Frequency Wavenumber Research Articles

On the Intraseasonal Oceanic Processes Constrained by Data Assimilation: A Case Study of the Tropical Pacific

Abstract This study investigates the ability of a global ocean reanalysis at 1/12° horizontal resolution, GLORYS12, to represent oceanic processes at intraseasonal and higher-frequency scales. GLORYS12, which includes data assimilation of satellite and multi-instrument in situ observations, is compared to a twin-free simulation (with no assimilation) in the tropical Pacific Ocean. Spectral analyses show that data assimilation improves the realism of sea surface height intraseasonal variability in the entire tropical Pacific Ocean, in both amplitude and phase, with an increase in the amplitude of more than 50% for the 20–90-day band and up to 15% for the 2–20-day band. The improvement is largest along the 5°N/S latitudes, where the magnitude of tropical instability waves is maximum, but is limited along the equator where steric height variability is dominated by intraseasonal oceanic Kelvin waves, already well represented in the free simulation. Wavenumber–frequency spectra show that data assimilation constraint improves both the spatial and temporal scales of intraseasonal waves and their timing. Data assimilation impacts the realism of oceanic simulations in two ways. By modifying the background oceanic stratification, it corrects the phase speed of westward-propagating waves. It is also shown that the intraseasonal component of analysis increments (data assimilation corrections applied) is dynamically consistent and exhibits clear intraseasonal propagation. By demonstrating the benefits of data assimilation for intraseasonal processes in the tropical Pacific Ocean, this study highlights the high value of both in situ and satellite observations to constrain ocean models in a wide range of time scales.

FDFK2D: Efficient Two-Dimensional Teleseismic Wavefield Modeling for Receiver Function Analysis Using a Hybrid Method

Abstract We develop a Fortran package with high programming optimization and parallel computing for simulating high-frequency (>1 Hz) teleseismic wavefields using a hybrid numerical method that couples the finite-difference (FD) and frequency–wavenumber (FK) methods. This method can simulate the interactions of incoming teleseismic wavefields with local heterogeneities but reduce computational region to a much smaller localized domain, which can significantly reduce the computing cost of the high-frequency teleseismic wavefields. The local heterogeneities are allowed to vary arbitrarily in a localized heterogeneous domain. In this package, the geographical locations of earthquakes are permitted, which can consider the real azimuthal effect of the source. Numerical benchmark tests first demonstrate the effectiveness of the developed method for P- and S-wave receiver functions (RFs). The consistent travel times of synthetic and theoretical RFs phases demonstrate its high accuracy. Application on a dense array generally obtains consistent RFs profiles with observed ones and successfully reproduces the observed common-converted-point (CCP) stacking image, which further verifies the effectiveness of the presented method. In addition, statistics of the time-consuming of typical models illustrate the high efficiency of this package, which needs very little computing resources even to be feasible on a laptop.

Interfacial instability in a viscoelastic microfluidic coflow system

Understanding interfacial instability in a coflow system has relevance in the effective manipulation of small objects in microfluidic applications. We experimentally elucidate interfacial instability in stratified coflow systems of Newtonian and viscoelastic fluid streams in microfluidic confinements. By performing a linear stability analysis, we derive equations that describe the complex wave speed and the dispersion relationship between wavenumber and angular frequency, thus categorizing the behaviour of the systems into two main regimes: stable (with a flat interface) and unstable (with either a wavy interface or droplet formation). We characterize the regimes in terms of the capillary numbers of the phases in a comprehensive regime plot. We decipher the dependence of interfacial instability on fluidic parameters by decoupling the physics into viscous and elastic components. Remarkably, our findings reveal that elastic stratification can both stabilize and destabilize the flow, depending on the fluid and flow parameters. We also examine droplet formation, which is important for microfluidic applications. Our findings suggest that adjusting the viscous and elastic properties of the fluids can control the transition between wavy and droplet-forming unstable regimes. Our investigation uncovers the physics behind the instability involved in interfacial flows of Newtonian and viscoelastic fluids in general, and the unexplored behaviour of interfacial waves in stratified liquid systems. The present study can lead to a better understanding of the manipulation of small objects and production of droplets in microfluidic coflow systems.

