Wavenumber Spectrum Research Articles

Estimation of the depth-variant seismic wavelet based on the modified unscaled S-transform

Seismic inversion is one of the key techniques used for reservoir characterization. Depth-domain seismic inversion eliminates the cumulative errors associated with depth-to-time and time-to-depth conversions, thus providing geologists and reservoir engineers with an intuitive basis for geological interpretation. The method has received increasing attention in the field of reservoir characterization. Extracting accurate depth-domain seismic wavelets is a prerequisite for successful depth-domain seismic inversion. However, the depth-domain wavelet is velocity-dependent and exhibits significant non-stationarity, which leads to the failure of seismic wavelet estimation methods based on the stationary convolutional model. To this end, we propose a modified wavenumber-domain unscaled S-transform (MWUST) method to accomplish accurate estimation of depth-domain seismic wavelets. The proposed method enhances the accuracy of wavenumber components by removing the linear wavenumber-dependent term from the S-transform. Furthermore, it introduces slope and intercept parameters to improve the depth resolution at low wavenumbers, thereby yielding a more reliable depth–wavenumber spectrum. Subsequently, the relationship between the non-stationary depth-domain seismic wavelet and the depth–wavenumber spectrum is established, allowing for the accurate extraction of non-stationary wavelets under the assumption that the depth-domain reflectivity is a random sequence. Synthetic and real data applications have been used to verify the effectiveness of the proposed method.

Detection of delamination using laser-generated Lamb waves with improved wavenumber analysis

Abstract Delamination is a typical failure mode in multilayered materials, which may potentially threaten the safety and reliability of the materials if not detected promptly. This paper proposes a novel quantitative detection method for delamination in multilayered materials based on laser-generated Lamb waves with improved wavenumber analysis. First, a three-dimensional(3D) finite element model is established to simulate the interaction between delamination and laser-generated Lamb waves. The propagation characteristics of Lamb waves in multilayered materials without defects and with delamination of three different shapes, i.e., rectangular, circular and triangular are analyzed. And the mechanism that delamination can lead to the appearance of scattered wave and new wavenumber components is investigated, facilitating the quantitative detection of delamination. Then, an improved wavenumber analysis method for quantitative detection of delamination is proposed. The new wavenumber components caused by delamination are extracted by broadband adaptive wavenumber filtering to reduce imaging interference and artifacts caused by irrelevant components, and the spatial wavenumber spectrum is obtained by fast broadband local wavenumber estimation algorithm to enhance the delamination imaging accuracy and spatial resolution. The experimental results indicate that, across various experimental scenarios, the proposed method achieves superior imaging precision compared to traditional wavenumber filtering or local wavenumber estimation methods, and can quantitatively identify delamination defects of various shapes and sizes.

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.

Gyrokinetic linear simulation of feedback instability in dipole magnetosphere

We perform a novel linear simulation of the feedback instability by applying a gyrokinetic model to the magnetosphere, where the geomagnetic field is modeled by a dipole magnetic field. In order to avoid huge numerical calculation costs, the effect of the fluctuating mirror force is neglected. It is found that kinetic effects, such as the finite Larmor radius effect and the electron Landau damping, strongly stabilize the feedback instability and form a peak in the perpendicular wave number spectrum of the growth rate. During the linear growth, it is observed that electron free energy has a much larger value than the electromagnetic field perturbation energy. Since such large electron free energy may lead to electron heating and acceleration, it is important to understand its generation mechanism. Analyses based on the energy conservation reveal that the coupling of the non-uniformity of the equilibrium fields along the geomagnetic field and the fluctuating electron distribution gives rise to thermodynamic power generating the electron free energy. A fine velocity space structure around an average Alfvén velocity of the fluctuating electron distribution mainly contributes to drive the thermodynamic power.

