One-dimensional Wave Field Research Articles

A ventilating acoustic barrier for attenuating broadband diffuse sound

Ventilating acoustic barriers made of open metasurfaces have exceptional properties that can be used to simultaneously block sound while allowing passage of air. However, most of them have been small and designed to operate in a one-dimensional wave field with a normally incident plane wave. In this work, we present a full-sized acoustic barrier based on a light-weight metasurface with internal helical sound paths. It has high transmission losses at low frequencies, allows flow-through of air for ventilation, and works in a broadband diffuse field. The effectiveness of the design is confirmed by simulations and experiments in reverberant environment. The barriers are thin (about λ/11 of the lower onset frequency) and offer sound transmission losses consistently higher than 10 dB from 610 to 1120 Hz in a diffuse field while retaining a ventilation fraction of 20%. This design has good potential for applications requiring a combination of ventilation and soundproofing, such as in green buildings.

Super compact equation for water waves

Mathematicians and physicists have long been interested in the subject of water waves. The problems formulated in this subject can be considered fundamental, but many questions remain unanswered. For instance, a satisfactory analytic theory of such a common and important phenomenon as wave breaking has yet to be developed. Our knowledge of the formation of rogue waves is also fairly poor despite the many efforts devoted to this subject. One of the most important tasks of the theory of water waves is the construction of simplified mathematical models that are applicable to the description of these complex events under the assumption of weak nonlinearity. The Zakharov equation, as well as the nonlinear Schrödinger equation (NLSE) and the Dysthe equation (which are actually its simplifications), are among them. In this article, we derive a new modification of the Zakharov equation based on the assumption of unidirectionality (the assumption that all waves propagate in the same direction). To derive the new equation, we use the Hamiltonian form of the Euler equation for an ideal fluid and perform a very specific canonical transformation. This transformation is possible due to the ‘miraculous’ cancellation of the non-trivial four-wave resonant interaction in the one-dimensional wave field. The obtained equation is remarkably simple. We call the equation the ‘super compact water wave equation’. This equation includes a nonlinear wave term (à la NLSE) together with an advection term that can describe the initial stage of wave breaking. The NLSE and the Dysthe equations (DystheProc. R. Soc. Lond.A, vol. 369, 1979, pp. 105–114) can be easily derived from the super compact equation. This equation is also suitable for analytical studies as well as for numerical simulation. Moreover, this equation also allows one to derive a spatial version of the water wave equation that describes experiments in flumes and canals.

Collapse of the wave field in a one-dimensional system of weakly coupled light guides

The analytical and numerical study of the radiation self-action in a system of coupled light guides is fulfilled on the basis of the discrete nonlinear Schr\odinger equation (DNSE). We develop a variational method for qualitative study of DNSE and classify self-action modes. We show that the diffraction of narrow (in grating scale) wave beams weakens in discrete media and, consequently, the ``collapse'' of the one-dimensional wave field with power exceeding the critical value occurs. This results in the ability to self-channel radiation in the central fiber. Qualitative analytical results were confirmed by numerical simulation of DNSE, which also shows the stability of the collapse mode.

Gaussian Convergence for Stochastic Acceleration of Particles in the Dense Spectrum Limit

The velocity of a passive particle in a one-dimensional wave field is shown to converge in law to a Wiener process, in the limit of a dense wave spectrum with independent complex amplitudes, where the random phases distribution is invariant modulo π/2 and the power spectrum expectation is uniform. The proof provides a full probabilistic foundation to the quasilinear approximation in this limit. The result extends to an arbitrary number of particles, founding the use of the ensemble picture for their behaviour in a single realization of the stochastic wave field.

Bragg scattering of surface waves over permeable rippled beds with current

In this study we develop a time-dependent wave equation for waves propagating with a current over permeable rippled beds. As well known, Bragg resonance occurs when the incident wavelength is twice the wavelength of the bottom ripple undulation and no current is present. However, the current in the near-shore region changes the resonance condition. A one-dimensional wave field is solved numerically based on the derived equation to study the effect of current on the Bragg resonance condition. Nonlinear wave–wave resonant interaction theory provides an explanation of the effect on Bragg resonance. Numerical results also indicate that the maximum reflection coefficient increases as current velocity increases from a negative to a positive value. Furthermore, the velocity of the current affects the position of the maximum reflection coefficient.

Reflection of one-dimensional wave field from a half space with conductivity fluctuations

Reflection of one-dimensional wave field from a half space with conductivity fluctuations