Coalescence Of Waves Research Articles

The Riemann problem for two-layer shallow water equations with bottom topography

Abstract In this article, we propose a model describing laminar shallow water flows with two velocities to handle an uneven bottom. The model is established by taking the different velocities into account. The source terms generated from the bottom topography prevent us from solving the Riemann problem directly. We first derive the elementary waves including the stationary wave where the global entropy condition is used to ensure uniqueness. Then, we analyze the resonance phenomenon and coalescence of waves by classifying the initial data into different regions. Finally, the Riemann problem is resolved explicitly on a case-by-case basis.

NASA unveils a supersonic plane with a quiet boom

A simple concept, a sophisticated process: Reshape contours to prevent coalescence of shock waves.

Study on the factors influencing the interaction and coalescence of shock waves from multiple explosion sources in free field

Study on the factors influencing the interaction and coalescence of shock waves from multiple explosion sources in free field

Unsteady mechanisms in shock wave and boundary layer interactions over a forward-facing step

The flow over a forward-facing step (FFS) at $Ma_\infty =1.7$ and $Re_{\delta _0}=1.3718\times 10^{4}$ is investigated by well-resolved large-eddy simulation. To investigate effects of upstream flow structures and turbulence on the low-frequency dynamics of the shock wave/boundary layer interaction (SWBLI), two cases are considered: one with a laminar inflow and one with a turbulent inflow. The laminar inflow case shows signs of a rapid transition to turbulence upstream of the step, as inferred from the streamwise variation of $\langle C_f \rangle$ and the evolution of the coherent vortical structures. Nevertheless, the separation length is more than twice as large for the laminar inflow case, and the coalescence of compression waves into a separation shock is observed only for the fully turbulent inflow case. The dynamics at low and medium frequencies is characterized by a spectral analysis, where the lower frequency range is related to the unsteady separation region, and the intermediate one is associated with the shedding of shear layer vortices. For the turbulent inflow case, we furthermore use a three-dimensional dynamic mode decomposition to analyse the individual contributions of selected modes to the unsteadiness of the SWBLI. The separation shock and Görtler-like vortices, which are induced by the centrifugal forces in the separation region, are strongly correlated with the low-frequency unsteadiness in the current FFS case. Similarly as observed previously for the backward-facing steps, we observe a slightly higher non-dimensional frequency (based on the separation length) of the low-frequency mode than for SWBLI in flat plate and ramp configurations.

An alternative form of the fundamental plasma emission through the coalescence of Z-mode waves with whistlers

Plasma emission (PE), i.e., electromagnetic radiation at the plasma frequency and its second harmonic, is a general process occurring in both astrophysical and laboratory plasmas. The prevailing theory presents a multi-stage process attributed to the resonant coupling of beam-excited Langmuir waves with ion-acoustic waves. Here, we examine another possibility of the fundamental PE induced by the resonant coupling of Z-mode and whistler (W) waves. Earlier studies have been controversial in the plausibility and significance of such process in plasmas. In this study, we show that the matching condition of three-wave resonant interaction (Z + W → O) can be satisfied over a wide regime of parameters based on the magnetoionic theory, demonstrate the occurrence of such process, and further evaluate the rate of energy conversion from the pumped Z or W mode to the fundamental O mode with particle-in-cell simulations of wave pumping. The study presents an alternative form of the fundamental PE, which could possibly play a role in various astrophysical and laboratory scenarios with both Z and W modes readily excited through the electron cyclotron maser instability.