A novel amplitude enhancement method of EMAT for High-frequency Rayleigh-like waves in Circumferential propagation

Currently, in terms of resolution and excitation efficiency for pipeline inspection, the high-frequency Rayleigh-like wave excited by an EMAT with a traditional Rayleigh wave EMAT structure is not optimal when using the same magnet volume. This paper introduces an EMAT performance evaluation method focused on 'bandwidth' in the high-frequency-thickness region of circumferential guided waves. A wavenumber spectrum analysis method utilizing combined equivalent surface stresses is proposed to quantify this optimize design. Comparative studies, including theoretical analysis and experimental validation, demonstrate that incorporating bandwidth significantly improves the design of Rayleigh-like waves at high frequencies. The proposed EMAT achieves a performance improvement of 2.4 times for inside pipe excitation and 2.6 times for outside pipe excitation over the conventional structure. The occurrence of multiple wave packets outside the optimal excitation frequency range is acknowledged. Therefore, this method offers a new approach for optimizing EMATs for Rayleigh-like waves.

Utilization of spent bleaching earth as green filler and plasticizer in the manufacture of rubber compounds for solid tire production

This study utilized spent bleaching earth (SBE) as a single form of filler and plasticizer in the manufacture of rubber components for solid tire vulcanizate. SBE, an underutilized byproduct of vegetable oil purification, is abundantly available globally and can be used as a filler and plasticizer in rubber compounds. This aligns with environmental sustainability principles, reduces disposal costs, and lowers raw material expenses in rubber manufacturing. In this research, the SBE was applied for each formula from SBE-02 to SBE-05 at ratios of 15–30 per hundred rubber (phr). As a comparison, carbon black (CB) filler (65 phr), CaCO3 (35 phr), and plasticizer derived from petroleum in the form of paraffinic oil (PO) (6 phr) were used. Rubber components were produced by masticating natural and synthetic rubber in an open mill, followed by the addition of filler, plasticizer, accelerator, co-activator, anti-degradant, and vulcanization agent. The resulting compounds were vulcanized at 150 °C and 10 MPa for 17 minutes. The test results demonstrated that incorporating SBE at a ratio of 15 phr (SBE-02) significantly reduced the cure time (t90) to 8 minutes and 20 seconds, the shortest among all tested formulations. The mechanical properties of the SBE-02 vulcanizate rubber met the requirements for solid wheelchair tire applications, with a hardness of 70 Shore A. However, its abrasion resistance test result of 189.1 g/cm³ was the lowest among the formulations tested. Furthermore, the scorch time (ts2) of the SBE-02 was determined to be 2 minutes and 35 seconds. Results from a 1000x magnification scanning electron microscope (SEM) reveal air gaps on all sample surfaces of different sizes. The elements C, O, Zn, Si, Ca, and Pb dominate the SEM-EDX results for all rubber vulcanizate samples from all three spectra, in varying weight percentages. The identification of functional groups with FTIR on all rubber vulcanizate samples shows Si–O–Si bending at 2, 4, and 5 and Si–O–Al stretching at 3, 5 on the wave number spectrum of 680–413 cm−1 Si–O–Si on the wave number spectrum 1100–1050 cm−1 from the infrared spectrum.

Physical Characteristics Controlling Radiation from Heterogeneous Ruptures—Finite Faults

ABSTRACT Kinematic simulations of ground motion require representations of the earthquake source: the distribution of final slip, parameters of the source time function, and the velocity of rupture travel. There is a significant ambiguity in prescribing these physical characteristics, causing uncertainty in the resulting motions that needs to be quantified. The representation integral is an appropriate tool: it allows exact calculation of the source effect in both the near and far fields in the frequency band of practical interest. The commonly used distributions of slip have a k-square shape of their wavenumber spectra. Various k-square slips change the slope of the radiated spectra in the range of ∼−2.5 and −4.0 in both the far and near fields. The spectra generated by randomly disturbed constant slip are indistinguishable from those emitted by k-square faults. In both cases, variations in peak values of ground velocity and acceleration between realizations are relatively insignificant: under ∼15% for the same hypocenter position. The slopes of the Fourier spectra produced exclusively by the form of the slip function and the slip heterogeneity are equivalent to using a formal kappa filter with κ ranging from ∼0.025 to 0.045 s. No ad hoc high-frequency filtering (of kappa or fmax type) is required if fault finiteness is accounted for. Geometric irregularity of rupture fronts, at least for the way the front progression is randomized in our case, does not appreciably affect the slopes of the spectra. Its principal effect is in blurring the directivity, reducing the sharpness of radiated pulses. The most influential parameter affecting the peak ground motions for several commonly used slip functions is the maximum velocity of slip: scaling of vmax causes a proportional scaling in peak ground acceleration. This parameter is the most important to constrain to reduce ambiguities in predicted ground motions.