Process-Based Evaluation of Intraseasonal Oceanic Kelvin Waves in the Pacific Ocean in CMIP6 Models

Abstract Oceanic intraseasonal Kelvin waves (KWs) help modulate upper-ocean thermal characteristics, providing feedbacks to important coupled air–sea phenomena in the tropics. The recent availability of daily thermocline depth fields from several phase 6 of the Coupled Model Intercomparison Project (CMIP6) models makes it possible to evaluate the performance of KWs and identify potential sources of bias. Most models fail to simulate a realistic spatial distribution of KW variability. Models simulate a large variability of KWs in the western or eastern Pacific rather than in the central Pacific as observed. The modeled KWs propagate slowly (about 1.5 m s−1) compared to observations (about 2.5 m s−1). This slow propagation is also identified in wavenumber–frequency spectra for KWs and meridional KW structures, which is more consistent with a second baroclinic mode structure in models compared to the first baroclinic mode structure in observations. An analysis of the relative contributions of the vertical wavenumber and background ocean stability to KW phase speeds indicates that the high vertical wavenumber bias in models contributes most to the slow propagation, in which the higher-than-observed vertical wavenumbers imply the biased incorporation of higher baroclinic modes in the model KW structure. This finding is further supported by the results of vertical mode decomposition that incorporates background density profiles. These results indicate that a realistic representation of the KW vertical structure is essential to produce realistic KW propagations in models. Significance Statement Oceanic intraseasonal Kelvin waves (KWs) play a significant role in regulating the heat content and temperature of the ocean, which provides feedbacks to coupled ocean–atmosphere phenomena in the tropics such as El Niño–Southern Oscillation (ENSO). Consequently, identifying the biases in KWs and the potential sources of those biases in state-of-the-art models is essential to improve simulations of ENSO and its diversity and advance forecasts of weather extremes around the globe induced by ENSO. We find that KWs in the models propagate slower than observations, mainly due to biases in their vertical structure, with secondary effects due to biases in model ocean stability. These issues may be potential sources for current imperfect ENSO model simulations and predictions.

Simulation of Scalar Wave Propagation with High-Order Temporal and Spatial Accuracy by a New Multi-Axial Staggered-Grid Finite-Difference Scheme

ABSTRACT Staggered-grid finite-difference (SFD) stencils are extensively applied for scalar wavefield simulations and inversions in seismology because of their easy implementation and effectiveness of propagating the wave in heterogeneous media. The conventional SFD (CSFD) stencil adopts second-order temporal and high-order spatial finite-difference operators to approximate the partial derivatives inside the wave equation. The spatial SFD operator only adopts grid points along one orthogonally axial direction to approximate the spatial partial derivative along that direction. Therefore, increasing the number of grid points along the axis will not improve the temporal accuracy. To simultaneously enhance the temporal and spatial accuracy, we propose a new multi-axial SFD (MASFD) stencil, which consists of grid points along three directions for each partial derivative in space. The MASFD weightings (coefficients) are derived by preserving the dispersion relation of the scalar wave in the frequency–wavenumber domain. We prove that increasing the number of the grid points of the new stencil can simultaneously reach high-order accuracy in time and space. The performance of the new MASFD scheme is compared with the CSFD schemes by quantitative dispersion analyses, stability analyses, and numerical examples. Our comprehensive comparisons demonstrate that the MASFD scheme can be more accurate than the CSFD ones because of improved temporal accuracy. Under comparable accuracy, the MASFD scheme can be more efficient than the CSFD ones because the MASFD scheme can adopt larger time steps to perform stable wave extrapolation.

The rebar corrosion length evaluation technique based on nonlinear ultrasonic guided wave energy flow

In offshore reinforced concrete (RC) structures, phenomena of rebar corrosion are widespread, seriously threatening the durability of the structures. However, the issue of entire rebar corrosion process detection, especially for the evaluation of local corrosion states and the scope, is also challengeable. The paper aims at utilizing the nonlinear ultrasonic guided wave (UGW) energy flow to identify reinforcement corrosion level and length during the entire corrosion process in RC structures and establishing a corresponding corrosion evaluation algorithm. Therefore, a corroded rebar with the surrounding concrete cover is simplified into a cylindrical layered structural model. Meanwhile, piezoelectric transducers are used for the actuation and reception of UGWs, and a granular material contact (GMC) model is applied to illustrate the mechanism for generating surface-contact-induced nonlinear components in scattering waves. Then, the propagation behavior of the nonlinear UGWs is analyzed by regarding the corrosion layer as a secondary sound source changing the wave energy flow. A corrosion evaluation algorithm based on the GMC model is established and validated by both experiment and finite element (FE) analysis. The results show that for a harmonic UGW excitation signal, the periodic relationship between the second-order nonlinear coefficient of received signal and the corrosion length is found in which the period is associated with the difference (kd) of 2 times of fundamental frequency wave number (2 kω) and double frequency wave number (k2ω). Particularly, as kd trends to zero, a degraded linear relationship is found for establishing the corrosion length evaluation algorithm with the relatively high evaluation precision and convenient evaluation technique.