Development and interaction of disturbance waves in downward annular gas-liquid flow

The behavior of the disturbance waves is studied in downward adiabatic air-water annular flow in a vertical pipe with an inner diameter of 11.7 mm. The range of liquid wetting densities is 2.5–4.6 cm2/s and the range of superficial gas velocities is 22–57 m/s. The paper is focused on the downstream evolution of the main properties of individual disturbance waves at the stage of flow development along with the process of coalescence of disturbance waves. Brightness-based laser-induced fluorescence technique enabled us to obtain spatiotemporal matrices of the local instantaneous thickness of liquid film along one longitudinal section of the pipe with a length of 400 mm. Dependencies of the main characteristics of the flow on the downstream distance are analyzed. Local shear stress, base film thickness, and longitudinal size of the disturbance waves are stabilized at the distance of 150–200 mm below the inlet. Disturbance wave velocity increases strongly up to this point; further downstream, the acceleration is reduced significantly. Disturbance wave amplitude grows approximately as the square root of distance within the whole region of interrogation. Entrained fraction grows linearly within this region. Disturbance wave frequency decreases exponentially due to the coalescence. It is found that an average disturbance wave surviving through the development stage absorbs two other waves. Individual acts of coalescence of disturbance waves are analyzed quantitatively to investigate their contribution to the change of disturbance wave properties. On average, when a disturbance wave absorbs another one, its speed increases by 2%, its amplitude – by 5–6% and its longitudinal size remains the same. Thus, the disturbance wave properties change downstream mainly due to their individual evolution, not due to coalescence.

On the influence of Langmuir wave spectra on the spectra of electromagnetic waves generated in solar plasma with double plasma frequency

ABSTRACT In this paper, we consider the spectral dependences of transverse electromagnetic waves generated in solar plasma at the coalescence of Langmuir waves. It is shown that different spectra of Langmuir waves lead to characteristic types of transversal electromagnetic wave spectra, what makes it possible to diagnose the features of the spectra of Langmuir waves generated in solar plasma.

Influence of the Angular Distribution of Langmuir Waves on the Directivity of Radio Emission at Double Plasma Frequency

The directivity of transverse electromagnetic waves generated in a plasma at a double plasma frequency during the coalescence of plasma waves is calculated for various angular distributions of these waves. It is shown that the directivity of the generated electromagnetic waves is determined by the angular distribution of the spectral energy density of the Langmuir waves and is practically independent of the turbulence spectrum. The case of axial symmetry of emitting area is considered. If the angular distribution of Langmuir waves is proportional to cosδ ϑ, where ϑ is the angle between the direction of the wave vector of the Langmuir wave and the axis of the symmetry of the emitting region, the maximum of the generated transverse waves corresponds to viewing angles of α = 30°–45°, where the viewing angle is the angle between the line of sight and the axis of the emitting-area symmetry. In this case, the ratio of the maximum intensity of the generated radiation to the minimum can reach 3. If the angular distribution of turbulence is proportional to sinδ ϑ, then the radio-emission maximum corresponds to viewing angles of α = 60°–120°. This anisotropy of the solar plasma radiation can be measured with radio observations, which will make it possible to draw a conclusion about the nature and source of Langmuir turbulence in the solar plasma.

Influence of cellophane diaphragm rupture processes on the shock wave formation in a shock tube

Diaphragm opening processes with a finite time affect the generated shock waves and shock tube flows. This effect is dominant in short and low-pressure shock tubes. In this research, a high-speed visualization of the opening process of a cellophane diaphragm, which is a suitable material for operation in a low-pressure shock tube, is conducted. The self-shaping opening morphology of cellophane diaphragms is observed at the initial stage with an approximate crack propagation speed of 807 m/s, which is greater than the speed of sound of the test gas. The initial opening motion of the petals, which are formed by cracks, is successfully modeled by the rotational equation of motion. Through analysis of the generation and coalescence of compression waves, whose characteristic velocities are calculated from the measured pressure histories, the shock formation distance is reasonably estimated. From the visualized diaphragm opening processes and analysis of coalescence of compression waves, we revealed that the initial stage of the diaphragm opening process plays a dominant role in shock wave formation rather than the entire process.

