We discuss the early history of an important field of “sturm and drang” in modern theory of nonlinear waves. It is demonstrated how scientific demand resulted in independent and almost simultaneous ...publications by many different authors on modulation instability, a phenomenon resulting in a variety of nonlinear processes such as envelope solitons, envelope shocks, freak waves, etc. Examples from water wave hydrodynamics, electrodynamics, nonlinear optics, and convection theory are given.
We give an outline of selected theoretical and experimental studies associated with the periodaverage action of an oscillating acoustic field (acoustic radiation force) on the medium and ...microparticles. The main attention is paid to two problems related to biomedical research. One is the generation of shear waves by ultrasonic beams in weakly compressible (rubber-like) media, particularly in soft biological tissues. The other is the dynamics of microparticles in acoustic resonators. Some other aspects of the problem, such as bubble dynamics and acoustic levitation, are briefly mentioned. Elements of the history of early studies are also included.
We report experimental data and theoretical analysis of Coulomb drag between two closely positioned graphene monolayers in a weak magnetic field. Close enough to the neutrality point, the coexistence ...of electrons and holes in each layer leads to a dramatic increase of the drag resistivity. Away from charge neutrality, we observe nonzero Hall drag. The observed phenomena are explained by decoupling of electric and quasiparticle currents which are orthogonal at charge neutrality. The sign of magnetodrag depends on the energy relaxation rate and geometry of the sample.
An approximate analytical description of the nonstationary evolution of cylindrical nonlinear solitary waves with a complex structure is given. A modified Gardner equation with a boundary condition ...in the form of a “wide” soliton close to the limiting one is analyzed. The analysis shows a qualitative difference in the behavior of converging and diverging waves, as well as a difference from the quasi-stationary dynamics of cylindrical solitons.
The objective of this paper is to study the dynamics of small-scale turbulence near a pycnocline, both in the free regime and under the action of an internal gravity wave (IW) propagating along a ...pycnocline, using direct numerical simulation (DNS). Turbulence is initially induced in a horizontal layer at some distance above the pycnocline. The velocity and density fields of IWs propagating in the pycnocline are also prescribed as an initial condition. The IW wavelength is considered to be larger by the order of magnitude as compared to the initial turbulence integral length scale. Stratification in the pycnocline is considered to be sufficiently strong so that the effects of turbulent mixing remain negligible. The dynamics of turbulence is studied both with and without an initially induced IW. The DNS results show that, in the absence of an IW, turbulence decays, but its decay rate is reduced in the vicinity of the pycnocline, where stratification effects are significant. In this case, at sufficiently late times, most of the turbulent energy is located in a layer close to the pycnocline center. Here, turbulent eddies are collapsed in the vertical direction and acquire the "pancake" shape. IW modifies turbulence dynamics, in that the turbulence kinetic energy (TKE) is significantly enhanced as compared to the TKE in the absence of IW. As in the case without IW, most of the turbulent energy is localized in the vicinity of the pycnocline center. Here, the TKE spectrum is considerably enhanced in the entire wave-number range as compared to the TKE spectrum in the absence of IW.
Nonlinear internal solitary waves observed in laboratory experiments are discussed from the standpoint of their relation to different soliton theories, from the classical integrable models such as ...the Korteweg-de Vries, Gardner, Benjamin-Ono, and Joseph-Kubota-Ko-Dobbs equations and their modifications, through the nonintegrable models describing higher-order nonlinear effects, viscosity, rotation, and cylindrical spreading, to the strongly nonlinear models. First, these theoretical models are briefly described and, then, laboratory data and their comparison with the theory are presented.
Interaction of a soliton with long background waves is studied within the framework of rotation modified Korteweg–de Vries (rKdV) equation. Using the asymptotic method for solitons propagating in the ...field of a long background wave we derive a set of ODEs describing soliton amplitude and phase with respect to the background wave. The shape of the background wave may range from a sinusoid to the limiting profile representing a periodic sequence of parabolic arcs. We analyse energy exchange between a soliton and the long wave taking radiation losses into account. It is shown that the losses can be compensated by energy pumping from the long wave and, as the result, a stationary soliton can exist, unlike the case when there is no variable background. A more complex case when a free long wave attenuates due to the energy consumption by a soliton is also considered. Some of the analytical results are compared with the results of direct numerical calculations within the framework of the rKdV equation.
•Interaction of a KdV soliton with a long wave is studied in a rotating ocean.•Long background waves are sinusoidal wave and periodic sequence of parabolic arcs.•The model dynamical system is derived and studied analytically and numerically.•Solitons riding on long wave can propagate on long distances in a rotating ocean.
This paper presents the results of modeling the interaction between internal waves (IWs) and turbulence using direct numerical simulation (DNS). Turbulence is excited and supported by a random ...forcing localized in a vertical layer separated from the pycnocline. The main attention is paid to the internal wave damping due to turbulence and comparison of the results with those obtained theoretically by using the semi-empirical approach. It is shown that the IW damping rate predicted by the theory agrees well with the DNS results when turbulence is sufficiently strong to be only weakly perturbed by the internal wave; however, the theory overestimates the damping rate of IWs for a weaker turbulence. The DNS parameters are matched to the parameters of the laboratory experiment, and an extrapolation to the oceanic scales is also provided.
This paper demonstrates the observation of what appears to be a partially developed solitary internal wave group using an airborne lidar over the Gulf of Alaska. The probable generation mechanism is ...the interaction of the tide with the continental shelf 130 km away. Detection by lidar was possible because of a planktonic layer associated with a shallow pycnocline.
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