Millimeter-wave high-wavenumber scattering diagnostic developments on EAST and NSTX-U.

A pioneering 4-channel, high-k poloidal, millimeter-wave collective scattering system has been successfully developed for the Experimental Advanced Superconducting Tokamak (EAST). Engineered to explore high-k electron density fluctuations, this innovative system deploys a 270GHz mm-wave probe beam launched from Port K and directed toward Port P (both ports lie on the midplane and are 110° part), where large aperture optics capture radiation across four simultaneous scattering angles. Tailored to measure density fluctuations with a poloidal wavenumber of up to 20cm-1, this high-k scattering system underwent rigorous laboratory testing in 2023, and the installation is currently being carried out on EAST. Its primary purpose lies in scrutinizing ion and electron-scale instabilities, such as the electron temperature gradient (ETG) mode, by furnishing measurements of the kθ (poloidal wavenumber) spectrum. This advancement significantly bolsters the capacity to probe high-k electron density fluctuations within the framework of EAST. Beam tracing and data interpretation modules developed for both EAST and NSTX-U high-k scattering diagnostics are described.

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.

Research on a Near-Field Millimeter Wave Imaging Algorithm and System Based on Multiple-Input Multiple-Output Sparse Sampling

In order to reduce the hardware cost and data acquisition time in near-field scenarios, such as airport security imaging systems, this paper discusses the layout of a multiple-input multiple-output (MIMO) radar array. In view of the existing multi-input multiple-output imaging algorithm, the reconstructed image artifacts and aliasing problems caused by sparse sampling are discussed. In this paper, a multi-station radar array and a corresponding sparse MIMO imaging algorithm based on combined sparse sub-channels are proposed. By studying the wave–number spectrum of backscattered MIMO synthetic aperture radar (SAR) data, the nonlinear relationship between the wave number spectrum and reconstructed image is established. By selecting a complex gain vector, multiple channels are coherently combined effectively, thus eliminating aliasing and artifacts in the reconstructed image. At the same time, the algorithm can be used for the MIMO–SAR configuration of arbitrarily distributed transmitting and receiving arrays. A new multi-station millimeter wave imaging system is designed by using a frequency-modulated continuous wave (FMCW) chip and sliding rail platform as a planar SAR. The combination of the hardware system provides reconfiguration, convenience and economy for the combination of millimeter wave imaging systems in multiple scenes.

A cylindrical shell model with distributed springs for a rotating tire

In a companion paper (Vol. 248, Article 108227), we demonstrated the dependence of tire parameters on the modal characteristics of a stationary tire. For a more realistic scenario, when tire rotation is considered, the modal characteristics are veered due to centrifugal, Coriolis, and gyroscopic effects. In this paper, we study the forced vibration response of a rotating tire and also consider the effect of static load on modal characteristics. The tire tread is modeled as a cylindrical shell and the sidewall is modeled using distributed springs in axial, circumferential, and radial directions. The tire inflation pressure is accounted for, which generates pre-stresses in the tire belt in circumferential and axial directions. The material model incorporates an orthotropic composite structure of the tire with multiple stacked layers of steel belt reinforcing. The governing equations of motion of the rotating shell are derived and further reduced to the corresponding eigenvalue problem. Galerkin’s projection with orthogonal basis functions is used to obtain the natural frequencies and associated mode shapes. For the forced vibration, the tire is excited by a harmonic point load at a fixed location, and the response is calculated by superimposing the basis functions of the free vibration problem. The analytical model predictions are compared against the computation finite element (FE) model developed in ABAQUS® and experimental modal testing results. To understand the effects of rotation on wave propagation, dispersion relations were obtained, and the wave number spectrum of the rotating tire was compared with that of the stationary one. Finally, to understand the dependence of natural frequencies on tire rotation and normal load, Campbell diagrams and frequency response functions (FRFs) were obtained from the proposed model. The model shows a fairly good agreement with experimental results and FE simulations.