High-Fidelity OC-Seislet Stacking Method for Low-SNR Seismic Data

Seismic stacking is a core technique in seismic data processing, aimed at enhancing the signal-to-noise ratio (SNR) of data by utilizing seismic data acquisition with multifold geometry. Traditional stacking methods always have certain limitations, such as the reliance on the accuracy of velocity analysis for dip moveout (DMO) in common midpoint (CMP) stacking. The seislet transform, a compression technique tailored to nonstationary seismic data, can compress and stack along the prediction direction of seismic data, which provides a new technical idea for high-fidelity seismic imaging based on the effectiveness of the compression. This paper introduces a high-order OC-seislet stacking method for low-SNR seismic data, capable of achieving the high-fidelity stacking of reflection and diffraction waves simultaneously. With the multi-scale analysis advantages of the seislet transform, this method addresses the dependency of DMO stacking on velocity analysis accuracy. In the frequency–wavenumber–scale domain, the correction compensation of the high-order CDF 9/7 basis function is used to obtain the compression coefficients of the high-order OC-seislet transform. This approach simultaneously stacks frequency–wavenumber information of reflection and diffraction waves with high fidelity while implementing DMO processing. After normalizing the weighting coefficients and applying soft thresholding for denoising, the final result is transformed back to the original time–space domain, yielding high-fidelity stacking sections. The results of applying this method to both synthetic and field data show that, compared with conventional DMO stacking methods, the high-order OC-seislet stacking technique reasonably represents dipping layers and fault amplitudes, and it can achieve a balance of a high SNR and high fidelity in stacked profiles.

Receptivity of Rayleigh-Taylor instability to acoustic pulses: Theoretical explanation of pulse propagation

Direct numerical simulation (DNS) of Rayleigh-Taylor instability (RTI) has been reported in Sengupta, et al. (2022) [35] using more than 4 billion points with initial time steps of 7.69 ×10−8s. The set-up consists of quiescent heavy (cold) fluid atop lighter (hot) fluid initially separated by an insulated partition. Removal of this partition creates acoustic pulses in the directions normal to the interface, which provides the receptivity route of RTI to transient acoustic pulses spread over several mega-Hz frequencies, far in excess of ultrasonic frequencies. The DNS and its analysis reveal the pulses to be severely attenuated, which cannot be explained by the classical wave equation. In the present research, after demonstrating the features of the DNS results, we report in detail, the theoretical development of a wave equation incorporating losses based on the Navier-Stokes equation without Stokes' hypothesis for a quiescent ambience. Apart from the physical properties of this altered wave equation, the numerical solution of the same is obtained. The governing partial differential equation (PDE) for the propagation of disturbances in the spectral plane, provides the dispersion relation between wavenumber and circular frequency in the dissipative medium accounting for viscous losses. The presented analysis provides physical properties using the global spectral analysis (GSA). This shows the far-field perturbation to propagate either as attenuated waves or strictly in a diffusive manner depending upon the wavenumber. The PDE is solved numerically by a high-accuracy compact scheme and the four-stage, Runge-Kutta scheme for time advancement. The computed solution is shown to match not only with the developed theoretical analysis but also explains the DNS results for RTI at early times when the computed flow field truly represents the quiescent ambience.

