Increasing Wave Number Research Articles

Two-Layer Electroosmotic Flow in a Parallel Plate Microchannel with Sinusoidal Corrugation

This study investigates the electroosmotic flow (EOF) of a two-layer Newtonian fluid system in a parallel plate microchannel with sinusoidal corrugated walls. The upper fluid is conducting, while the lower fluid is nonconducting. This analysis is performed under the Debye–Hückel approximation, utilizing perturbation expansion and the separation of variables. The potential distribution, velocity field, and the dependence of average velocity on roughness are derived. It is observed that the velocity distribution w(x, y), is significantly influenced by the phase difference θ between the corrugations on the upper and lower walls. The velocity w(x, y) decreases with an increase in the viscosity ratio μr of the bottom to top fluid, and w(x, y) is directly proportional to the dimensionless pressure gradient G and the zeta potential ratio ζ. The variation of the average velocity increment (roughness function) u2m related to wall roughness tends to decrease with the increase of the corrugation wave number λ, the electrokinetic width K, the depth ratio hr of the bottom to top fluid, the zeta potential ratio ζ and the dimensionless pressure gradient G; and increases with the increase of the viscosity ratio μr of the bottom to top fluid. Furthermore, the effect of uI2m is smaller than that of uII2m.

Simultaneous Occurrence of Electromagnetic and Quasi‐Electrostatic Magnetosonic Waves

AbstractMagnetosonic (MS) waves usually manifest as electromagnetic fluctuations, while quasi‐electrostatic magnetosonic (QEMS) waves have been recently reported. Here we present an intriguing coexistence of low harmonic electromagnetic magnetosonic (EMMS) waves and QEMS waves within the same band. Ion Bernstein instabilities are calculated based on the observed proton distribution. Effective growth rates can occur in the first‐fourth harmonic bands with a broad wave number range when the wave normal angle is sufficiently large. In each harmonic band, the MS waves would transform from electromagnetic to electrostatic as the wave number increases. This study reveals that the simultaneous occurrence of EMMS and QEMS arises from the expansive excitation range of MS waves in ‐space, thereby implying the potential resonant interactions between MS and particles in a broad energy spectrum.

Characteristic frequencies of transverse electric modes in a double negative slab waveguide with Kerr-type nonlinearity

The evolution equation for guided transverse electrical modes in a slab waveguide having a double negative core is derived for the electrical field. Special solutions of the dispersion equation for the case with double positive symmetric cladding are searched for. Relevant eigenmodes are formulated in terms of characteristic frequencies as a new method, and these frequencies corresponding to the oscillating guided modes are found for different wave numbers and core widths assuming the lossless Drude model can be used for the core medium with a Kerr-type nonlinearity. Results show that normalized characteristic frequencies increase with increasing wave numbers and mode numbers.

Faraday instability of viscous liquid films on a heated substrate with Maxwell–Cattaneo heat flux

Faraday instability of viscous liquid films with Maxwell–Cattaneo (MC) heat flux on an infinite, heated horizontal substrate subject to vertical time-varying periodic vibration is investigated theoretically. The MC effect means that the response of the heat flux to a temperature gradient obeys a relaxation time law rather than a classical Fourier time law. Applying the classic Floquet theory to linear analysis, a recursive relation is obtained. When considering the MC effect, a new phenomenon appears at a large wave number k. The neutral stability curves branch new tongues that turn left rather than right as before, but the tongues still move up and right as the wave number increases. Furthermore, typical harmonic (H) and subharmonic (SH) alternation behavior continues to exist. Interestingly, the first tongue of a branch is H or SH, implying that there is a transition following the branches. However, near the critical wave number kc of a branch, the SH and H almost overlap. As Cattaneo number C increases, the tongue-like unstable zones of branches become wider, and the critical wave number kc of the appeared branch becomes small. As the driving frequency ω decreases, the branch tongues become elongated and the critical wave number kc of the appeared branch becomes small.

