Planetary waves in a stratified ocean of variable depth. Part 1. Two-layer model

1999 ◽  
Vol 388 ◽  
pp. 115-145 ◽  
Author(s):  
G. M. REZNIK ◽  
T. B. TSYBANEVA
Keyword(s):  
Multiple Scales ◽  
Lower Layer ◽  
Numerical Technique ◽  
Bottom Topography ◽  
Relative Magnitude ◽  
Relative Strength ◽  
Small Scale ◽  
Bottom Relief ◽  
Stratified Ocean ◽  
Mesoscale Motion

Linear Rossby waves in a two-layer ocean with a corrugated bottom relief (the isobaths are straight parallel lines) are investigated. The case of a rough bottom relief (the wave scale L is much greater than the bottom relief scale Lb) is studied analytically by the method of multiple scales. A special numerical technique is developed to investigate the waves over a periodic bottom relief for arbitrary relationships between L and Lb.There are three types of modes in the two-layer case: barotropic, topographic, and baroclinic. The structure and frequencies of the modes depend substantially on the ratio Δ = (Δh/h2)/(L/a) measuring the relative strength of the topography and β-effect. Here Δh/h2 is the typical relative height of topographic inhomogeneity and a is the Earth's radius. The topographic and barotropic mode frequencies depend weakly on the stratification for small and large Δ and increase monotonically with increasing Δ. Both these modes become close to pure topographic modes for Δ>1.The dependence of the baroclinic mode on Δ is more non-trivial. The frequency of this mode is of the order of f0L2i/aL (Li is the internal Rossby scale) irrespective of the magnitude of Δ. At the same time the spatial structure of the mode depends strongly on Δ. With increasing Δ the relative magnitude of motion in the lower layer decreases. For Δ>1 the motion in the mode is confined mainly to the upper layer and is very weak in the lower one. A similar concentration of mesoscale motion in an upper layer over an abrupt bottom topography has been observed in the real ocean many times.Another important physical effect is the so-called ‘screening’. It implies that for Lb<Li the small-scale component of the wave with scale Lb is confined to the lower layer, whereas in the upper layer the scale of the motion L is always greater than or of the order of, Li. In other words, the stratification prevents the ingress of motion with scale smaller than the internal Rossby scale into the main thermocline.

scholarly journals Nonlinear vibration analysis of the nanobeams subjected to magneto-electro-thermo loading based on a novel HSDT

2021 ◽  
Author(s):  
Reza Mohammadi
Keyword(s):  
Nonlinear Vibration ◽  
Frequency Ratio ◽  
Vibration Analysis ◽  
Multiple Scales ◽  
Numerical Technique ◽  
Perturbation Technique ◽  
Equations Of Motion ◽  
Nonlocal Elasticity Theory ◽  
Small Scale ◽  
Nonlinear Frequency

Abstract In this paper, the nonlinear vibration analysis of the nanobeams subjected to magneto-electro-thermo loading based on a novel HSDT is studied. Nonlocal elasticity theory is applied to consider the small scale effect. The nonlinear equations of motion are derived using Hamilton’s principle. First, a Galerkin-based numerical technique is applied to reduce the nonlinear governing equation into a set of Duffing-type time-dependent differential equations. Afterward, the analytical solutions are derived based on the method of multiple scales (MMS) and perturbation technique. All of the mechanical properties of the beam are temperature dependent. The impacts of the several variables are investigated on the nonlinear frequency ratio of the nanobeams. The results illustrate that when maximum deflection is smaller/ greater than 0.2, its impact on the nonlinear frequency ratio will decrease/increase.

Geomechanical and Fracture Network Interpretation of a Devonian Outcrop

2021 ◽  
pp. 1-16
Author(s):  
Scott McKean ◽  
Simon Poirier ◽  
Henry Galvis-Portilla ◽  
Marco Venieri ◽  
Jeffrey A. Priest ◽  
...  
Keyword(s):  
Large Scale ◽  
Multiple Scales ◽  
Fracture Network ◽  
Natural Fracture ◽  
Small Scale ◽  
Nugget Effect ◽  
Schmidt Hammer ◽  
Unconventional Reservoir ◽  
Fracture Anisotropy ◽  
Fracture Intensity