How Accurate Numerical Simulation of Seismic Waves in a Heterogeneous Medium Can Be?

ABSTRACT Analysis of equations of motion by Moczo et al. (2022) led to the conclusion that the discrete (grid) representation of the heterogeneous medium must be wavenumber bandlimited up to the Nyquist frequency. This is a consequence of the spatial discretization. Mittet (2021a) reported that if the discrete grid model of medium coincides with the true medium up to some wavenumber, the simulated wavefield is accurate only up to a half of this wavenumber. Here, we present results of the systematic and comprehensive analysis focused on the principal limits of accuracy of numerically simulated wavefields. First, we analyze wavenumber spectra of (1) exact wavefields in a heterogeneous elastic medium, (2) wavenumber bandlimited wavefields, and (3) spatially discretized wavefields. Then, we derive spatial dependence of the frequency spectrum of waves generated by a finite source, and perturbing wavefields due to a small perturbation of the medium and due to a small wavenumber bandlimited perturbation of the medium. We analyze an interaction of an incoming wave with the medium perturbation through a change of phase difference and through wavenumber spectra. We draw conclusions on the wavenumber limitation of wavefields in the wavenumber bandlimited heterogeneous medium. We numerically verify the fundamental finding using exact solutions. The main consequence for the finite-difference (FD) modeling based on spatial discretization of the computational domain is: Due to spatial sampling, the medium must be wavenumber limited up to the Nyquist frequency. Then, the wavefield should not be sampled by less than four spatial grid spacings per shortest wavelength to obtain sufficiently accurate results. This applies to any heterogeneous FD scheme.

Resonant standing surface waves excited by an oscillating cylinder in a narrow rectangular cavity

Resonant standing waves excited on the water surface in a deep narrow rectangular cavity by a fully immersed cylinder harmonically oscillating in the vertical direction are studied theoretically and experimentally. The effect of the finite wavemaker size is considered in the framework of the potential two-dimensional flow theory. Nonlinearities and weak dissipation at solid surfaces are accounted for. The spatio-temporal structure of the waves in the presence of detuning between the forcing and the natural frequency of the system is analysed. The variation of the surface shape in space and time studied in experiments supports the assumption of two-dimensional flow. The finite size of the wavemaker causes a downshift of the effective resonant frequency of the cavity; this effect is enhanced by the nonlinearity. For small amplitude waves, the surface elevation evolution in time is decomposed into the sum of the time-periodic function, corresponding to the forcing frequency, and its second harmonic; the shape of the wavenumber spectra of these components depends on the forcing frequency. For larger wave amplitudes, additional peaks in the frequency spectrum appear. The theoretical predictions are compared with the experimental results.

High-flexibility reconstruction of small-scale motions in wall turbulence using a generalized zero-shot learning

This study proposes a novel super-resolution (or SR) framework for generating high-resolution turbulent boundary layer (TBL) flow from low-resolution inputs. The framework combines a super-resolution generative adversarial neural network (SRGAN) with down-sampling modules (DMs), integrating the residual of the continuity equation into the loss function. The DMs selectively filter out components with excessive energy dissipation in low-resolution fields prior to the super-resolution process. The framework iteratively applies the SRGAN and DM procedure to fully capture the energy cascade of multi-scale flow structures, collectively termed the SRGAN-based energy cascade reconstruction framework (EC-SRGAN). Despite being trained solely on turbulent channel flow data (via ‘zero-shot transfer’), EC-SRGAN exhibits remarkable generalization in predicting TBL small-scale velocity fields, accurately reproducing wavenumber spectra compared to direct numerical simulation (DNS) results. Furthermore, a super-resolution core is trained at a specific super-resolution ratio. By leveraging this pretrained super-resolution core, EC-SRGAN efficiently reconstructs TBL fields at multiple super-resolution ratios from various levels of low-resolution inputs, showcasing strong flexibility. By learning turbulent scale invariance, EC-SRGAN demonstrates robustness across different TBL datasets. These results underscore the potential of EC-SRGAN for generating and predicting wall turbulence with high flexibility, offering promising applications in addressing diverse TBL-related challenges.