Nonmodal stability analysis of Poiseuille flow through a porous medium

We unravel the nonmodal stability of a three-dimensional nonstratified Poiseuille flow in a saturated hyperporous medium constrained by impermeable rigid parallel plates. The primary objective is to broaden the scope of previous studies that conducted modal stability analysis for two-dimensional disturbances. Here, we explore both temporal and spatial transient disturbance energy growths for three-dimensional disturbances when the Reynolds number and porosity of the material are high, based on evolution equations with respect to time and space, respectively. Modal stability analysis reveals that the critical Reynolds number for the onset of shear mode instability increases as porosity increases. Moreover, the Darcy viscous drag term stabilizes shear mode instability, resulting in a delay in the transition from laminar flow to turbulence. In addition, it demonstrates the suppression of three-dimensional shear mode instability as the spanwise wavenumber increases, thereby confirming the statement of Squire’s theorem. By contrast, nonmodal stability analysis discloses that both temporal and spatial transient disturbance energy growths curtail as the effect of the Darcy viscous drag force intensifies. But their maximum values behave like O(Re2) for a fixed porous material, where Re is the Reynolds number. However, for different porous materials, the scalings for both temporal and spatial transient disturbance energy growths are different. Furthermore, increasing porosity also suppresses both temporal and spatial disturbance energy growths. Finally, we observe that temporal transient disturbance energy growth becomes larger for a spanwise perturbation, while spatial transient disturbance energy growth becomes larger for a steady perturbation when angular frequency vanishes. The initial disturbance that excites the largest temporal energy amplification generates two sets of alternating high-speed and low-speed elongated streaks in the streamwise direction.

Modal and non-modal stability for Hagen–Poiseuille flow with non-ideal fluid

Modal and non-modal stability analyses are applied to Hagen–Poiseuille flow with a non-ideal fluid. The non-ideal fluid is defined as a fluid close to its vapor–liquid critical point. In this region, properties of the fluid deviate significantly from the assumptions of the ideal gas model. In this paper, the specific example of CO2 near the critical point is taken as a non-ideal fluid. We studied fluids at supercritical pressure and different wall temperatures so that the centerline temperatures can be lower, equal, and higher than the pseudo-critical temperature. Flow instability is characterized by the Reynolds number, and the product of the Prandtl and Eckert numbers. In modal stability analysis, we observe that there is no unstable mode in Hagen–Poiseuille flow with a non-ideal fluid. Regarding the growth rate, as the axial wavenumber increases, another mode becomes the least stable. The non-modal theory is employed to investigate the optimal response to harmonic external force and transient energy growth. The influence of axial and azimuthal wave numbers, Prandtl and Eckert numbers, and thermodynamic states are also taken into account. In this study, we identify an generalized inflection point in the transcritical base profile, causing the transcritical state to be the most unstable. In non-modal instability, we observe that the optimal response mainly occurs at time invariant axisymmetric disturbance. This suggests that the axisymmetric disturbance could potentially initiate the transition to turbulence.

Experimental study on upstream pressure characteristics of rotating detonation engine with methane and oxygen-enriched air

The interaction mechanism between the rotating detonation engine (RDE) and its upstream is one key issue that needs to be explored when considering its application. In this study, experimental tests with methane and 50% oxygen-enriched air are conducted to investigate the relationship between upstream pressure characteristics and the detonation wave. As a result of operational considerations, a hollow chamber and a rear ignitor are used and the initiation process is discussed. Upstream pressure characteristics are analyzed under varied injection pressures and equivalence ratios. Stable modes including single-wave and double-wave modes are recorded in most cases. Notably, two unstable modes are also captured at low injection pressure in which the detonation quenches quickly. The results highlight that significant feedback pressure pulsations synchronize with the rotation frequency of detonation waves after ignition due to the upstream oblique shock wave (UOSW). But the inherent frequency of injection should also be emphasized at elevated injection pressure. The detonation wave can also cause injection blockage, particularly at low injection pressure, leading to the bifurcation of unstable mode. Such unstable is attributed to an inadequate upstream pressure increase after ignition, which hinders the injection reconstruction. Further analysis reveals that higher injection pressures or lower equivalence ratios diminish the differential between the detonation wave and upstream pressure, and consequently, the pulsation amplitude. An increase in the detonation wave number can also reduce the pulsation amplitude, which can even be lower than 10% in a double-wave mode. The results are beneficial for integrating RDE and its upstream components.

