scholarly journals Mean and variance of the Eulerian and Lagrangian horizontal velocities induced by nonlinear multi-directional irregular water waves

2021 ◽  
Vol 477 (2256) ◽  
Author(s):  
Mathias Klahn ◽  
Per A. Madsen ◽  
David R. Fuhrman
Keyword(s):  
Water Waves ◽  
Second Order ◽  
Wave Number ◽  
Order Effects ◽  
Wave Fields ◽  
Fully Nonlinear ◽  
Vertical Coordinate ◽  
Irregular Wave ◽  
Mean And Variance ◽  
The Mean

In this paper, we study the mean and variance of the Eulerian and Lagrangian fluid velocities as a function of depth below the surface of directionally spread irregular wave fields given by JONSWAP spectra in deep water. We focus on the behaviour of these quantities in the bulk of the water, and using second-order potential flow theory we derive new simple asymptotic approximations for their decay in the limit of large depth below the surface. Specifically, we show that when the depth is greater than about 1.5 peak wavelengths, the variance of the Eulerian velocity decays in proportion to exp ⁡ ( − ( 135 4 ) 1 / 3 ( − k p z ) 2 / 3 ) , and the mean Lagrangian velocity decays in proportion to 1 ( − k p z ) 1 / 6 exp ⁡ ( − ( 135 4 ) 1 / 3 ( − k p z ) 2 / 3 ) . Here, k p is the peak wave number and z is the vertical coordinate measured positively upwards from the still water level. We test the accuracy of the second-order formulation against new fully nonlinear simulations of both short crested and long crested irregular wave fields and find a good match, even when the simulations are known to be affected substantially by third-order effects. To our knowledge, this marks the first fully nonlinear investigation of the Eulerian and Lagrangian velocities below the surface in irregular wave fields.

On some consequences of the canonical transformation in the Hamiltonian theory of water waves

2009 ◽  
Vol 637 ◽  
pp. 1-44 ◽  
Author(s):  
PETER A. E. M. JANSSEN
Keyword(s):  
Frequency Spectrum ◽  
Deep Water ◽  
Canonical Transformation ◽  
Water Waves ◽  
Second Order ◽  
Order Effects ◽  
Hamiltonian Theory ◽  
Wavenumber Spectrum ◽  
Second Order Effects ◽  
Change In Mean

We discuss some consequences of the canonical transformation in the Hamiltonian theory of water waves (Zakharov, J. Appl. Mech. Tech. Phys., vol. 9, 1968, pp. 190–194). Using Krasitskii's canonical transformation we derive general expressions for the second-order wavenumber and frequency spectrum and the skewness and the kurtosis of the sea surface. For deep-water waves, the second-order wavenumber spectrum and the skewness play an important role in understanding the so-called sea-state bias as seen by a radar altimeter. According to the present approach but in contrast with results obtained by Barrick & Weber (J. Phys. Oceanogr., vol. 7, 1977, pp. 11–21), in deep water second-order effects on the wavenumber spectrum are relatively small. However, in shallow water in which waves are more nonlinear, the second-order effects are relatively large and help to explain the formation of the observed second harmonics and infra-gravity waves in the coastal zone. The second-order effects on the directional-frequency spectrum are as a rule more important; in particular it is shown how the Stokes-frequency correction affects the shape of the frequency spectrum, and it is also discussed why in the context of the second-order theory the mean-square slope cannot be estimated from time series. The kurtosis of the wave field is a relevant parameter in the detection of extreme sea states. Here, it is argued that in contrast perhaps to one's intuition, the kurtosis decreases while the waves approach the coast. This is related to the generation of the wave-induced current and the associated change in mean sea level.

scholarly journals Wave-Generated Current: A Second-Order Formulation

2020 ◽  
Vol 8 (6) ◽  
pp. 418
Author(s):  
Anne Katrine Bratland
Keyword(s):  
Wave Theory ◽  
Second Order ◽  
Stokes Drift ◽  
Wave Number ◽  
Stokes Wave ◽  
Wave Loads ◽  
Third Order ◽  
The Third ◽  
Computational Fluid Dynamics Cfd ◽  
The Mean

