal vortices. The interaction between such vortices can be controlled and used to create stationary surface flows of desired topology. These results offer new methods of surface flow generation, which allow engineering inward and outward surface jets, large-scale vortices and other complex flows. The new principles can be also be used to manipulate floaters on the water surface and to form well-controlled Lagrangian coherent structures on the surface. The resulting flows are localized in a narrow layer near the surface, whose thickness is less than one wavelength.