Instability and transition control by steady local blowing/suction in a hypersonic boundary layer

The efficacy of steady large-amplitude blowing/suction on instability and transition control for a hypersonic flat plate boundary layer with Mach number 5.86 is investigated systematically. The influence of the blowing/suction flux and amplitude on instability is examined through direct numerical simulation and resolvent analysis. When a relatively small flux is used, the two-dimensional instability critical frequency that distinguishes the promotion/suppression mode effect closely aligns with the synchronisation frequency. For the oblique wave, as the spanwise wavenumber increases, the suppression effects would become weaker and the mode suppression bandwidth diminishes/increases in general in the blowing/suction control. Increasing the blowing/suction flux can effectively broaden the frequency bandwidth of disturbance suppression. The influence of amplitude on disturbance suppression is weak in a scenario of constant flux. To gain a deeper insight into disturbance suppression mechanism, momentum potential theory (MPT) and kinetic energy budget analysis are further employed in analysing disturbance evolution with and without control. When the disturbance is suppressed, the blowing induces the transport of certain acoustic components along the compression wave out of the boundary layer, whereas the suction does not. The velocity fluctuations are derived from the momentum fluctuations of the MPT. Compared with the momentum fluctuations, the evolutions indicated by each component's velocity fluctuations greatly facilitate the investigations of the acoustic nature of the second mode. The rapid variation of disturbance amplitude near the blowing is caused by the oscillations of the acoustic component and phase speed differences between vortical and thermal components. Kinetic energy budget analysis is performed to address the non-parallel effect of the boundary layer introduced by blowing/suction, which tends to suppress disturbances near the blowing. Moreover, viscous effects leading to energy dissipation are identified to be stronger in regions where the boundary layer is rapidly thickening. Finally, it is demonstrated that a flat plate boundary layer transition triggered by a random disturbance can be delayed by a blowing/suction combination control. The resolvent analysis further demonstrates that disturbances with frequencies that dominate the early transition stage are dampened in the controlled base flow.

Nonlinear wave propagation in homogenized strain gradient 1D and 2D lattice materials: Applications to hexagonal and triangular networks

AbstractThis work aims to analyze the propagation of fully nonlinear waves, encompassing shear, extension, and bending deformation modes, within homogenized periodic nonlinear hexagonal and triangular networks, successively considering 1D and 2D situations. The wave analysis is conducted from the expression of the effective strain energy density of periodic hexagonal and triangular lattices in the nonlinear regime by a continualization of the discrete lattice equations, considering all forms of energy. We incorporate strain gradient effects into the continuous model to account for the wave‐dispersive nature. The resulting second‐gradient nonlinear continuum exhibits subsonic and supersonic propagation modes. We first examine in a 1D situation the dynamical response of the hexagonal and triangular lattices, considering varying levels of nonlinearity quantified by a single scalar valued parameter. We further evaluate the impact of a fully nonlinear analysis compared to an analysis solely based on the shear energy, regarding both supersonic and subsonic modes. The nonlinear wave propagation analysis is then extended to a 2D situation for the same two lattices. It is shown that the longitudinal mode exhibits a higher frequency at a low degree of nonlinearity; however, as the degree of nonlinearity increases, the shear mode surpasses the longitudinal mode in terms of frequency. As the wavenumber increases, the nonlinearity has a lesser impact on the frequency behavior, and the phase velocity is more influenced by other factors, such as the second gradient contributions of the effective constitutive law. Such a behavior indicates a transition from a highly nonlinear behavior at lower wave numbers to a more linear behavior at higher wave numbers.

Numerical simulation of wave-number effects on the performance of traveling wave pump-turbine in turbine mode

Pumped storage represents an economically viable, highly efficient, and extensive energy storage solution, receiving substantial research attention worldwide. This study utilized the energy dissipation of fish swimming in the water, and the traveling wave plate was arranged in a vertical rectangular flow channel to obtain energy through reverse thinking. Numerical simulation was employed to investigate the performance characteristics of the traveling wave turbine under varying wave number across high and low water head. The results reveal that the efficiency at low water head starts to increase and then decreases with the increase of wave number. There is an optimal wave number N = 4 to maximize turbine efficiency, and the maximum efficiency under low water head condition is 89.35 %. The efficiency of the high head condition shows a continuous upward trend, with a maximum value of 92.27 % in the range of wave number studied. With the increase of wave number, the instantaneous mass flow coefficient and power coefficient become more stable. The advantage of increasing the wave number is that more traveling wave plates can participate in energy capture, which is conducive to reducing the force required by each traveling wave plate and making the pressure distribution in each working cavity more regular.

