Frequency-wavenumber Spectrum Research Articles

Characterization of SOL profiles and turbulence in ICRF-heated plasmas in EAST

Scrape-off layer (SOL) profiles and turbulence in ion cyclotron range of frequency (ICRF)-heated plasmas are investigated by the reciprocating probe diagnostic system (FRPs) and gas puff imaging (GPI) diagnostic in EAST. A radio-frequency (RF) sheath potential reaching up to 100 V is identified proximate to the ICRF antennas. Notably, the amplitude of this RF sheath potential escalates in response to rising ICRF power and inversely with plasma density. When a RF sheath is present in the far SOL, a pronounced density ‘shoulder’ forms in front of the ICRF antennas, while the ‘shoulder’ fade away as the antenna and associated RF sheath shift outwards. A strong E r shear is revealed by measurements from both FRPs and GPI. Analysis of the poloidal wave number-frequency spectrum reveals suppression of high-frequency turbulence in the far SOL due to the RF sheath. This effect is manifested in the reduced autocorrelation time τ c and reduced average blob size δ blob of the SOL plasma. Intriguingly, the poloidal propagation direction of the low-frequency turbulence reverses from the electron to the ion diamagnetic drift direction at the RF sheath location. A surge of tungsten impurity is potentially attributed to the heightened interaction between the SOL plasmas and the wall material. Shifting the ICRF antennas outward, to alleviate heat spots, results in the relocation of the RF sheath to the shaded region of the main limiter. This shift amplifies the radial velocity of blobs in the far SOL and concurrently diminishes the SOL density when compared to conditions without ICRF injection. The properties of ion saturation current fluctuations are consistent with the stochastic model predictions.

Subconvective wall-pressure fluctuations in low-Mach-number turbulent channel flow

Compressible direct numerical simulations are employed to elucidate the low-wavenumber behaviour of wall-pressure fluctuations in turbulent channel flow and the effect of flow Mach number in the nearly incompressible regime. Simulations are conducted at bulk Mach numbers 0.4, 0.2 and 0.1, and friction Reynolds number 180. In addition to the convective ridge that is virtually Mach-number-independent, acoustic ridges, whose magnitudes are orders of magnitude lower, are identified in the two-dimensional wavenumber–frequency spectrum. At lower frequencies, the acoustic ridges represent propagating longitudinal and oblique waves that match the theoretical predictions of two-dimensional duct modes with a uniform mean flow. They decay with decreasing Mach number but remain distinctly identifiable even at Mach 0.1. At high frequencies, in contrast, no propagating waves are found, and the spectral level in the supersonic wavenumber range is broadly elevated and increases with decreasing Mach number.

An efficient methodology for simulating multivariate non-Gaussian stochastic processes

Simulation of multivariate non-Gaussian stochastic processes is still a challenging task, where the efficiency and accuracy may not be balanced. In this paper, an efficient methodology is presented to address this challenge. This methodology makes use of a probability weighted moments-based Hermite polynomial model and a wavenumber–frequency spectrum density-based spectral representation approach. First, a probability weighted moments-based Hermite polynomial model is employed to establish a transformation relationship between Gaussian and non-Gaussian samples. Importantly, this model only requires the solution of a solvable system of equations. Second, the target non-Gaussian wavenumber–frequency spectrum density can be promptly transformed into the Gaussian one, where a fast root matching strategy and fast Fourier transform are utilized. Finally, the underlying Gaussian samples are generated by the spectral representation method, and the non-Gaussian samples are obtained via the proposed transformation model. The computational results from numerical examples demonstrate that the proposed methodology is considered to be an accurate, applicable, and efficient approach for simulating multivariate non-Gaussian stochastic processes.

Experimental study on spatiotemporal correlation and similarity law of transonic buffeting loads

The spatiotemporal correlation of transonic buffet, driven by strong shock waves and boundary-layer separation, plays a critical role in causing structural vibrations in launch vehicles. To investigate this correlation, a wind tunnel experiment was conducted to measure the time-frequency characteristics of wall fluctuation pressures. The phase array approach was employed to obtain the spatial correlation of buffeting load. The results indicate that the low-frequency hydrodynamic modes dominate the separation flow and shock oscillation, while the attached flow is predominantly influenced by broadband acoustic modes. The space-time correlation analysis reveals that the peak buffeting load, for typical flows, results from the convergence of energy beneath the turbulent boundary layer. Furthermore, a similarity law for the spatial correlation of buffeting load was derived and validated by the measurement data. Based on the measured buffeting load data, an improved W–F (Wavenumber–Frequency spectrum) model with scaling spatiotemporal correlation was developed. This model serves as a theoretical foundation for predicting buffeting loads under flight conditions.

