Large-amplitude Waves Research Articles

On the shape and size of granular roll waves

This paper describes, from a theoretical point of view, the appearance and characteristics of granular roll waves in chute flow, and the maximal size these waves can attain for a given influx of material into the system. Granular roll waves are steady travelling wave solutions of the generalized Saint-Venant equations for flowing granular matter, appearing when the Froude number $Fr$ of the incoming flow exceeds a critical value, $Fr>Fr_{cr}$ . We focus upon the phase space of the corresponding dynamical system, where the roll waves take the form of a stable limit cycle around an unstable fixed point; this limit cycle gives precise information on the size and periodicity of the roll wave. It is found that, for any given value of $Fr$ , the limit cycle cannot become arbitrarily large because it is constrained by a homoclinic loop in phase space. Roll waves of larger amplitude can be generated by increasing the Froude number $Fr$ .

Study of hydromagnetic solitary waves in the Earth's inner magnetosphere via the Adlam-Allen model

Solitary hydromagnetic waves propagating perpendicular to the ambient magnetic field are nonlinear structures that were first analysed by Adlam and Allen in 1958. Although they were first studied for electron-ion plasmas in the controlled thermonuclear reaction experiment, they can also occur in other plasma media. Satellite observations have confirmed that these large-amplitude hydromagnetic waves are ubiquitous in many space plasma environments. In this paper, using Sagdeev pseudopotential technique, we study the properties of large amplitude hydromagnetic waves using the physical model employed by Adlam-Allen. It is confirmed that the waves exist with Mach numbers within the range from 1 to 2. Applications to observations of di-polarization fronts (DFs) in the Earth's inner magnetosphere are discussed.

On finite amplitude solitary waves—A review and new experimental data

The existing analytical solutions for finite amplitude solitary waves, including the perturbation solutions, based on either the nonlinearity parameter, α=H/h, or the dispersion parameter, ε=k2h2, and the closed form solutions, are reviewed. The convergence characteristics of the perturbation solutions are discussed, showing that the perturbation solutions for the velocity field diverge for large wave amplitude. The relationships between three existing closed form solutions are discussed. The analytical solutions are then compared with exact numerical solutions. The agreement is generally good for the free surface profiles, but not for the velocity field. One of the closed form solutions [Clamond, D. and Fructus, D., “Accurate simple approximation for the solitary wave,” C. R. Mec. 331, 727 (2003)] is in almost perfect agreement with the exact numerical solutions for both the free surface profiles and the velocity fields. New laboratory experiments, measuring both free surface profile and velocity field over a wide range of α values (up to 0.6) are then presented. High speed particle image velocimetry is used to measure the velocity field in the entire water column. Detailed comparisons among the experimental data, analytical theories, and numerical solutions show that for relatively small amplitude solitary waves, say, α≤0.2, all theories and numerical results agree very well with the experimental data. However, when α≥0.3 only [Clamond, D. and Fructus, D., “Accurate simple approximation for the solitary wave,” C. R. Mec. 331, 727 (2003)]'s solution and the numerical agree with the experimental data.

Beam-driven whistler mode nonlinear saturation and turbulence in the magnetopause

This work presents a model to understand the generation of whistler turbulence in the magnetic reconnection region of magnetopause by the energetic electron beams (generated by magnetic reconnection process) as observed by magnetospheric multiscale mission [Zhao et al., J. Geophys. Res.: Space Phys. 126, e2020JA028525 (2021)]. In this model, the magnetic reconnection process has been replaced by the energetic electron beam source. Hence, the beam-driven whistler-mode dynamical equation has been set up by anticipating that it will grow from noise level due to beam energy and then will attain large amplitude such that nonlinear effects due to ponderomotive force will lead to the localization of whistler waves, and finally, this will lead to the turbulent state. For this, a non-linear two-dimensional fluid model is developed in which nonlinear interaction between high-frequency whistler wave and low-frequency ion acoustic wave (IAW) is pertinent to the magnetopause region. Due to large-amplitude whistler waves, ponderomotive force components emerge, which are included in IAW's nonlinear dynamics. The system of the dimensionless equations consists of the dynamics of whistler wave and IAW, and this has been solved by the numerical method. The results of the simulation show that the whistler's temporal evolution results in localized structures that eventually lead to turbulence. The relevance of the present investigation to the recent observations has also been pointed out.