Characterization of noise sources in two- and three-element high-lift airfoil configurations

To improve the current understanding of flap noise generation mechanisms in high-lift devices used by small- to large-size commercial aircraft, a detailed study of both two- and three-element configurations of the canonical high-lift 30P30N airfoil has been conducted. Results from unsteady Reynolds-Averaged Navier-Stokes simulations are compared with aerodynamic and acoustic measurements in the hybrid anechoic wind tunnel at the University of Toronto to gain better physical insights into the flow phenomena associated with the noise sources in multi-element configurations. It is shown that the slat element has little impact on the flow in and around the flap and flap gap when the main wing is at the same orientation relative to the incoming flow. Tonal peaks are found both in the flap cove and on the flap, matching the tonal noise produced by the slat when in the three-element configuration. These peaks are present at the flap due to pressure waves that emanate from the slat and propagate downstream. Analysis of the frequency wavenumber spectra of the unsteady pressure along the main element pressure surface shows the existence of forward- and backward-traveling acoustic waves, providing evidence of a feedback loop between the two coves, which amplifies the narrowband tonal peaks in both coves. These tones disappear from the flap when the slat is removed in a two-element configuration, with the flap-cove overall broadband pressure fluctuation levels remaining unchanged.

Damage Analysis of High-Speed Railway Bridge-Track System with Unequal Pier Heights Under Near-Fault Earthquake Based on FK-FE Method

ABSTRACT Canyons have a significant influence on near-fault earthquakes, and near-fault earthquakes exhibit strong amplitude and large spatial variability. In turn, this causes the damage and deformation of the high-speed railway (HSR) bridge-track system with unequal pier heights, which affects the normal service of the unequal pier heights bridge and the safe running of the train. This study investigates the damage and deformation of HSR bridge-track systems with unequal pier height in canyon areas under near-fault seismic based on FK (frequency wavenumber)-FE (finite element) method. It aims to offer suggestions for seismic design in canyon regions of HSR unequal pier height bridges. First, a finite fault kinematic hybrid source model and a canyon site model were established, and the FK-FE hybrid method was employed to simulate the three-dimensional (3D) site motion considering the full process of the seismic source-propagation medium-complex site (SSPC). Then, the influence of near-fault earthquakes and the canyon topography on the spatial distribution of near-fault ground motions were analyzed, and the non-uniform near-fault seismic excitation at the bottom of each pier considering the canyon topography effect was obtained. Finally, a nonlinear dynamic FE model of the HSR bridge-track system was established, and its damage patterns and mechanism in canyon near-fault earthquakes were analyzed. The results indicate that near-fault earthquakes in the canyon exhibit significant vertical and sliding effects with significant spatial variability and the FK-FE method can provide more accurate ground motion input. The seismic damage to HSR bridge-track systems increases as the fault distance decreases, and topography effects further aggravates seismic damage to HSR bridges. Moreover, vulnerable areas in the track system are often found at girder ends. Therefore, for HSR bridges in canyon regions, seismic input needs to comprehensively consider the effects of near-fault earthquakes and topography, with post-earthquake focus on damage assessment at girder ends.

Marine Radar Constant False Alarm Rate Detection in Generalized Extreme Value Distribution Based on Space-Time Adaptive Filtering Clutter Statistical Analysis

The performance of marine radar constant false alarm rate (CFAR) detection method is significantly influenced by the modeling of sea clutter distribution and detector decision rules. The false alarm rate and detection rate are therefore unstable. In order to address low CFAR detection performance and the modeling problem of non-uniform, non-Gaussian, and non-stationary sea clutter distribution in marine radar images, in this paper, a CFAR detection method in generalized extreme value distribution modeling based on marine radar space-time filtering background clutter is proposed. Initially, three-dimensional (3D) frequency wave-number (space-time) domain adaptive filter is employed to filter the original radar image, so as to obtain uniform and stable background clutter. Subsequently, generalized extreme value (GEV) distribution is introduced to integrally model the filtered background clutter. Finally, Inclusion/Exclusion (IE) with the best performance under the GEV distribution is selected as the clutter range profile CFAR (CRP-CFAR) detector decision rule in the final detection. The proposed method is verified by utilizing real marine radar image data. The results indicate that when the Pfa is set at 0.0001, the proposed method exhibits an average improvement in PD of 2.3% compared to STAF-RCBD-CFAR, and a 6.2% improvement compared to STCS-WL-CFAR. When the Pfa is set at 0.001, the proposed method exhibits an average improvement in PD of 6.9% compared to STAF-RCBD-CFAR, and a 9.6% improvement compared to STCS-WL-CFAR.