Heat Treatment of Calcite to Enhance Its Removal of Color Dye Alizarin Red S

The use of color dyes in modern society presents a great challenge to the environment. Thus, extensive studies have been conducted in the last 30 years on the removal of color dyes from aqueous solutions such industrial wastewater. In this study, the removal of alizarin red S (ARS), an anionic dye, from solution by raw calcite (Cal) and heat-treated calcite (HCal) was conducted and compared under different physico-chemical conditions. Based on the isotherm study, the ARS removal capacities increased from 167 to 251 mmol/kg after the Cal was heated to 1000 °C for 3 h. The X-ray diffraction analyses showed no difference in the calcite phase between Cal and HCal after ARS sorption. Fourier-transform infrared results also showed no change in the calcite phase after ARS sorption, except a slightly increase in wavenumber from 713 to 727 cm−1 for the OCO bending of HCal at high ARS sorption levels. SEM observations showed about the same particle size and morphology before and after ARS sorption. The TGA data showed the formation of CaO after Cal was heated, and CaO converted back into calcite after being in contact with water or ARS solution for 24 h and then being air-dried. Thus, the high ARS removal could be due to CaO produced after Cal being heated. The findings from this research proved that there is great potential in the use of calcite, a low-cost and readily available Earth material, after heat treatment for the removal of contaminants from water.

Quasi-10-day waves in temperature and polar mesospheric clouds: Results of AIM/SOFIE and Aura/MLS observations

Planetary waves, including quasi-2, -5, -10, −16-day waves, play significant roles in stratospheric dynamics. However, the existing knowledge on quasi-10-day waves (Q10DWs) at high latitudes is limited. This paper investigated the interannual and seasonal variations of Q10DWs with zonal wave numbers varying from the −3 (westward propagation) to 3 (eastward propagation) modes from 2008 to 2022, using temperature data measured by the Microwave Limb Sounder instrument (316−0.001 hPa, corresponding to an altitude of approximately 8–97 km) and temperature/ice water content data measured by the Solar Occultation for Ice Experiment (SOFIE) instrument (10−100 km at latitudes >55°). The findings revealed that the amplitude of Q10DWs in winter was higher than that in other seasons. The amplitude of Q10DWs was observed to substantially decrease with an increase in wavenumber. In addition, the amplitude of stationary Q10DWs in the northern polar region exceeded that in the southern polar region. Moreover, we used observational data from the SOFIE instrument, which simultaneously measures temperature and ice water content (IWC) in the mesosphere, to examine the variations of Q10DWs with respect to the temperature and IWC. Our findings suggest that in the northern polar region, the maximum value of Q10DWs in IWC was occasionally observed earlier than the lowest value of Q10DWs in temperatures.

Impact of external magnetic field on temperature anisotropy driven Weibel instability in a magnetized plasma

In this paper, we investigate the impact of an external magnetic field on the Weibel instability driven by temperature anisotropy in a magnetized plasma. The study provides the influence of electron temperature anisotropy, considering both cold as well as warm ions. We derive expressions for the growth rate Γ (s−1) in each case to quantify the effect of some specific parameters on the instability. For example, the growth rate is plotted against the magnetic field for three distinct cases: considering only electrons, including cold ions, and incorporating warm ions. It is observed that the growth rate decreases as the applied magnetic field increases. Furthermore, the addition of both cold and warm ions to the plasma significantly influences the observed effects. It can be explained as follows: in the presence of cold ions, the growth rate is decreased with an increase in the wave number kz (cm−1). In addition, a decrease in the growth rate is observed with an increasing wave number in the case of warm ions. Therefore, it can be seen that the Weibel instability, propelled by thermal anisotropy, holds significant implications owing to its prevalence in both astrophysical and laboratory plasmas. The findings presented here are expected to contribute to the advancements in magnetic field generation and particle acceleration in various astrophysical phenomena, including gamma-ray bursts, relativistic collisionless shock fronts, radio supernovae, and pulsar winds.