Slug generation processes in co-current turbulent-gas/laminar-liquid flows in horizontal channels

We theoretically and computationally investigate the physical processes of slug-flow development in concurrent two-phase turbulent-gas/laminar-liquid flows in horizontal channels. The objective is to understand the fundamental mechanisms governing the initial growth and subsequent nonlinear evolution of interfacial waves, starting from a smooth stratified flow of two fluids with disparity in density and viscosity and ultimately leading to the formation of intermittent slug flow. We numerically simulate the entire slug development by means of a fully coupled immersed flow (FCIF) solver that couples the two disparate flow dynamics through an immersed boundary (IB) method. From the analysis of spatial/temporal interface evolution, we find that slugs develop through three major cascading processes: (I) stratified-to-wavy transition; (II) development and coalescence of long solitary waves; and (III) rapid channel bridging leading to slugging. In Process I, relatively short interfacial waves form on the smooth interface, whose growth is governed by the Orr–Sommerfeld instability. In Process II, interfacial waves evolve into long solitary waves through multiple resonant and near-resonant wave–wave interactions. From instability analysis of periodic solitary waves, we show that these waves are unstable to their subharmonic disturbances and grow in amplitude and primary wavelength through wave coalescence. The interfacial forcing from the turbulent gas–laminar liquid interactions significantly precipitates the growth of instability of solitary waves and enhances coalescence of solitary waves. In Process III, we show by an asymptotic analysis that interfacial waves achieve multiple-exponential growth right before bridging the channel, consistent with observations in existing experiments. The present study provides important insights for effective modelling of slug-flow dynamics and the prediction of slug frequency and length, important for design and operation of (heavy-oil/gas) pipelines and production facilities.

Analysis of the Riemann Problem for a Shallow Water Model with Two Velocities

Some shallow water type models describing the vertical profile of the horizontal velocity with several degrees of freedom have been recently proposed. The question addressed in the current work is the hyperbolicity of a shallow water model with two velocities. The model is written in a nonconservative form and the analysis of its eigenstructure shows the possibility that two eigenvalues coincide. A definition of the nonconservative product is given which enables us to analyse the resonance and coalescence of waves. Eventually, we prove the well-posedness of the two dimensional Riemann problem with initial condition constant by half-plane.

Generation of parallel and quasi‐perpendicular EMIC waves and mirror waves by fast magnetosonic shocks in the solar wind

AbstractThis paper presents a simulation study on the generation of electromagnetic ion cyclotron (EMIC) waves and mirror waves associated with fast magnetosonic shocks in the solar wind or the bow shock ahead of the magnetosphere. Strong fast magnetosonic shocks are often observed in these regions. In the shock downstream region, hydrogen ions (H+) and helium ions (He++) are strongly heated to high ion beta and large temperature anisotropy. The helium ions have a bunch distribution in the perpendicular velocity phase space in the immediate downstream region. These conditions can lead to generation of strong EMIC waves and mirror waves, which are often identified in satellite observations. In the simulations with a background magnetic field being in the simulation plane, the dominant EMIC waves are left‐handed polarized and propagate parallel to the background field. The nearly perpendicular (~85°) EMIC waves of right‐handed polarization excited at large wave numbers (kVA1/ΩH1 ≈ 3) show weak but nonnegligible wave energy. The effect of minor helium ions on wave excitation is found to be small. Mirror waves grow to large amplitudes when both the downstream ion beta and temperature anisotropy are high. Various wave modes are identified by ω − k dispersion analysis. For the cases with a background magnetic field making a large angle with the simulation plane, the mirror waves dominate, and nonlinear coalescence of mirror waves is clearly observed downstream.