Propagation of underwater wave groups in a compressible ocean coupled with an elastic seafloor

The overall system of interest is an infinite half-space in which a compressible ocean is the top layer and an elastic seafloor (together with the crust beneath) forms a semi-infinite bottom layer. Whereas water-column compression waves and seafloor waves individually have received considerable attention, not much is known about their propagation as groups. This work utilizes the group behaviour of these waves to derive energy balance relations for wavenumber spectra for wave groups propagating through a mildly non-uniform water-column–seafloor system. Dispersion relations for the coupled system are derived using known kinematic and kinetic conditions at the interface, and free and forced wave solutions for the wavenumber spectra are obtained, with particular attention to the case when certain frequency–wavenumber combinations in the forcing excite the two-media system into resonance. Wavenumber spectra predicted using the theory for mildly non-uniform media are found to be close to those predicted assuming uniform media, though the effect of non-uniformity becomes more noticeable as the groups propagate farther from the generation area. Here, nonlinear interactions among stationary, random multi-directional surface-wave fields provide the forcing for groups of compression waves in the water and surface waves on the seafloor. The formulation includes the cumulative effect of multiple generation areas along the group propagation direction. Comparisons with observational data from a sensor array in the Atlantic Ocean indicate that the theory can be applied to reconstruct plausible combinations of generation areas and interaction times that are consistent with the measured data, for deriving approximate predictions at down-wave distances along the group propagation directions. Implications of this and other findings are discussed for (i) the potential for energy conversion from water-column compression waves on the seafloor, (ii) tracking of tropical cyclones from the seafloor, and (iii) quantification and comparative assessment of low-frequency mid-ocean ambient noise and microseism activity.

Spectral proper orthogonal decomposition analysis of a spatially developing underexpanded round jet at Re = 45 000

This study conducts a comprehensive analysis of the coherent structures within a spatially developing underexpanded axisymmetric jet at a Reynolds number of 45 000, utilizing high-fidelity implicit large eddy simulations (iLES) in conjunction with spectral proper orthogonal decomposition (SPOD). In the frequency–wavenumber space, the global SPOD analysis identifies three distinct coherent structures, corresponding to three different mechanisms, namely, Kelvin–Helmholtz (KH), Orr, and lift-up. Their salient characteristics are discussed in detail. Local SPOD analysis further explores the streamwise evolution of these coherent structures, revealing that the influence of KH mechanism is confined to the near field, while the lift-up mechanism persists and dominates the energy content beyond the potential core, with the streaks of azimuthal wavenumbers one and two being the most energetic. The reconstruction of turbulent kinetic energy (TKE) and Reynolds shear stress from SPOD modes is assessed, and the first few azimuthal modes with low wavenumbers and frequencies are found crucial for capturing the dominant features of the flow. It is found that only the m = 0 and m = 1 modes contribute to the TKE at the centerline. The Reynolds shear stress reconstruction quality is comparable to TKE, but with a negligible contribution from the m = 0 mode. The azimuthal mode m = 1 captures the slope of the actual Reynolds shear stress profile in the vicinity of centerline, while m = 2 and higher modes capture the peak location of the actual profile.

Southern Hemisphere baroclinic activity in seasonal forecasts

Accurate prediction of mid-latitude baroclinic activity is extremely relevant for understanding global climate dynamics and improving long-term weather forecasts. However, current seasonal forecast models struggle to accurately represent the variability of baroclinic activity in the Southern Hemisphere, which may affect their reliability and usefulness. Baroclinic instability in the mid-latitudes is a significant component of the climate system, as it is associated with the meridional transport of a large amount of energy and momentum. Therefore, the ability of the models to correctly predict the properties of the atmospheric circulation in this latitudinal region is a very important requirement. The aim of this study is to estimate the energy of atmospheric phenomena typical of the mid-latitudes, such as baroclinic perturbations, and to understand how seasonal forecasts can be practically used to assess the energy transfer in the atmosphere. We compare the Southern Hemisphere mid-latitude winter variability of the seasonal forecasts of the ECMWF, DWD and Météo France forecasting systems with the ERA5 reanalysis. The analysis is performed by computing the Hayashi spectra of the 500-hPa geopotential height field. Both the reanalysis and the seasonal forecast show a series of peaks in the spectral region of eastward-travelling waves, which corresponds to the high frequency and high wavenumber domain. We quantify the amount of energy released from the atmosphere by calculating the Baroclinic Amplitude Index. The results suggest that seasonal forecasts may not accurately capture the variability of geopotential height power spectra in the Southern Hemisphere, which poses a challenge in correctly distributing the energy over spatial and temporal dimensions. This study will show that this problem is particularly pronounced for wavenumber 4 over a period of 8 days. This misrepresentation likely contributes to the uncertainties in precipitation forecasting, with discrepancies exacerbated by a suboptimal description of baroclinic instability and dynamical components in the models. Our findings highlight the need for an improved representation of baroclinic processes in seasonal forecast models, which could lead to substantial advancements in long-term weather prediction capabilities and in a more complete understanding of climate dynamics.