Theoretical study of short-range exchange interaction based on semiconductor dielectric function model toward time-dependent dielectric density functional theory

This study explores various models of semiconductor dielectric functions, with a specific emphasis on the large wavenumber spectrum and the derivation of the screened exchange interaction. Particularly, we discuss the short-range effect of the screened exchange potential. Our investigation reveals that the short-range effect originating from the high wavenumber spectrum is contingent upon the dielectric constant of the targeted system. To incorporate dielectric-dependent behaviors concerning the short-range aspect into the dielectric density functional theory (DFT) framework, we utilize the local Slater term and the Yukawa-type term, adjusting the ratio between these terms based on the dielectric constant. Additionally, we demonstrate the efficacy of the time-dependent dielectric DFT method in accurately characterizing the electronic structure of excited states in dyes and functional molecules. Several theoretical approaches have incorporated parameters dependent on the system to elucidate short-range exchange interactions. Our theoretical analysis and discussions will be useful for those studies.

Advanced feature extraction for the characterization of impact events on composites using multiresolution wavelet-based simulations

The detection and characterization of impact events on composite structures from the induced wave responses, involves many challenges. Coexisting guided waves of high dispersive nature propagate after impact, entailing continuous time variations in their wavenumber, frequency and group velocity content, which complicate the exact estimation of the time-of-flight and the extraction of impact characteristics. A multiresolution finite wavelet domain computational method, combined with appropriate contact laws, is presented to provide enhanced simulation and characterization capabilities of impact events. An explicit multiresolution time integration scheme involves a coarse solution, followed by finer solutions that are sequentially added to the coarse one, until convergence is achieved. The hierarchical character of the approach makes the impact simulation very fast and accurate. Moreover, due to the filtering properties of Daubechies wavelet functions, each resolution component effectively models and isolates specific wavenumber spectra, providing the capability to separate coexisting wave modes, and to overcome difficulties imposed by the dispersive nature of the resultant guided waves. It is demonstrated that the multiresolution simulation can reveal wave characteristics and time-of-flight features that no other traditional single-resolution method can do, and provides the basis for the development of powerful inverse methods that can localize the impact and characterize the impactor parameters. The method is first applied on impacted composite strips and the structural responses of each resolution component are assessed in order to obtain the desired features for impact location estimation and characterization. Finally, the method is implemented on an impacted composite plate structure and the various wave characteristics simulated by the fine components are presented, evincing the advanced features that the proposed method provides.

Efficient Guided Wave Modelling for Tomographic Corrosion Mapping via One-Way Wavefield Extrapolation

Mapping corrosion depths along pipeline sections using guided-wave-based tomographic methods is a challenging task. Accurate defect sizing depends heavily on the precision of the forward model in guided wave tomography. This model is fitted to measured data using inversion techniques. This study evaluates the effectiveness of a recursive extrapolation scheme for tomography applications and full waveform inversion. It employs a table-driven approach, with precomputed extrapolation operators stored across a spectrum of wavenumbers. This enables fast modelling for extensive pipe sections, approaching the speed of ray tracing while accurately handling complex velocity models within the full frequency band. This ensures an accurate representation of diffraction phenomena. The study examines the assumptions underlying the extrapolation approach, namely, the negligible reflection and conversion of modes at defects. In our tomography approach, we intend to use multiple wave modes—A0, S0, and SH1—and helical paths. The acoustic extrapolation method is validated through numerical studies for different wave modes, solving the 3D elastodynamic wave equation. Comparison with an experimentally measured single-mode wavefield from an aluminium plate with an artificial defect reveals good agreement.