Right‐hand polarized 4fce auroral roar emissions: 1. Observations

AbstractA receiving system installed at Sondrestrom, Greenland, was used to monitor all detectable auroral radio emissions at the fourth harmonic of the electron cyclotron frequency (called 4fce roar emissions) between May 2015 and March 2016. Of 88 events detected, 86 occurred during daylit conditions and were left‐hand polarized. Two occurred during darkness conditions and were right‐hand polarized. The left‐hand and right‐hand polarized events had entirely different frequency distributions. One of the right‐hand polarized 4fce emissions occurred at the same time as and at exactly twice the frequency of a second harmonic emission (2fce roar). The occurrence rate of 4fce emissions during premidnight hours under daylit conditions at Sondrestrom is 5%, comparable to previously reported occurrence rates of 2fce roar in darkness conditions at optimum latitudes of occurrence, but the occurrence rate of 4fce emissions during dark conditions is much lower, suggesting that if the right‐hand polarized events arise from coalescence of 2fce waves, only for a small fraction of nighttime 2fce roar emissions does such a process yield 4fce emissions detectable at ground level.

Vector rogue waves in the mixed coupled nonlinear Schrödinger equations

In this paper, via the generalized Darboux transformation we derive the reduced and non-reduced vector rogue wave solutions of the focusing-defocusing mixed coupled nonlinear Schrodinger equations. The dynamics of reduced vector rogue waves is the same as that for the known scalar ones. The non-reduced solutions can exhibit both the one-peak-two-valleys structure with one peak and two valleys lying in a straight line, and the two-peaks-two-valleys structure with two peaks and two valleys located at the four vertices of a parallelogram. We also find that the amplitude of the non-reduced vector rogue wave is not three times as that of the exciting plane wave, and that the coalescence of multiple fundamental rogue waves does not generate larger-amplitude rogue waves. In addition, we discuss the relationship of the free parameters in the solutions with the positions and relative distances of rogue waves in the xt-plane.

Numerical Investigation on Roll-Wave Properties: Wave–Wave Interactions, Generality, and Spectrum

Modeling natural roll waves in unstable open channel flows where Froude number F>2 has not been well understood. In this investigation, some evolution properties of natural roll waves are numerically disclosed, with the intention to advance the development of modeling unstable open channel flows. To simulate natural roll waves, the diffusive Saint-Venant equations are solved using a high-resolution scheme based on the finite-volume formulation. The numerical solutions of detailed wave–wave interaction processes, including wave overtaking, absorption, and spawning, are displayed. Wave overtaking and absorption result in the coalescence of multiple waves; wave spawning results in the birth of new waves. The spatial evolution of roll waves always undergoes initial, transition, and final phases. The three phases constitute a generality for roll-wave evolutions. Finally, the spectral analysis along channel reveals that both the wave period and nonperiodicity increase from upstream to downstream channel locations.

Reduction of the sonic boom level by heating the flow in front of the body

A numerical study of the possibility of reducing the sonic boom level in the case of local heat release to a supersonic gas flow at Mach number equal to 2 ahead of a body is described. The computations are performed for a spherical heat supply zone located on the flight trajectory ahead of the tip of an axisymmetric thin body. For the numerical study the combined method of “phantom bodies” is used. Different magnitudes of heat supply to the incoming flow are tested. These calculations are performed with allowance for interaction of shock waves emanating from the heated gas region and from the body in the far field. The computational results show that the local heat supply to a supersonic gas flow ahead of a body can reduce the sonic boom level by more than 20 %. The reduction of the sonic boom level is ensured by changing the free-stream parameters ahead of the body and by preventing the coalescence of shock waves from the heat supply zone and from the body in the far field.

Numerical Study of Solid-Rocket Motor Ignition Overpressure Wave Including Infrared Radiation

The ignition overpressure wave generated during the pressure build-up of a solid-rocket motor is numerically investigated in this study. Numerical simulations are compared to the LP10 experiments, consisting of the horizontal firing of a scaled-down model for the Ariane 5 P230 booster. The present work aims at the prediction of the main characteristics of the ignition overpressure in the far field and the assessment of afterburning influence on both its formation mechanisms and its alteration by the jet plume. Two three-dimensional large-eddy simulations are performed, one considering inert flow and one modeling the afterburning. Infrared images of the plume are also computed with a dedicated radiation transfer solver. An overall good agreement with the experimental results is reported on amplitude and duration. Nevertheless, the reactive case is found to provide better results on amplitude and directivity. The signature is also better reproduced on the microphones near the jet centerline, and the emitted infrared intensity is well captured. Computations indicate that the formation of the shock wave is obtained by coalescence of compression waves emitted by the accelerating jet at early times. For the reactive case, computations show an increased interaction between the jet and the overpressure wave.