Effects of Mach number on space-time characteristics of wall pressure fluctuations beneath turbulent boundary layers

Wall pressure fluctuations beneath turbulent boundary layers are a fundamental source of aerodynamic noise by exciting the wall structure, with their space-time characteristics serving as the basic ingredient for predicting the wall structural response. To this end, direct numerical simulations of fully developed compressible turbulent boundary layers at Mach numbers of 0.5, 1.2, and 2.0 are conducted to investigate wall pressure fluctuations comprehensively. The effects of Mach number on the single-point statistics of wall pressure fluctuations, such as the root mean square, skewness and flatness factors, probability density function, and frequency spectrum, are assessed to be very weak. Regarding the space-time characteristics, the convection velocity Uc determined by the space-time correlation of wall pressure fluctuations increases slightly with the Mach number, which only reflects the convective behavior of turbulent vortices. On the wavenumber–frequency spectrum, characteristic peaks of both the acoustic wave and convective vortices are identified. At Mach 0.5, the peaks of the fast (Uc+c) and slow (Uc−c) acoustic waves are unattached to others with c denoting acoustic speed, while only the peak of the fast acoustic wave is distinguishable from the convective peak at Mach 1.2 and 2.0. Due to the aerodynamic heating at supersonic conditions, the thermal effect on acoustic speed should be taken into account in determining the acoustic wavenumber. By introducing a convective Prandtl–Glauert parameter, a refined relation is proposed to provide a more accurate depiction of the acoustic domain in the wavenumber–frequency spectrum.

Characterization of Shallow Sedimentary Layers in the Oran Region Using Ambient Vibration Data

This study investigates the structure of shear-wave velocities (Vs) in the shallow layers of the Oran region, north-west of Algeria, using non-invasive techniques based on ambient vibration arrays. The region has experienced several moderate earthquakes, including the historical Oran earthquake of 1790. Ambient vibration measurements were carried out at 15 sites throughout the study area. Two methods were used: spatial autocorrelation (SPAC) and frequency–wavenumber analysis (f-k), which allowed us to better constrain Rayleigh wave dispersion curves. The inversion of the dispersion curves derived from the f-k analysis allowed for estimating the shear-wave velocity profiles and the Vs30 value at the sites under study. The other important result of the present study is an empirical equation that has been proposed to predict Vs30 in the Oran region. The determination of near-surface shear-wave velocity profiles is an important step in the assessment of seismic hazard. This study has demonstrated the effectiveness of using ambient vibration array techniques to estimate the soil Vs structure.

Scaling of turbulence-forced capillary waves

We simulate the propagation of capillary waves at the interface between two liquid layers of equal density, viscosity and thickness, which flow in stratified conditions inside a turbulent Poiseuille channel. This setup gives us the possibility to single out the effect of inertia and surface tension – in isolation from gravity – on the propagation of interfacial capillary waves. Numerical simulations, which are based on a combined pseudo spectral/phase field method, are run keeping the shear Reynolds number constant, Reτ=300, and considering four different values of the Weber number: We=0.5, We=1.0, We=1.5 and We=2.0. In the present case, waves are naturally forced by turbulence over a broad range of scales, from the larger ones, whose size is of order of the channel height h, down to the smaller dissipative scales. We show that, by increasing the Weber number, the interface is deformed more vigorously, and is prone to sustain the propagation of waves over a broader range of scales. Upon computation of the power spectra of wave elevation, we show that the behavior of waves agrees with the theoretical predictions given by the weak wave turbulence theory, which predicts a decay Sη(k)∼k−4 in the inertial regime, followed by a steeper decay at large k, in the surface-tension-dominated regime. We clearly show that the transition between the inertial and the surface-tension-dominated regime is pushed towards larger k by increasing the Weber number. In addition, we show that the two-dimensional frequency–wavenumber spectra of the wave elevation – the dispersion relation – is in good agreement with well established theoretical prediction, ω(k)∼k3/2, and that the range of validity of such prediction broadens for increasing Weber number.