Peristaltic flow of a viscous fluid in a curved duct with a rectangular cross section

Most flow systems in the human body are duct shaped, such as the pancreatic, bile, and gallbladder ducts. Such flow systems are also common in industrial applications like HVAC systems. This study presents a novel mathematical model to analyze the peristaltic motion of a viscous fluid in a three-dimensional curved duct with a rectangular cross section; specifically, such geometries are used more in industrial and medical applications. In the current investigation, the constraints of lubrication theory are considered, and a perturbation technique is used to solve the Navier–Stokes partial differential equations. The major focus of this work is on the aspect ratio of the duct and curvature of the flow axis. Curvilinear coordinates of cylindrical systems are considered for the derivations because of the curved geometry; homogeneous no-slip boundary conditions are proposed at the flexible surfaces, and the expression for pressure increase is found numerically using the NIntegrate tool of computing software Mathematica. A comprehensive graphical discussion is presented to determine the effects of all salient physical factors related to the problem. The results show that the large curvature and aspect ratio reduce the fluid speed gradually but that the flow rate promotes fluid velocity. The pumping rate is a decreasing function of the curvature and aspect ratio; however, reverse pumping can occur for large curvature values. Streamline evaluations suggest that large wave amplitudes increase the number of circulating boluses.

Thermal-hydraulic characteristics analysis in porous-wall corrugated microchannel with microencapsulated phase change slurry

To enlarge surface area and convection between the coolant and wall, the bottom and upper corrugated surface, as well as porous layer on sidewall are set in wavy flowing channels with microencapsulated phase change material (MPCM) slurry as coolant will lead to more heat to be dissipated to outside. The performance evaluation factor (PEF) is defined to evaluate the thermal-hydraulic performance of MCSH. The effects of corrugated surface and porous layer, as well as MPCM concentration and inflowing velocity on heat transfer are numerically analyzed. The simulation results agree with experimental data. Compared to the straight channel with water as coolant and no porous layer, the 37.2% and 61.5% PEF rise can be obtained respectively in the straight or corrugated channel with porous layer on sidewall and MPCM slurry as coolant. The lower thermal resistance occurs in the mode with larger wave amplitude and smaller wavelength, and the higher PEF happens in the cases with smaller wave amplitude and wavelength. The optimized porous layer thickness of 0.06 mm can be obtained. The inflowing velocity needs to be above a certain value (e.g. uin = 1 m/s), and the optimized MPCM concentration (5% or 10%) in MPCM slurry relates to wave amplitude closely.

Passive Control of Supersonic Shear Layer in Rectangular Multistream Jet

Supersonic multistream engines with single-expansion ramp nozzles use splitter plates to separate the core from bypass streams. The resulting shear-layer instability imposes unsteady loading on proximal surfaces and generates acoustic tones. The present work develops a passive control strategy to alleviate these effects. The thick splitter plate subcomponent of the full configuration is isolated, and Mach 1.6 and sonic boundary layers are allowed to develop on either side to form the shear layer. Instability mechanisms and optimal forcing-response characteristics are identified from linear analysis of time-averaged large-eddy simulations (LESs). These results are then used to guide splitter plate trailing-edge modifications with different wave numbers and amplitudes to interfere with the internal forcing mechanism. LESs of the altered configurations at small wave numbers reveal a diamond-grid-like pattern of cells and dislocations, similar to those observed in low-speed active control studies. Modal decomposition displays an increase in rank behavior, with the dominant mode in good agreement with linear predictions. At large wave numbers and amplitudes, where nonlinear effects are stronger, LESs show that control introduces streamwise vorticity into the wake, reduces coherent structure size (streamwise correlation length) and inhibits the tonal content. These effects are confirmed in companion experiments.

Analytical results for phase bunching in the pendulum model of wave-particle interactions

Radiation belt electrons are strongly affected by resonant interactions with cyclotron-resonant waves. In the case of a particle passing through resonance with a single, coherent wave, a Hamiltonian formulation is advantageous. With certain approximations, the Hamiltonian has the same form as that for a plane pendulum, leading to estimates of the change at resonance of the first adiabatic invariant I, energy, and pitch angle. In the case of large wave amplitude (relative to the spatial variation of the background magnetic field), the resonant change in I and its conjugate phase angle ξ are not diffusive but determined by nonlinear dynamics. A general analytical treatment of slow separatrix crossing has long been available and can be used to give the changes in I associated with “phase bunching,” including the detailed dependence on ξ, in the nonlinear regime. Here we review this treatment, evaluate it numerically, and relate it to previous analytical results for nonlinear wave-particle interactions. “Positive phase bunching” can occur for some particles even in the pendulum Hamiltonian approximation, though the fraction of such particles may be exponentially small.