Detonation-driven–shock wave interactions with perforated plates

The study of detonations and their interactions is vital for the understanding of the high-speed flow physics involved and the ultimate goal of controlling their detrimental effects. However, producing safe and repeatable detonations within the laboratory can be quite challenging, leading to the use of computational studies which ultimately require experimental data for their validation. The objective of this study is to examine the induced flow field from the interaction of a shock front and accompanying products of combustion, produced from the detonation taking place within a non-electrical tube lined with explosive material, with porous plates with varying porosities, 0.7–9.7%. State of the art high-speed schlieren photography alongside high-resolution pressure measurements is used to visualise the induced flow field and examine the attenuation effects which occur at different porosities. The detonation tube is placed at different distances from the plates' surface, 0–30 mm, and the pressure at the rear of the plate is recorded and compared. The results indicate that depending on the level of porosity and the Mach number of the precursor shock front secondary reflected and transmitted shock waves are formed through the coalescence of compression waves. With reduced porosity, the plates act almost as a solid surface, therefore the shock propagates faster along its surface.

Generation of powerful terahertz emission in a beam-driven strong plasma turbulence

The generation of terahertz electromagnetic radiation due to the coalescence of upper-hybrid waves in the long-wavelength region of strong plasma turbulence driven by a high-current relativistic electron beam in a magnetized plasma is investigated. The width of the frequency spectrum and the angular characteristics of this radiation for various values of plasma density and turbulence energy are calculated using the simple theoretical model adequately describing beam–plasma experiments at mirror traps. It is shown that the power density of electromagnetic emission at the second harmonic of plasma frequency in the terahertz range for these laboratory experiments can reach the level of 1 MW cm−3 with 1% conversion efficiency of beam energy losses to electromagnetic emission.

Spectral and spatial observations of microwave spikes and zebra structure in the short radio burst of May 29, 2003

The unusual radio burst of May 29, 2003 connected with the M1.5 flare in AR 10368 has been analyzed. It was observed by the Solar Broadband Radio Spectrometer (SBRS/Huairou station, Beijing) in the 5.2-7.6 GHz range. It proved to be only the third case of a neat zebra structure appearing among all observations at such high frequencies. Despite the short duration of the burst (25 s), it provided a wealth of data for studying the superfine structure with millisecond resolution (5 ms). We localize the site of emission sources in the flare region, estimate plasma parameters in the generation sites, and suggest applicable mechanisms for interpretating spikes and zebra-structure generation. Positions of radio bursts were obtained by the Siberian Solar Radio Telescope (SSRT) (5.7 GHz) and Nobeyama radioheliograph (NoRH) (17 GHz). The sources in intensity gravitated to tops of short loops at 17 GHz, and to long loops at 5.7 GHz. Short pulses at 17 GHz (with a temporal resolution of 100 ms) are registered in the R-polarized source over the N-magnetic polarity (extraordinary mode). Dynamic spectra show that all the emission comprised millisecond pulses (spikes) of 5-10 ms duration in the instantaneous band of 70 to 100 MHz, forming the superfine structure of different bursts, essentially in the form of fast or slow-drift fibers and various zebra-structure stripes. Five scales of zebra structures have been singled out. As the main mechanism for generating spikes (as the initial emission) we suggest the coalescence of plasma waves with whistlers in the pulse regime of interaction between whistlers and ion-sound waves. In this case one can explain the appearance of fibers and sporadic zebra-structure stripes exhibiting the frequency splitting.