Identification method of the hydrodynamic and acoustic natures of wall pressure fluctuation based on dynamic mode decomposition

In this study, an analysis method is proposed to explain the dynamic mode decomposition (DMD) mode of wall fluctuating pressure from the perspective of hydrodynamics and acoustics. According to the phase velocity, the wavenumber–frequency spectrum is divided into hydrodynamic, acoustic, and subconvective regions. Multiple DMD modes of the pressure field are calculated to obtain the wavenumber–frequency spectrum of the reconstructed pressure, which is characterized by the fact that the energy is concentrated at different wavenumber positions of the same frequency. This behavioral feature enables the DMD mode to be identified as a hydrodynamic, acoustic, and hybrid property according to the wavenumber position where the energy spot appears. This method can realize the classification and contribution analysis of the hydrodynamic and acoustic properties of the wall pressure DMD mode, and establish the mapping relationship between the acoustic mode and the eddy current characteristics through the eigenvalues. The coherent structure of the trace acoustic energy radiation in the incompressible fluid is observed from the statistical perspective, which increases understanding of the flow noise. The zero-pressure gradient wall flow experiment of Abraham is numerically analyzed using the aforementioned method. The results indicate that most of the DMD modes are identified as hydrodynamic, and only the nineteenth-order DMD mode is identified as acoustic. The frequency of the acoustic mode is 23.9 Hz, which has obvious wave-packet characteristics, whereas the hydrodynamic mode exhibits nonradiative convection characteristics, and its eddy current structure is closer to the wall transfer.

Transient internal wave excitation of resonant modes in a density staircase

The density of the ocean generally increases continuously with depth as a consequence of variations in salinity and temperature. In some regions, however, the density profile of the ocean adopts a (double diffusive) staircase structure in which successive layers of uniform density fluid are separated by rapid density jumps. Previous work has theoretically examined the transmission and reflection of periodic internal (gravity) waves incident upon a density staircase. This predicted the existence of transmission spikes (global modes) for certain combinations of frequency and horizontal wave number in which the incident waves transmit perfectly across a density staircase. It was hypothesized that the transmission spikes occur when the incident waves resonate with natural modes of disturbances in the staircase. Here we derive theory to investigate the interactions between incident internal waves and modes. We demonstrate a close correspondence between the frequency for incident waves at a transmission spike and the real part of the frequency of modes at the same horizontal wave number. However, the frequency of the corresponding modes has a negative imaginary part corresponding to exponential decay of the modes in time. We perform numerical simulations to examine the impact of this near-resonant coupling when a vertically localized, quasimonochromatic internal wave packet interacts with a density staircase. In a range of simulations with fixed incident wave frequency and varying horizontal wave number, the measured transmission coefficient does not exhibit transmission spikes, but decreases monotonically with increasing horizontal wave number about the critical wave number separating strong and weak transmission. We show this occurs because the incident wave excites modes that then slowly transmit energy above and below the staircase at a rate consistent with the predicted decay rate of the modes. This rate is slower for staircases with more steps with the decay time increasing as the cube of the number of steps. Published by the American Physical Society 2024

A Numerical Analysis of the Non-Uniform Layered Ground Vibration Caused by a Moving Railway Load Using an Efficient Frequency–Wave-Number Method

The ground vibration caused by the operation of high-speed trains has become a key challenge in the development of high-speed railways. In order to study the train-induced ground vibration affected by geotechnical heterogeneity, an efficient frequency–wave-number method coupled with the random variable theory model is proposed to quickly obtain the numerical results without losing accuracy. The track is regarded as a composite Euler–Bernoulli beam resting on the layered ground, and the spatial heterogeneity of the ground soil is considered. The ground dynamic characteristics of an elastic, layered, non-uniform foundation are investigated, and numerical results at three typical train speeds are reported based on the developed Fortran computer programs. The results show that as the soil homogeneity coefficient increases, the peak acceleration continuously decreases in the transonic case, while it gradually increases in the supersonic case, and the ground acceleration spectrum at a far distance obviously decreases; the maximum acceleration occurs at the track edge, and a local rebound in vibration attenuation occurs in the supersonic case.