Reconstruction of the Frequency-Wavenumber Spectrum of Water Waves With an Airborne Acoustic Doppler Array for Noncontact River Monitoring

Reconstruction of the Frequency-Wavenumber Spectrum of Water Waves With an Airborne Acoustic Doppler Array for Noncontact River Monitoring

Oceanic Rossby wave predictability in ECMWF's subseasonal‐to‐seasonal reforecasts

AbstractIn recent years, studies have put forth various theories on the role of oceanic equatorial Rossby waves (OERW) in the subseasonal‐to‐seasonal (S2S) predictability of the Indian Ocean (IO). While much of the scientific literature uses data from in‐situ, satellite, and/or reanalysis datasets, this study focuses on reforecast fields from the European Centre for Medium‐Range Weather Forecasting's (ECMWF) S2S dataset. Evaluation of the model's predictive skill in representing OERWs and the associated variations in subsurface‐to‐surface interaction and air–sea coupling are discussed. This work provides a unique methodology to calculate and evaluate the predictability of OERWs from model forecast data. Our results indicate that the model forecasts OERWs with high skill (anomaly correlation > 0.8 out to 40 days), indicating they are a key source of oceanic subseasonal predictability at extended lead times. Analysis of the wavenumber–frequency spectra for the IO indicates a strong reduction in power throughout the model forecast time period in the oceanic equatorial Kelvin wave (OEKW) regime and modest reduction of the OERW power. Both Kelvin and Rossby waves are modulated by the subseasonal zonal wind stress anomalies and the reduction of power is impacted by biases in winds at longer forecast leads. The erroneous weakening of the OEKWs contributes to the weakening of the reflected OERWs. Previous studies have documented that ocean heat content (OHC), particularly associated with downwelling OERWs, is important to maintaining and amplifying subseasonal precipitation in the IO. The reduced OERW power results in weaker advection of enhanced OHC anomalies by the OERWs, which has numerous implications for air–sea and subsurface‐to‐surface coupling, as discussed. The atmospheric response to the waning westward transport of OHC anomalies in the western IO by OERWs is associated with a weakening of intraseasonal precipitation anomalies associated with the intraseasonal oscillation.

Response of a Turbulent Boundary Layer to an Imposed Synthetic Large-Scale Structure

The dynamic response of a zero-pressure gradient turbulent boundary layer (TBL) to an active flow control actuator was experimentally investigated. The experimental TBL had a sufficiently low momentum thickness Reynolds number, such that there were no energetic organized large-scale structures in the outer region, as evidenced from measurements of the premultiplied wavenumber–frequency spectra. The periodically pulsed plasma actuator, placed inside the outer region of TBL, introduced a synthetic large-scale structure, and the boundary-layer response to this synthetic structure downstream of the actuator at select wall-normal and streamwise locations was investigated. The turbulence amplitude modulating effect of the synthetic large-scale structure, within the inner and log-linear regions of the boundary layer, was isolated and analyzed using a phase-locked analysis. The dynamic interaction of the synthetic large-scale structure and smaller-scale turbulent motions was quantified using a modulation coefficient, and a strong positive correlation within the inner and log regions of the boundary layer was measured. The streamwise development of the synthetic large-scale structure and its modulating effect on the near-wall turbulence across several streamwise locations are described. Profiles of the phase speed at these streamwise locations were extracted and were found to be constant within the log region, further confirming a strong coupling between the near-wall fluctuations in turbulence intensity and the synthetic large-scale motions introduced in the outer region. Overall, the turbulence amplitude modulation effect induced by the synthetic large-scale structure was found to be dynamically similar to the large-scale modulation measured in canonical TBLs at higher Reynolds numbers.

A frequency-dependent uniform discretization scheme for simulating fluctuating wind field based on a frequency-wavenumber spectrum

The frequency-wavenumber spectrum-based spectral representation method (FWS-based SRM) serves as an effective and broadly utilized technique for simulating multivariate fluctuating wind fields. Despite its usefulness, it struggles with accuracy in low frequency range during simulations involving structures of considerable length when employing conventional uniform discretization in both frequency and wavenumber domains. To overcome this challenge, this study introduces a frequency-dependent uniform discretization scheme. This strategy first applies uniform discretization to the frequency domain, and then ascertains the cut-off wavenumbers based on the truncation error, and finally implements uniformly discretization in the wavenumber domain. Subsequently, the uniformly discrete wavenumbers and frequencies are integrated into the FWS-based SRM to generate wind speed time histories, in combination with the FFT technique. The numerical example serves to validate the exceptional accuracy exhibited by the frequency-dependent uniform discretization scheme in low frequency range.