Summary The Duvernay Formation is an unconventional reservoir characterized by induced seismicity and fluid migration, with natural fractures likely contributing to both cases. An alpine outcrop of the Perdrix and Flume formations, correlative with the subsurface Duvernay and Waterways formations, was investigated to characterize natural fracture networks. A semiautomated image-segmentation and fracture analysis was applied to orthomosaics generated from a photogrammetric survey to assess small- and large-scale fracture intensity and rock mass heterogeneity. The study also included manual scanlines, fracture windows, and Schmidt hammer measurements. The Perdrix section transitions from brittle fractures to en echelon fractures and shear-damage zones. Multiple scales of fractures were observed, including unconfined, bedbound fractures, and fold-relatedbed-parallel partings (BPPs). Variograms indicate a significant nugget effect along with fracture anisotropy. Schmidt hammer results lack correlation with fracture intensity. The Flume pavements exhibit a regionally extensive perpendicular joint set, tectonically driven fracturing, and multiple fault-damage zones with subvertical fractures dominating. Similar to the Perdrix, variograms show a significant nugget effect, highlighting fracture anisotropy. The results from this study suggest that small-scale fractures are inherently stochastic and that fractures observed at core scale should not be extrapolated to represent large-scale fracture systems; instead, the effects of small-scale fractures are best represented using an effective continuum approach. In contrast, large-scale fractures are more predictable according to structural setting and should be characterized robustly using geological principles. This study is especially applicable for operators and regulators in the Duvernay and similar formations where unconventional reservoir units abut carbonate formations.

scholarly journals RFaNet: Receptive Field-Aware Network with Finger Attention for Fingerspelling Recognition Using a Depth Sensor

Mathematics ◽  
2021 ◽  
Vol 9 (21) ◽  
pp. 2815
Author(s):  
Shih-Hung Yang ◽  
Yao-Mao Cheng ◽  
Jyun-We Huang ◽  
Yon-Ping Chen
Keyword(s):  
Receptive Field ◽  
American Sign Language ◽  
Multiple Scales ◽  
Receptive Fields ◽  
Depth Image ◽  
Small Scale ◽  
Feature Maps ◽  
Depth Sensor ◽  
Depth Images ◽  
Effective Transfer

Automatic fingerspelling recognition tackles the communication barrier between deaf and hearing individuals. However, the accuracy of fingerspelling recognition is reduced by high intra-class variability and low inter-class variability. In the existing methods, regular convolutional kernels, which have limited receptive fields (RFs) and often cannot detect subtle discriminative details, are applied to learn features. In this study, we propose a receptive field-aware network with finger attention (RFaNet) that highlights the finger regions and builds inter-finger relations. To highlight the discriminative details of these fingers, RFaNet reweights the low-level features of the hand depth image with those of the non-forearm image and improves finger localization, even when the wrist is occluded. RFaNet captures neighboring and inter-region dependencies between fingers in high-level features. An atrous convolution procedure enlarges the RFs at multiple scales and a non-local operation computes the interactions between multi-scale feature maps, thereby facilitating the building of inter-finger relations. Thus, the representation of a sign is invariant to viewpoint changes, which are primarily responsible for intra-class variability. On an American Sign Language fingerspelling dataset, RFaNet achieved 1.77% higher classification accuracy than state-of-the-art methods. RFaNet achieved effective transfer learning when the number of labeled depth images was insufficient. The fingerspelling representation of a depth image can be effectively transferred from large- to small-scale datasets via highlighting the finger regions and building inter-finger relations, thereby reducing the requirement for expensive fingerspelling annotations.

scholarly journals WS-AM: Weakly Supervised Attention Map for Scene Recognition

Electronics ◽  
2019 ◽  
Vol 8 (10) ◽  
pp. 1072 ◽  
Author(s):  
Shifeng Xia ◽  
Jiexian Zeng ◽  
Lu Leng ◽  
Xiang Fu
Keyword(s):  
Large Scale ◽  
Multiple Scales ◽  
Scene Recognition ◽  
Small Scale ◽  
Great Success ◽  
Global Feature ◽  
Benchmark Datasets ◽  
Local Mean ◽  
Weakly Supervised ◽  
Fully Connected

Recently, convolutional neural networks (CNNs) have achieved great success in scene recognition. Compared with traditional hand-crafted features, CNN can be used to extract more robust and generalized features for scene recognition. However, the existing scene recognition methods based on CNN do not sufficiently take into account the relationship between image regions and categories when choosing local regions, which results in many redundant local regions and degrades recognition accuracy. In this paper, we propose an effective method for exploring discriminative regions of the scene image. Our method utilizes the gradient-weighted class activation mapping (Grad-CAM) technique and weakly supervised information to generate the attention map (AM) of scene images, dubbed WS-AM—weakly supervised attention map. The regions, where the local mean and the local center value are both large in the AM, correspond to the discriminative regions helpful for scene recognition. We sampled discriminative regions on multiple scales and extracted the features of large-scale and small-scale regions with two different pre-trained CNNs, respectively. The features from two different scales were aggregated by the improved vector of locally aggregated descriptor (VLAD) coding and max pooling, respectively. Finally, the pre-trained CNN was used to extract the global feature of the image in the fully- connected (fc) layer, and the local features were combined with the global feature to obtain the image representation. We validated the effectiveness of our method on three benchmark datasets: MIT Indoor 67, Scene 15, and UIUC Sports, and obtained 85.67%, 94.80%, and 95.12% accuracy, respectively. Compared with some state-of-the-art methods, the WS-AM method requires fewer local regions, so it has a better real-time performance.