Three-dimensional imaging of waves and floes in the marginal ice zone during a cyclone

The marginal ice zone is the dynamic interface between the open ocean and consolidated inner pack ice. Surface gravity waves regulate marginal ice zone extent and properties, and, hence, atmosphere-ocean fluxes and ice advance/retreat. Over the past decade, seminal experimental campaigns have generated much needed measurements of wave evolution in the marginal ice zone, which, notwithstanding the prominent knowledge gaps that remain, are underpinning major advances in understanding the region’s role in the climate system. Here, we report three-dimensional imaging of waves from a moving vessel and simultaneous imaging of floe sizes, with the potential to enhance the marginal ice zone database substantially. The images give the direction–frequency wave spectrum, which we combine with concurrent measurements of wind speeds and reanalysis products to reveal the complex multi-component wind-plus-swell nature of a cyclone-driven wave field, and quantify evolution of large-amplitude waves in sea ice.

Jupiter's Low-Altitude Auroral Zones: Fields, Particles, Plasma Waves, and Density Depletions.

The Juno spacecraft's polar orbits have enabled direct sampling of Jupiter's low‐altitude auroral field lines. While various data sets have identified unique features over Jupiter's main aurora, they are yet to be analyzed altogether to determine how they can be reconciled and fit into the bigger picture of Jupiter's auroral generation mechanisms. Jupiter's main aurora has been classified into distinct “zones”, based on repeatable signatures found in energetic electron and proton spectra. We combine fields, particles, and plasma wave data sets to analyze Zone‐I and Zone‐II, which are suggested to carry upward and downward field‐aligned currents, respectively. We find Zone‐I to have well‐defined boundaries across all data sets. H+ and/or H3 + cyclotron waves are commonly observed in Zone‐I in the presence of energetic upward H+ beams and downward energetic electron beams. Zone‐II, on the other hand, does not have a clear poleward boundary with the polar cap, and its signatures are more sporadic. Large‐amplitude solitary waves, which are reminiscent of those ubiquitous in Earth's downward current region, are a key feature of Zone‐II. Alfvénic fluctuations are most prominent in the diffuse aurora and are repeatedly found to diminish in Zone‐I and Zone‐II, likely due to dissipation, at higher altitudes, to energize auroral electrons. Finally, we identify significant electron density depletions, by up to 2 orders of magnitude, in Zone‐I, and discuss their important implications for the development of parallel potentials, Alfvénic dissipation, and radio wave generation.

New Localized Structure for (2+1) Dimensional Boussinesq-Kadomtsev-Petviashvili Equation

In this work, we use a variable separation approach to construct some novel exact solutions of a (2+1)-dimensional Boussinesq-Kadomtsev-Petviashvili equation. Thanks to two variable-separated arbitrary functions, some new soliton excitations and localized structures are obtained. It is observed that large amplitude waves are generated in the process of interaction between two solitons.

Influence of a vertical baffle on suppressing sway motion response of a tank coupled with sloshing actions in waves

The present work is a direct extension of our previous work in Jiang and Bai (2020) where the sway motion response of a box section coupled with an internal sloshing flow was studied. In the present work, vertical baffles are equipped at the bottom of the internal tank, and the influence of the vertical baffles on suppressing the internal sloshing flow as well as the sway response of the system in waves is assessed. The IRF method and the CFD simulation are applied to consider the internal and external fluid flows, respectively. Numerical simulations show that the increased vertical baffle height can generate a more significant effect on suppressing the coupled sloshing action, where the sway motion amplitudes of the baffled sloshing tank tend to the empty tank results. Whether the internal sloshing flow breaks or not seems to play an important role in affecting the sway response of the tank. The vertical baffle can block the sloshing flow and generate a significant effect on the sway motion response when the sloshing flow is of the breaking pattern. For a specific relative vertical baffle height, the shallow filling depth or the large incident wave amplitude is more prone to generate the breaking sloshing flow, and hence better suppressing action can be obtained. As for the non-breaking sloshing flow motion, the vertical baffle is hard to generate the evident effect on the minimal and maximal sway motion amplitudes, but it can cause the variation of frequency range of the essential coupled sloshing action. Generally speaking, the vertical baffle is an effective method for suppressing the sway motion response of the sloshing tank in waves.