Structural vibration damping by the use of poro-elastic layers: a summary

A properly designed limp porous materials such as fibrous layers can provide damping equivalent to conventional viscoelastic dampers while providing advantages such as light weight and effective sound absorption. This then allows porous layers to be used as multi-functional noise and vibration control solutions in automotive and aerospace applications. Further, the addition of bulk elasticity to the solid phase of the porous medium is beneficial since it improves damping performance compared to equivalent limp treatments. In the work summarized here, porous media, such as fibers and foams, were designed to serve as treatments for various vibrating structures to examine their damping effectiveness. Both analytical modeling and numerical simulation based on finite element methods were involved depending on the complexity of the structure. Specifically, a Fourier transform-based computational method was introduced as the key step to allow accurate prediction of a panel's spatial response based on its wavenumber-frequency spectrum. Parametric studies have been conducted to identify the optimal bulk properties that would allow a porous layer to provide the largest possible damping within a target frequency region. Finally, design concepts for achieving the maximum damping potential of porous layers are summarized.

Wall-pressure fluctuations associated with turbulent boundary layer of pump-jet duct and empirical spectrum modeling

This study establishes the relationship between the pressure fluctuation on outer wall of the pump-jet duct and the source term of velocity-field in the Turbulent Boundary Layer (TBL) based on the Poisson equation and develops it in frequency-wavenumber domain. The wall-pressure fluctuations caused by source terms of different TBL regions are investigated and the spatial-temporal distribution is compared through the wavenumber-frequency spectrum. The characteristics of turbulent structures are revealed in detail using the vortex scale and intensity. The empirical spectrum model is developed for the estimation of the wall-pressure fluctuations. Besides, the simulation of velocity-field source is carried out by using the Large Eddy Simulation (LES) numerical method. Results show that the logarithmic subrange has a dominant contribution to the wall-pressure fluctuations. The remarkable energy distribution at low-frequency and low-wavenumber domain is mainly reflected in the logarithmic subrange and a low-frequency diffusion exists due to the rotor and pressure gradient. The small-scale vortices corresponding to high-wavenumbers are in the viscous subrange and the contribution of large-scale vortices corresponding to low-wavenumbers are reflected in viscous, buffer and logarithmic subranges. The deformation and rotation forms of vortices migration represent in different subranges of TBL. Moreover, the empirical spectrum model can qualitatively predict the pressure fluctuations at different positions of the duct wall, providing a reference for engineering applications.

Noise generation mechanisms of a micro-tube porous trailing edge

The noise generation and flow characteristics of a forced-transitioned NACA 0012 airfoil with a micro-tube porous trailing edge and its solid counterpart have been numerically investigated. The near-field flow dynamics and far-field noise predictions are obtained using compressible large-eddy simulations and the Ffowcs-William and Hawkings acoustic analogy, respectively. The computed far-field noise levels agree with experimental data, showing that the micro-tube structure reduces low-frequency trailing-edge noise without noticeably altering the noise directivity but induces additional high-frequency noise along the direction perpendicular to the airfoil chord. An in-depth analysis of the trailing-edge flow and surface pressure fields reveals that the noise reduction is largely linked to the ‘cross-jet-like’ flow permeation through the micro-tube structures. The interaction between the flow permeation and the boundary layer turbulence leads to a reduction in the strength of the Reynolds-stress source term in the pressure-side flow field and a reduction in the magnitude of the source terms in Amiet’s trailing-edge noise model. Spectral proper orthogonal decomposition is performed to identify flow structures that are spatially and temporally coherent within the micro-tube geometries and to link the flow features to the attenuation in noise scattering efficiency. The effect of the micro-tube structure on the wavenumber–frequency spectra of the trailing-edge surface pressure field is quantitatively analysed. Additional high-energy regions exist in the wavenumber–frequency spectra of the porous trailing edge, resulting from the turbulent eddies that permeate through the micro-tubes. Further, the high-frequency noise increase mechanism is identified as the acoustic dipole noise arising from interactions of edge-induced flow separation with the suction-side surface.