Electrostatic microturbulence in W7-X: comparison of local gyrokinetic simulations with Doppler reflectometry measurements

The first experimental campaigns of Wendelstein 7-X (W7-X) have shown that turbulence plays a decisive role in the performance of neoclassically optimized stellarators. This stresses the importance of understanding microturbulence from the theoretical and experimental points of view. To this end, this paper addresses a comprehensive characterization of the turbulent fluctuations by means of nonlinear gyrokinetic simulations performed with the code stella in two W7-X scenarios. In the first part of the paper, the amplitude of the density fluctuations is calculated and compared with measurements obtained by Doppler reflectometry (DR) in the OP1 experimental campaigns. It is found that the trend of the fluctuations along the radius is explained by the access of the DR system to different regions of the turbulence wavenumber spectrum. In the second part of the article, frequency spectra of the density fluctuations and the zonal component of the turbulent flow are numerically characterized for comparisons against future experimental analyses. Both quantities feature broad frequency spectra with dominant frequencies of O(1)–O(10) kHz.

Wavelet-based wavenumber spectral estimate of eddy kinetic energy: Application to the North Atlantic

An ensemble of eddy-rich North Atlantic simulations is analyzed, providing estimates of eddy kinetic energy (EKE) wavenumber spectra and spectral budgets below the mixed layer where energy input from surface convection and wind stress are negligible. A wavelet transform technique is used to estimate a spatially localized ‘pseudo-Fourier’ spectrum (Uchidaet al., 2023b), permitting comparisons to be made between spectra at different locations in a highly inhomogeneous and anisotropic environment. The EKE spectra tend to be stable in time but the spectral budgets are highly time dependent. We find evidence of a Gulf Stream imprint on the near Gulf Stream eddy field appearing as enhanced levels of EKE in the (nominally) North–South direction relative to the East–West direction. Surprisingly, this signature of anisotropy holds into the quiescent interior with a tendency of the orientation aligned with maximum EKE being associated with shallower spectral slopes and elevated levels of inverse EKE cascade. Conversely, the angle associated with minimum EKE is aligned with a steeper spectral slope and forward cascade of EKE. Our results also indicate that vertical motion non-negligibly affects the direction of EKE cascade. A summary conclusion is that the spectral characteristics of eddies in the wind-driven gyre below the mixed layer where submesoscale dynamics are expected to be weak tend to diverge from expectations built on inertial-range assumptions, which are stationary in time and horizontally isotropic in space.

Surface and Sub‐Surface Kinetic Energy Wavenumber‐Frequency Spectra in Global Ocean Models and Observations

AbstractThis paper examines spectra of horizontal kinetic energy (HKE) in the surface and sub‐surface ocean, with an emphasis on internal gravity wave (IGW) motions, in global high‐resolution ocean simulations. Horizontal wavenumber‐frequency spectra of surface HKE are computed over seven oceanic regions from two global simulations of the HYbrid Coordinate Ocean Model (HYCOM) and three global simulations of the Massachusetts Institute of Technology general circulation model (MITgcm). In regions with high IGW activity, high surface HKE variance in the horizontal wavenumber‐frequency spectra is aligned along IGW linear dispersion curves. For both HYCOM and MITgcm, and in almost all regions, finer horizontal resolution yields more energetic supertidal IGW continuum spectra. The ratio of high‐horizontal‐wavenumber variance in semi‐diurnal and supertidal motions relative to lower‐frequency motions, a quantity of great interest for swath altimetry, depends on the model employed and the horizontal resolution within the model, implying that quantitative predictions of the partition between low‐ and high‐frequency motions taken from particular simulations should be treated with care. The frequency‐vertical wavenumber spectra, frequency spectra, and vertical wavenumber spectra from the models are compared to spectra computed from McLane profilers at nine locations. In general, MITgcm spectra match the McLane profiler spectra more closely at high frequencies (|ω| > 4.5 cpd). In both models, vertical wavenumber spectra roll off more steeply than observations at high vertical wavenumbers (m > 10−2 cpm). The vertical wavenumber spectra in such models is an important target for improvement, due to turbulence production and dissipation that takes place at high vertical wavenumbers.