Small-amplitude Compressible Magnetohydrodynamic Turbulence Modulated by Collisionless Damping in Earth’s Magnetosheath: Observation Matches Theory

Plasma turbulence is a ubiquitous dynamical process that transfers energy across many spatial and temporal scales and affects energetic particle transport. Recent advances in the understanding of compressible magnetohydrodynamic (MHD) turbulence demonstrate the important role of damping in shaping energy distributions on small scales, yet its observational evidence is still lacking. This study provides the first observational evidence of substantial collisionless damping (CD) modulation on the small-amplitude compressible MHD turbulence cascade in Earth’s magnetosheath using four Cluster spacecraft. Based on an improved compressible MHD decomposition algorithm, turbulence is decomposed into three eigenmodes: incompressible Alfvén modes and compressible slow and fast (magnetosonic) modes. Our observations demonstrate that CD enhances the anisotropy of compressible MHD modes because CD has a strong dependence on wave propagation angle. The wavenumber distributions of slow modes are mainly stretched perpendicular to the background magnetic field ( B 0) and weakly modulated by CD. In contrast, fast modes are subjected to a more significant CD modulation. Fast modes exhibit a weak, scale-independent anisotropy above the CD truncation scale. Below the CD truncation scale, the anisotropy of fast modes enhances as wavenumbers increase. As a result, fast-mode fractions in the total energy of compressible modes decrease with the increase of perpendicular wavenumber (to B 0) or wave propagation angle. Our findings reveal how the turbulence cascade is shaped by CD and its consequences for anisotropies in the space environment.

Modulational instability of the interacting electron whistlers and magnetosonic perturbations

A modulational instability of nonlinearly interacting electron whistlers and magnetosonic perturbations is studied in the present paper. For typical parameters, there is no modulational instability. However, modulational instability appears in special cases. For example, when the whistler wavenumber is small enough, there is modulational instability. Its growth rate decreases as the angle between the external magnetic field and the perturbed wave's direction increases, while it increases as the whistler wavenumber increases. It is also found that there is no modulational instability when the whistler wavenumber is larger than a critical value ( $k_0 > 0.05$ ), in which the perturbed wave frequency increases as the angle between the external magnetic field and the perturbed wave's direction increases when the angle between the external magnetic field and the perturbed wave's direction is large enough. Whereas, the perturbed wave frequency first increases as the whistler wavenumber increases, reaches a peak value and then decreases as whistler wavenumber increases.

Effect of Oldroyd-B fluid on thermal convection stability in a bidispersive porous media with relatively large macropores

This study investigates the effect of Oldroyd-B fluids on the thermal convection instability in a bi-disperse porous medium with relatively large macropores. The modified momentum equation of Oldroyd-B fluid in the macro- and micropores is first derived, assuming local thermal equilibrium. The Orr–Sommerfeld (O–S) equation is derived using the new modified incompressible Navier–Stokes equations of Oldroyd-B fluid. The Chebyshev collocation method is employed to solve the generalized eigenvalue problem, and the neutral stability curves and temporal growth rates are obtained. The results demonstrate that the relaxation time enhances the convective instability, while the retardation time suppresses it. Furthermore, the effect of relaxation time is generally small for smaller wave number, but the effect of relaxation time is significant for large wave number, and this effect becomes accentuated as the wave number increases. The retardation time does not have any influence when the wavenumber is small, and the influence of retardation time becomes small with the large relaxation time. Moreover, the convection instability is enhanced with the higher micropermeability and a higher ratio of momentum transfer coefficient between the macro- and microphases will suppress the instability.

Impact of Convection and Rotation on Advanced Thermal Energy Storage Using Nanoencapsulated Phase Change Materials in Wavy Enclosures

Free convection heat transfer in hybrid nanofluids in a differentially heated wavy enclosure is studied. The wavy enclosure moves at a constant counterclockwise rotational speed along its longitudinal axis. The enclosure is filled with a hybrid nanofluids consisting of water (H2O) and nanoencapsulated phase change materials (NEPCMs). These NEPCMs consist of a polyurethane coating and a core of N‐nonadecane, which undergoes a phase transition and has the capacity to retain or emit a significant quantity of latent heat. The dimensionless forms of the governing equations have been solved using finite element method. The validity of the present code is demonstrated by comparing its predictions with published results. The governing parameters under consideration are the corrugated number, 0 ≤ N ≤ 3, the volume fraction of hybrid nanoparticles, 0.0 ≤ ϕ ≤ 0.05, the Taylor number, 8 × 102 ≤ TaH2O ≤ 2 × 104. Changing the rotation speed is found to alter the melting and solidification zones in terms of pathways and size zones. The melting zone has a large size at moderate wave number, and its size shrinks and shifts downward as the wave number increases. An increase in the heat transfer rate values up to 38% is obtained when the concentration is adjusted from 1% to 5% for N = 1.