Wall-pressure fluctuations in weakly compressible turbulent channel flow

Wall-pressure fluctuations in turbulent wall-bounded flows are detrimental in many applications because they can cause structural vibrations and acoustic radiation. Their spectral behavior at subconvective wavenumbers are to date poorly understood and predicted, particularly in low-Mach-number flows. In this study, compressible direct numerical simulation is employed to elucidate the low-wavenumber behavior of wall-pressure fluctuations in turbulent channel flow and the effect of flow Mach number in the nearly incompressible regime. Simulations are conducted at bulk Mach numbers of 0.4, 0.2, and 0.1, and friction Reynolds number of 180. In addition to the convective ridge that is virtually Mach-number independent, acoustic ridges representing longitudinal and oblique waves are clearly identified in the two-dimensional wavenumber-frequency spectrum. The acoustic peaks are orders of magnitude weaker than the convective peak and decay with flow Mach number, but remain distinctly identifiable even at Mach 0.1. The acoustic energy in the supersonic wavenumber range is significantly enhanced by the onset of the first oblique mode but not much affected by the higher modes. The effect of a small, two-dimensional surface hump is also considered, which is shown to elevate the spectral level of the fluctuating wall pressure in the subconvective wavenumber range by several decades due to acoustic diffraction by the hump. [Work supported by the U.S. Office of Naval Research.]

Validation of zero-group-velocity feature guided waves in a welded joint

Extensive research has been conducted on zero-group-velocity (ZGV) Lamb waves in elastic plates, demonstrating significant progress in the field of nondestructive testing. However, there is a scarcity of studies focusing on ZGV modes in complex structures. In this paper, we present our research investigating the presence of ZGV feature guided waves (FGWs) in a welded joint. Our approach follows a similar methodology used to study ZGV Lamb waves in elastic plates. By employing two-dimensional (2D) finite element (FE) modeling, we analyze the response spectra of the welded joint when subjected to a force source, revealing the occurrence of resonance in the response spectra. To investigate resonance modes in the welded joint, we employ the three-dimensional (3D) time-step FE method. By applying spatial 2D and short-time Fourier transforms to the received time-domain signals, we analyze the frequency content and spatial distribution of the signals. This analysis allows us to verify the existence of non-propagation and propagation modes in the welded joint. The non-propagation mode refers to the presence of signals with a zero wavenumber, indicating that they do not propagate or travel along the welded joint. These signals are typically associated with local resonances or vibrations within the welded joint itself. On the other hand, the propagation mode corresponds to signals with nonzero wavenumbers, suggesting that they propagate or travel along the welded joint. Furthermore, by further analyzing the propagation mode in the welded joint, similar to the analysis of ZGV modes in solid plates, we have observed that it also exhibits ZGV characteristics based on the wavenumber-frequency spectra. To further analyze acoustic field distributions at resonance frequencies, we utilize the semi-analytical finite element method in conjunction with the perfectly matched layer method. The results obtained from this analysis are consistent with those obtained from the 2D FE method and 3D time-step FE method, thereby confirming that propagation modes with ZGV characteristics at resonance frequencies correspond to FGWs, which we refer to as ZGV-FGWs. Through this step-by-step analysis, we ultimately establish the existence of ZGV-FGWs in the welded joint. This study introduces fresh ideas and serves as a point of reference for future research on ZGV-FGWs in complex structures.

An efficient method for simulating fluctuating wind speed fields in two-spatial dimensions based on a frequency-dependent acceptance-rejection scheme

The simulation of fluctuating wind speed fields holds paramount importance in the wind-resistant design of significant structures such as high-rise buildings, long-span bridges, and wind turbines. To address the computational challenges posed by the original spectral representation method (SRM), a novel approach has emerged. This approach, rooted in the frequency-wavenumber spectrum (FWS), offers a solution to the complexities associated with the original SRM. An enhanced non-uniform discrete technique based on the acceptance-rejection (A-R) criterion was introduced to improve the efficiency of the FWS-based SRM. Nonetheless, this technique currently faces certain constrains, including its demand for a substantial allocation of random access memory (RAM) and its inability to be seamlessly integrated with the fast Fourier transform (FFT) algorithm. Given this scenario, a notably more effective strategy for selecting representative points emerges -the frequency-dependent acceptance-rejection (A-R) scheme. This innovative scheme holds the advantage of diminishing RAM utilization, transforming wind field modeling from a supercomputers-exclusive task to one feasible on personal computers. Moreover, its seamless integration with FFT technology bolsters simulation efficiency. The provided numerical simulation instances of two-spatial dimensional fluctuating wind speed fields underscore the proficiency of this proposed frequency-dependent A-R scheme. The outcomes demonstrated the combined A-R and FFT technique’s efficiency and precision, in simulating two-spatial dimensions fluctuating wind speed fields.