Predicting heat transfer and flow features of supercritical CO2 in printed circuit heat exchangers with novel wavy minichannels

Printed circuit heat exchangers (PCHEs) are unrivaled choices for heat exchange purposes in power cycles working with natural refrigerants such as carbon dioxide (CO2). Minichannels play a major role in heat transferring in these devices. They take up more than 95% of PCHEs volume; therefore, increasing the performance or compactness of PCHEs will be realized, provided that novel designs are adopted for the minichannels. In this study, the investigation of non-uniform wavy minichannels applying supercritical carbon dioxide (SCO2) as working fluid is carried out. To fulfill defined goals, a 3D conjugated model is developed to analyze the performance of novel geometries in both cooling and heating modes by considering the variations of SCO2's thermophysical properties. The results demonstrate that the proposed structures for the wavy minichannels create an upsurge in the heat transfer coefficient under the given operating conditions. It is explored that replacing the conventional wavy minichannel with the cases having short wavelengths at the upstream can increase the heat transfer enhancement factor from 36.1 to 51.1% in the cooling mode and from 40.8 to 56.5% in the heating mode. Furthermore, the larger the wave amplitudes at the upstream are, the more superiority it takes. Compared to all the proposed structures, the case with the largest wave amplitude and the smallest wavelength at the upstream attains the best overall performance. This structure of wavy minichannel can be utilized to manufacture highly efficient PCHEs with the capability of improving the overall performance index more than 1.5 times compared to the conventional wavy minichannel.

Experimental study on hydrodynamic characteristics of a new type floating breakwater with opening pass and wing structure

To attenuate long-period waves better, a new type of floating breakwater (FB) with an opening pass is proposed. When the waves act on the FB, the wave can spray upward along the radian opening and convert part of the kinetic energy of the incident wave into potential energy. This will lead to wave breaking, which improves the wave elimination efficiency. In addition, the new type of FB design with an arc-shaped wing structure under water improves the damping effect and induces wave slamming and breaking phenomena on the back wall. A series of experiments, including a traditional dual-box FB and five new type FB models with different outlet radii, were carried out to investigate and compare the hydrodynamic performance. The results show that, with the same weight and principal size, the transmission coefficient of the new type of FB was 8.2%–17.8% smaller than that of the traditional dual-box FB in long-period and large-amplitude waves. In addition, the new type has smaller mooring forces and heave responses. A smaller outlet radius of the opening pass can give rise to a higher water spraying phenomenon, but the outlet radius generally has a small effect on the hydrodynamic performance and the mooring forces.

Transparency of fast radio burst waves in magnetar magnetospheres

ABSTRACT At least some fast radio bursts (FRBs) are produced by magnetars. Even though mounting observational evidence points towards a magnetospheric origin of FRB emission, the question of the location for FRB generation continues to be debated. One argument suggested against the magnetospheric origin of bright FRBs is that the radio waves associated with an FRB may lose most of their energy before escaping the magnetosphere because the cross-section for e± to scatter large-amplitude electromagnetic waves in the presence of a strong magnetic field is much larger than the Thompson cross-section. We have investigated this suggestion and find that FRB radiation travelling through the open field line region of a magnetar’s magnetosphere does not suffer much loss due to two previously ignored factors. First, the plasma in the outer magnetosphere ($r \gtrsim 10^9$ cm), where the losses are potentially most severe, is likely to be flowing outwards at a high Lorentz factor γp ≥ 103. Secondly, the angle between the wave vector and the magnetic field vector, θB, in the outer magnetosphere is likely of the order of 0.1 radian or smaller due in part to the intense FRB pulse that tilts open magnetic field lines so that they get aligned with the pulse propagation direction. Both these effects reduce the interaction between the FRB pulse and the plasma substantially. We find that a bright FRB with an isotropic luminosity $L_{\rm frb} \gtrsim 10^{42} \, {\rm erg \ s^{-1}}$ can escape the magnetosphere unscathed for a large section of the γp − θB parameter space, and therefore conclude that the generation of FRBs in magnetar magnetosphere passes this test.

Observations of Whistler-mode Waves and Large-amplitude Electrostatic Waves Associated with a Dipolarization Front in the Bursty Bulk Flow

Plasma jets and jet fronts are common phenomena in planetary magnetospheres. They are usually associated with many plasma waves and can play a key role in the energy conversion, the excitation of wave emissions, particle acceleration, and the evolution of many astrophysical phenomena, which are major issues in the study of helio-terrestrial space physics. In this paper, we carefully investigated the properties of the whistler-mode wave and large-amplitude electrostatic wave in a plasma jet (bursty bulk flow (BBF)) using the Magnetospheric Multiscale mission data on the Earth's magnetosphere. At the leading part of the BBF, intense whistler-mode waves were observed inside the ion mirror-mode structures, which should be excited by the perpendicular temperature anisotropy of trapping electrons. A small-scale dipolarization front (DF) was then observed at the center of this BBF as a boundary between the leading and trailing parts of the BBF. Behind the DF, both an ion mirror-mode structure and whistler-mode waves disappear, while a large-amplitude electrostatic wave was detected and was associated with the cold ions at the trailing part of the BBF. The electrostatic wave is supposed to be generated by ion beam instability. These results will significantly improve the understanding of the kinetic process associated with the important boundary layer DF within plasma jets. The corresponding wave–particle interaction in space and the plasma environment can be further understood.