Dynamics of the Ningaloo Current off Point Cloates, Western Australia

2006 ◽  
Vol 57 (3) ◽  
pp. 291 ◽  
Author(s):  
Mun Woo ◽  
Charitha Pattiaratchi ◽  
William Schroeder
Keyword(s):  
Numerical Model ◽  
Continental Shelf ◽  
Western Australia ◽  
Bottom Topography ◽  
Volume Transport ◽  
Relative Strength ◽  
Cross Sectional ◽  
Leeuwin Current ◽  
The North ◽  
Tropical Water

The Ningaloo Current (NC) is a wind-driven, northward-flowing current present during the summer months along the continental shelf between the latitudes of 22° and 24°S off the coastline of Western Australia. The southward flowing Leeuwin Current is located further offshore and flows along the continental shelf break and slope, transporting warm, relatively fresh, tropical water poleward. A recurrent feature, frequently observed in satellite images (both thermal and ocean colour), is an anti-clockwise circulation located offshore Point Cloates. Here, the seaward extension of the coastal promontory blocks off the broad, gradual southern shelf, leaving only a narrow, extremely steep shelf to the north. The reduction in the cross-sectional area, from the coast to the 50 m contour, between southward and northward of the promontory is ~80%. Here, a numerical model study is undertaken to simulate processes leading to the development of the recirculation feature offshore Point Cloates. The numerical model output reproduced the recirculation feature and indicated that a combination of southerly winds, and coastal and bottom topography, off Point Cloates is responsible for the recirculation. The results also demonstrated that stronger southerly winds generated a higher volume transport in the NC and that the recirculation feature was dependent on the wind speed, with stronger winds decreasing the relative strength of the recirculation.

scholarly journals The relative contributions of scattering and viscoelasticity to the attenuation of S waves in Earth's mantle

Solid Earth ◽  
2020 ◽  
Vol 11 (1) ◽  
pp. 161-171
Author(s):  
Susini deSilva ◽  
Vernon F. Cormier
Keyword(s):  
Dominant Frequency ◽  
Relative Strength ◽  
Density Fluctuations ◽  
Body Waves ◽  
Small Scale ◽  
Thermodynamic Models ◽  
S Waves ◽  
Intrinsic Attenuation ◽  
Apparent Attenuation ◽  
Deep Focus

Abstract. The relative contributions of scattering and viscoelastic attenuation to the apparent attenuation of seismic body waves are estimated from synthetic and observed S waves multiply reflected from Earth's surface and the core–mantle boundary. The synthetic seismograms include the effects of viscoelasticity and scattering from small-scale heterogeneity predicted from both global tomography and from thermodynamic models of mantle heterogeneity that have been verified from amplitude coherence measurements of body waves observed at dense arrays. Assuming thermodynamic models provide an estimate of the maximum plausible power of heterogeneity measured by elastic velocity and density fluctuations, we predict a maximum scattering contribution of 43 % to the total measured attenuation of mantle S waves having a dominant frequency of 0.05 Hz. The contributions of scattering in the upper and lower mantle to the total apparent attenuation are estimated to be roughly equal. The relative strength of the coda surrounding observed ScSn waves from deep focus earthquakes is not consistent with a mantle having zero intrinsic attenuation.

Scattering of internal tides by irregular bathymetry of large extent

2014 ◽  
Vol 747 ◽  
pp. 481-505 ◽  
Author(s):  
Yile Li ◽  
Chiang C. Mei
Keyword(s):  
Gravity Waves ◽  
Method Of Characteristics ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Internal Gravity Waves ◽  
Internal Tides ◽  
Two Dimensional ◽  
One Dimensional ◽  
Stratified Ocean ◽  
Stationary Random Function

AbstractWe present an analytical theory of scattering of tide-generated internal gravity waves in a continuously stratified ocean with a randomly rough seabed. Based on a linearized approximation, the idealized case of constant mean sea depth and Brunt–Väisälä frequency is considered. The depth fluctuation is assumed to be a stationary random function of space, characterized by small amplitude and a correlation length comparable to the typical wavelength. For both one- and two-dimensional topographies the effects of scattering on the wave phase over long distances are derived explicitly by the method of multiple scales. For one-dimensional topography, numerical results are compared with Bühler & Holmes-Cerfon (J. Fluid Mech., vol. 678, 2011, pp. 271–293), computed by the method of characteristics. For two-dimensional topography, new results are presented for both statistically isotropic and anisotropic cases.