Deep learning-based upgoing and downgoing wavefield separation for vertical seismic profile data

The vertical seismic profile (VSP) considerably aids attenuation analysis and velocity calibration, enabling high-resolution seismic exploration. However, the imaging and interpretation of VSP data require pure upgoing and downgoing wavefields, and their separation is critical in processing and interpretation. Often, achieving high precision and efficient wavefield separation can be regarded as a challenging issue. To automate this process with higher accuracy, we develop a deep-learning high-precision intelligent separation method. First, to construct a physics-driven and data-generic training set, the well-log data from different geologic environments are used to simulate the upgoing and downgoing VSP data independently. Thereafter, we train a multitask-learning neural network to regress the network weights before and after separation to tune a mapping model, which is used to implement intelligent upgoing and downgoing wavefield separation. Validation data confirm the feasibility of our method. To further study the generalizability and robustness of the method, we apply the trained model to separate the modeled and real VSP data. By analyzing the separated profiles and frequency-wavenumber spectra, it is observed that the intelligent separation method is superior to conventional methods with a balance between accuracy and efficiency. It can be concluded that our method can separate upgoing and downgoing wavefields in VSP data with excellent performance, even in complex geologic environments. Our study indicates that the multitask-learning neural network combined with a physics-driven and data-generic training set is a new strategy to separate upgoing and downgoing wavefields and deserves to be popularized and applied.

A mathematical model for the interaction of anisotropic turbulence with a rigid leading edge

This paper investigates the effect of anisotropic turbulence on generating leading-edge aerofoil–turbulence interaction noise. Thin aerofoil theory is used to model an aerofoil as a semi-infinite plate, and the scattering of incoming turbulence is solved via the Wiener–Hopf technique. This theoretical solution encapsulates the diffraction problem for gust–aerofoil interaction and is integrated over a wavenumber–frequency spectrum to account for general incoming anisotropic turbulence. We develop a novel axisymmetric wavenumber–frequency model that captures the wall-normal variation in turbulence characteristics, differing from previous approaches. Then, the method of Gaussian decomposition, in which the generalised spectra are approximated through the weighted sum of individual Gaussian eddy models, is applied to fit the turbulence model to experimental data. Comparisons with experimental data show good agreement for a range of anisotropic ratios.

Numerical study of the effects of ventilation rates on supercavity dynamics and acoustic characteristics

This paper presents a numerical simulation investigation of the hydrodynamic and acoustic characteristics of ventilated supercavities that operate at various ventilation rates. The large eddy simulation (LES) and Ffowcs Williams–Hawkings (FW-H) methods are used to solve the unsteady flow field and noise. The results show that the ventilation rate plays an important role in cavity closure forms and can improve hydrodynamic performance. There is a transition from re-entrant flow closure to a stable double-vortex tube closure form at the supercavity tail as the ventilation rate increases. Meanwhile, under the condition of a high ventilation rate, the re-entrant flow region in the cavity gradually shrinks and hairpin vortices appear, the body length of the cavity increases,and the unsteadiness at the supercavity tail is weakened. However, the turbulence intensity and integral scale both increase with the ventilation rate. Moreover, it is found that the noise is closely related to supercavity closure form. Ventilated supercavities with closure forms of double-vortex tubes have better noise performance. Interestingly, as the ventilation rate increases, the total sound pressure levels are improved. The wavenumber-frequency spectra of supercavity turbulent pulsating pressures under studied ventilation rates are similar, but there are some differences in some local areas.