On the High Winds in the Tianshan Grand Canyon in Northwest China: General Features, Synoptic Conditions, and Mesoscale Structures

This work studies the characteristics of high winds in the Tianshan Grand Canyon (TGC), Northwest China by using surface wind observations at six automatic weather stations during 2017–2018. Three high wind indices are examined, namely, high wind hour (HWH), station high wind event (SHWE) and regional high wind event (RHWE). SHWE denotes persistent high winds of more than 3 h at an individual station while RHWE is defined for the southern TGC as a whole. High winds are mainly northwesterly/westerly, occurring predominantly in southern TGC. HWHs most often occur in spring and summer, while winter and spring HWHs possess the strongest intensity. The occurrence of HWHs exhibits an apparent diurnal variation, most frequent in the afternoon and evening while least from mid-night to early morning. SHWEs and RHWEs are prone to take place in spring, possessing relatively long lifetime and strong intensity. According to composite analysis of the 0.25° FNL reanalysis, favorable synoptic conditions are obtained for the persistent high winds in spring. Of great importance is the mid-tropospheric trough in the mid-high latitudes located to the north (i.e., upstream) of the TGC. The cold advection behind the trough cools and stabilizes the mid-lower troposphere, while the post-trough sinking motion causes a surface high that accelerates the low-level northwesterly wind. The synoptic thermal and dynamical forcing help set an upstream flow of moderate Froude number such that the mesoscale orographic flow traversing the TGC is in the nonlinear high-drag regime. Large-amplitude gravity waves are excited, with the isentropes descending abruptly over the lee slope which resembles internal hydraulic jump. Downslope windstorms are produced at the expense of flow potential energy as the subcritical upstream flow is transitioned to supercritical at the TGC peak. These findings have important implications on the formation and prediction of high winds in the TGC.

Equations of Motion Near Cyclotron Resonance

This work compares several versions of the equations of motion for a test particle encountering cyclotron resonance with a single, field-aligned whistler mode wave. The gyro-averaged Lorentz equation produces both widespread phase trapping (PT) and “positive phase bunching” of low pitch angle electrons by large amplitude waves. Approximations allow a Hamiltonian description to be reduced to a single pair of conjugate variables, which can account for PT as well as phase bunching at moderate pitch angle, and has recently been used to investigate this unexpected bahavior at low pitch angle. Here, numerical simulations using the Lorentz equation and several versions of Hamiltonian-based equations of motion are compared. Similar behavior at low pitch angle is found in each case.

Current-sheet Oscillations Caused by the Kelvin–Helmholtz Instability at the Loop Top of Solar Flares

Current sheets (CSs), long stretching structures of magnetic reconnection above solar flare loops, are usually observed to oscillate; their origins, however, are still puzzled at present. Based on a high-resolution 2.5D MHD simulation of magnetic reconnection, we explore the formation mechanism of CS oscillations. We find that large-amplitude transverse waves are excited by the Kelvin–Helmholtz instability at the highly turbulent cusp-shaped region. The perturbations propagate upward along the CS with a phase speed close to local Alfvén speed thus resulting in the CS oscillations we observe. Though the perturbations damp after propagating for a long distance, the CS oscillations are still detectable. In terms of detected CS oscillations, with a combination of differential emission measure techniques, we propose a new method for measuring the magnetic field strength of the CS and its distribution in height.

Giant nonlinear self-phase modulation of large-amplitude spin waves in microscopic YIG waveguides

Nonlinear self-phase modulation is a universal phenomenon responsible, for example, for the formation of propagating dynamic solitons. It has been reported for waves of different physical nature. However its direct experimental observation for spin waves has been challenging. Here we show that exceptionally strong phase modulation can be achieved for spin waves in microscopic waveguides fabricated from nanometer-thick films of magnetic insulator, which support propagation of spin waves with large amplitudes corresponding to angles of magnetization precession exceeding 10°. At these amplitudes, the nonstationary nonlinear dynamic response of the spin system causes an extreme broadening of the spectrum of spin-wave pulses resulting in a strong spatial variation of the spin-wave wavelength and a temporal variation of the spin-wave phase across the pulse. Our findings demonstrate great complexity of nonlinear wave processes in microscopic magnetic structures and importance of their understanding for technical applications of spin waves in integrated devices.