The Small Scale Effect on Linear Vibration of Beam-Like Nanostructures

2012 ◽  
Vol 446-449 ◽  
pp. 3432-3435
Author(s):  
Cheng Li ◽  
Lin Quan Yao
Keyword(s):  
Axial Load ◽  
Vibration Mode ◽  
Multiple Scales ◽  
Separation Of Variables ◽  
Classical Mechanics ◽  
Small Scale ◽  
Transverse Displacement ◽  
Linear Vibration ◽  
Small Scale Effect ◽  
Multiple Scales Analysis

Transverse free dynamics of a beam-like nanostructure with axial load is investigated. The effects of a small size at nano-scale unavailable in classical mechanics are presented. Explicit solutions for natural frequency, vibration mode and transverse displacement are obtained by separation of variables and multiple scales analysis. Results by two methods are in close agreement.

scholarly journals Scattering of surface gravity waves by bottom topography with a current

2007 ◽  
Vol 576 ◽  
pp. 235-264 ◽  
Author(s):  
FABRICE ARDHUIN ◽  
RUDY MAGNE
Keyword(s):  
Gravity Waves ◽  
Bottom Topography ◽  
Wave Spectrum ◽  
Action Spectrum ◽  
Wave Action ◽  
Surface Gravity ◽  
Small Scale ◽  
Surface Gravity Waves ◽  
Reflected Wave ◽  
A Current

A theory is presented that describes the scattering of random surface gravity waves by small-amplitude topography, with horizontal scales of the order of the wavelength, in the presence of an irrotational and almost uniform current. A perturbation expansion of the wave action to order η2 yields an evolution equation for the wave action spectrum, where η = max(h)/H is the small-scale bottom amplitude normalized by the mean water depth. Spectral wave evolution is proportional to the bottom elevation variance at the resonant wavenumbers, representing a Bragg scattering approximation. With a current, scattering results from a direct effect of the bottom topography, and an indirect effect of the bottom through the modulations of the surface current and mean surface elevation. For Froude numbers of the order of 0.6 or less, the bottom topography effects dominate. For all Froude numbers, the reflection coefficients for the wave amplitudes that are inferred from the wave action source term are asymptotically identical, as η goes to zero, to previous theoretical results for monochromatic waves propagating in one dimension over sinusoidal bars. In particular, the frequency of the most reflected wave components is shifted by the current, and wave action conservation results in amplified reflected wave energies for following currents. Application of the theory to waves over current-generated sandwaves suggests that forward scattering can be significant, resulting in a broadening of the directional wave spectrum, while back-scattering should be generally weaker.

A FINITE ELEMENT CODE FOR THE NUMERICAL SOLUTION OF THE HELMHOLTZ EQUATION IN AXIALLY SYMMETRIC WAVEGUIDES WITH INTERFACES

1999 ◽  
Vol 07 (02) ◽  
pp. 83-110 ◽  
Author(s):  
NIKOLAOS A. KAMPANIS ◽  
VASSILIOS A. DOUGALIS
Keyword(s):  
Finite Element ◽  
Helmholtz Equation ◽  
Nonlocal Boundary Condition ◽  
Bottom Topography ◽  
Nonlocal Boundary ◽  
Small Scale ◽  
Far Field ◽  
Axially Symmetric ◽  
Fortran Code ◽  
Iterative Linear Solvers

We consider the Helmholtz equation in an axisymmetric cylindrical waveguide consisting of fluid layers overlying a rigid bottom. The medium may have range-dependent speed of sound and interface and bottom topography in the interior nonhomogeneous part of the waveguide, while in the far-field the interfaces and bottom are assumed to be horizontal and the problem separable. A nonlocal boundary condition based on the DtN map of the exterior problem is posed at the far-field artificial boundary. The problem is discretized by a standard Galerkin/finite element method and the resulting numerical scheme is implemented in a Fortran code that is interfaced with general mesh generation programs from the MODULEF finite element library and iterative linear solvers from QMRPACK. The code is tested on several small scale examples of acoustic propagation and scattering in the sea and its results are found to compare well with those of COUPLE.

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