Optimal Estimation Inversion of Ionospheric Electron Density from GNSS-POD Limb Measurements: Part I-Algorithm and Morphology

GNSS-LEO radio links from Precise Orbital Determination (POD) and Radio Occultation (RO) antennas have been used increasingly in characterizing the global 3D distribution and variability of ionospheric electron density (Ne). In this study, we developed an optimal estimation (OE) method to retrieve Ne profiles from the slant total electron content (hTEC) measurements acquired by the GNSS-POD links at negative elevation angles (ε < 0°). Although both OE and onion-peeling (OP) methods use the Abel weighting function in the Ne inversion, they are significantly different in terms of performance in the lower ionosphere. The new OE results can overcome the large Ne oscillations, sometimes negative values, seen in the OP retrievals in the E-region ionosphere. In the companion paper in this Special Issue, the HmF2 and NmF2 from the OE retrieval are validated against ground-based ionosondes and radar observations, showing generally good agreements in NmF2 from all sites. Nighttime hmF2 measurements tend to agree better than the daytime when the ionosonde heights tend to be slightly lower. The OE algorithm has been applied to all GNSS-POD data acquired from the COSMIC-1 (2006–2019), COSMIC-2 (2019–present), and Spire (2019–present) constellations, showing a consistent ionospheric Ne morphology. The unprecedented spatiotemporal sampling of the ionosphere from these constellations now allows a detailed analysis of the frequency–wavenumber spectra for the Ne variability at different heights. In the lower ionosphere (~150 km), we found significant spectral power in DE1, DW6, DW4, SW5, and SE4 wave components, in addition to well-known DW1, SW2, and DE3 waves. In the upper ionosphere (~450 km), additional wave components are still present, including DE4, DW4, DW6, SE4, and SW4. The co-existence of eastward- and westward-propagating wave4 components implies the presence of a stationary wave4 (SPW4), as suggested by other earlier studies. Further improvements to the OE method are proposed, including a tomographic inversion technique that leverages the asymmetric sampling about the tangent point associated with GNSS-LEO links.

Preconditioned boundary-implicit subiterative DDADI method for accuracy and efficiency enhancement in low-Mach number flows

For low-speed turbulent flows governed by compressible Navier–Stokes equations, the large disparity of phase velocities between hydrodynamic wave and acoustic wave leads to an ill-conditioned system where the numerical accuracy and efficiency are seriously affected. To tackle this issue, a preconditioned boundary-implicit subiterative diagonally dominant alternating direction implicit (DDADI) method is proposed, where a series of accuracy and convergence enhancement techniques are combined, including the Weiss-Smith’s preconditioning to reduce condition number, subiterative technique to eliminate approximation-factorization error in DDADI method, and boundary-implicit treatment to remove the accumulated error at multiblock interfaces. Several low-Mach number flows, consisting of inviscid, laminar, RANS steady flows and LES unsteady flows, are subsequently simulated to validate the good accuracy, strong robustness, and enhanced efficiency of the proposed method. Compared with unpreconditioning method, quantitative studies reveal that the residual convergence histories are significantly accelerated with preconditioning, as well as the accuracy being remarkably improved. Particularly, a low-Mach number flow past a generic-side view mirror is investigated to demonstrate the capability of present method in predicting the wavenumber-frequency spectra of the pressure fluctuations, where the acoustic and hydrodynamic modes of pressure fluctuations are both correctly presented. These results indicate that the proposed method would be a suitable selection for low-Mach turbulent and aeroacoustic problems.

Estimation of wavenumber–frequency spectra of wall pressure due to turbulent flow over a flat plate using large-eddy simulation

The wavenumber–frequency spectra (WFS) of turbulent wall pressure fluctuations are used to design underwater acoustic systems, and a method is presented to determine them for flat plate flow using large-eddy simulations (LES). First, the Reynolds averaged Navier–Stokes (RANS) analysis is carried out for flow over the plate using k–ω shear-stress transport model. Flow parameters are extracted from the output of this analysis and used to impose boundary conditions for large-eddy simulations using a smaller domain with finer mesh. Mesh convergence studies are done to establish the adequacy of the proposed meshing scheme for estimating the turbulent boundary layer wall pressures. The stream-wise velocity profiles, turbulence intensities, and power spectra obtained using LES are compared with other computational and experimental results. The time history of fluctuating pressure on the wall at various stream-wise locations is used to estimate the WFS. Estimations are made of the convective ridge as well as sub-convective and low wavenumber portions of the spectrum. The computations are performed at momentum thickness-based Reynolds numbers (Rθ) of 5761, 7988, and 7709. The effect of downstream distance on the WFS is studied by computing it at three downstream locations and shown that the downstream distance has little effect on the WFS once the flow has become fully turbulent. The use of a desktop workstation for the estimation of WFS has not been reported earlier. The results show that the WFS of turbulent pressure due to flow over more complex geometries can be estimated using a similar method.