Phase velocity analysis by multi-parametric variations in a highly heterogeneous sandwich plate structure embedded in the Pasternak foundations with viscoelastic interlayer

This investigation explores the vibrational response of a sandwich plate with material parameter nonhomogeneity and a viscoelastic core, incorporating Pasternak foundations. The study views the equation of motion from an anti-plane shear perspective, presenting a generalized exact dispersion relation (GEDR). It analyzes the impact of parameters like material nonhomogeneity, viscoelasticity, and Pasternak foundation properties on the dimensionless phase velocity against wave number. Findings reveal decreasing phase velocity with increasing wave number, with nonhomogeneity and Pasternak parameters exerting substantial influence. The study offers valuable insights into composite material wave behavior, benefiting design methodologies for diverse applications.

Investigation on Quasi Lamb Wave Modes in AlN-on-Si MEMS Resonators.

Aluminum nitride (AlN)-on-Si MEMS resonators operating in Lamb wave modes have found wide applications for physical sensing and frequency generation. Due to the inherent layered structure, the strain distributions of Lamb wave modes become distorted in certain cases, which could benefit its potential application for surface physical sensing. This paper investigates the strain distributions of fundamental and first-order Lamb wave modes (i.e. S0, A0, S1, A1 modes) associated with their piezoelectric transductions in a group of AlN-on-Si resonators. The devices were designed with notable change in normalized wavenumber resulting in resonant frequencies ranging from 50 to 500 MHz. It is shown that the strain distributions of four Lamb wave modes vary quite differently as normalized wavenumber changes. In particular, it is found that the strain energy of A1-mode resonator tends to concentrate to the top surface of acoustic cavity as the normalized wavenumber increases, while that of S0-mode device becomes more confined in the central area. By electrically characterizing the designed devices in four Lamb wave modes, the effects of vibration mode distortion on resonant frequency and piezoelectric transduction were analyzed and compared. It is shown that designing A1-mode AlN-on-Si resonator with identical acoustic wavelength and device thickness benefits its surface strain concentration as well as piezoelectric transduction, which are both demanded for surface physical sensing. We herein demonstrate a 500-MHz A1-mode AlN-on-Si resonator with decent unloaded quality factor (Qu = 1500) and low motional resistance (Rm = 33 Ω) at atmospheric pressure.

Dynamic characteristics of rockbolt anchorage structure under radial cylindrical P wave

The anchorage structure formed of rockbolt, anchoring agent and surrounding rock plays a significant role in supporting underground engineering, however, there are still damage and failure cases of rockbolt supporting systems under blasting load. Therefore, it is important to clarify the mechanical behavior of rockbolt anchorage structure subjected to dynamic load. In this paper, we derive the analytical solution of dynamic response around anchorage structure subjected to radial cylindrical P wave based on the wave function expansion method, and the transient response is obtained by using Fourier transform. Two cases with and without anchoring agent are taken into consideration, and the elastic-slip model is introduced into describing the interaction between the surrounding rock and rockbolt without anchoring agent. The influence of multiple parameters such as thickness, stiffness and distance from the disturbance source on dynamic response is investigated in detail. The steady-state results demonstrates that the alternating tensile and compressive stress concentration is generated with the increase of wavenumber. The dynamic stress concentration can be reduced by appropriately decreasing the thickness and stiffness of anchoring agent, and the optimal values are obtained. The dynamic stress distribution in rock is opposite to that in anchoring agent under transient incidence and the tensile damage in rock along the incident direction and that in anchoring agent at the vertical direction of propagation must be alert. The novelty of the manuscript consists in studying the dynamic mechanical behaviors of anchorage structure subjected to radial dynamic load. The implications of these investigations for practical engineering will serve as a reference to design supporting methods and improve anchoring agent parameters.