In Stokes’ wave theory, wave numbers are corrected in the third order solution. A change in wave number is also associated with a change in current velocity. Here, it will be argued that the current is the reason for the wave number correction, and that wave-generated current at the mean free surface in infinite depth equals half the Stokes drift. To demonstrate the validity of this second-order formulation, comparisons to computational fluid dynamics (CFD) results are shown; to indicate its effect on wave loads on structures, model tests and analyses are compared.

scholarly journals EVOLUTION OF DAMAGED ARMOR LAYER PROFILE

2011 ◽  
Vol 1 (32) ◽  
pp. 40
Author(s):  
Ali Farhadzadeh ◽  
Nobuhisa Kobayashi ◽  
Jeffrey Melby
Keyword(s):  
Water Depth ◽  
Hydrodynamic Model ◽  
Water Waves ◽  
Shallow Water Waves ◽  
Irregular Wave ◽  
Progression Model ◽  
Damage Progression ◽  
Dry Zone ◽  
The Mean ◽  
Exponential Probability

A probabilistic hydrodynamic model for the wet and dry zone on a permeable structure is developed to predict irregular wave action on the structure above the still water level. The model is based on the time-averaged continuity and momentum equations for nonlinear shallow-water waves coupled with the exponential probability distribution of the water depth. The model predicts the cross-shore variations of the mean and standard deviation of the water depth and horizontal velocity. Damage progression of a stone armor layer is predicted by modifying a formula for bed load on beaches with input from the hydrodynamic model. The damage progression model is compared with three tests by Melby and Kobayashi (1998) that lasted up to 28.5 hours. The model predicts the temporal progression of the eroded area quite well. The numerical model is very efficient and suited for a risk-based design of rubble mound structures.

Nonlinear phase-resolved reconstruction of irregular water waves

2018 ◽  
Vol 838 ◽  
pp. 544-572 ◽  
Author(s):  
Yusheng Qi ◽  
Guangyu Wu ◽  
Yuming Liu ◽  
Moo-Hyun Kim ◽  
Dick K. P. Yue
Keyword(s):  
Wave Field ◽  
Nonlinear Wave ◽  
Water Waves ◽  
Three Dimensional ◽  
Reconstruction Error ◽  
High Order ◽  
Order Effects ◽  
Wave Fields ◽  
Wave Measurements ◽  
Wave Nonlinearity

We develop and validate a high-order reconstruction (HOR) method for the phase-resolved reconstruction of a nonlinear wave field given a set of wave measurements. HOR optimizes the amplitude and phase of $L$ free wave components of the wave field, accounting for nonlinear wave interactions up to order $M$ in the evolution, to obtain a wave field that minimizes the reconstruction error between the reconstructed wave field and the given measurements. For a given reconstruction tolerance, $L$ and $M$ are provided in the HOR scheme itself. To demonstrate the validity and efficacy of HOR, we perform extensive tests of general two- and three-dimensional wave fields specified by theoretical Stokes waves, nonlinear simulations and physical wave fields in tank experiments which we conduct. The necessary $L$, for general broad-banded wave fields, is shown to be substantially less than the free and locked modes needed for the nonlinear evolution. We find that, even for relatively small wave steepness, the inclusion of high-order effects in HOR is important for prediction of wave kinematics not in the measurements. For all the cases we consider, HOR converges to the underlying wave field within a nonlinear spatial-temporal predictable zone ${\mathcal{P}}_{NL}$ which depends on the measurements and wave nonlinearity. For infinitesimal waves, ${\mathcal{P}}_{NL}$ matches the linear predictable zone ${\mathcal{P}}_{L}$, verifying the analytic solution presented in Qi et al. (Wave Motion, vol. 77, 2018, pp. 195–213). With increasing wave nonlinearity, we find that ${\mathcal{P}}_{NL}$ contains and is generally greater than ${\mathcal{P}}_{L}$. Thus ${\mathcal{P}}_{L}$ provides a (conservative) estimate of ${\mathcal{P}}_{NL}$ when the underlying wave field is not known.

scholarly journals Influence of Second-Order Effects on Thermoelastic Behaviour in the Proximity of Crack Tips on Titanium

2021 ◽  
Author(s):  
D. Palumbo ◽  
R. De Finis ◽  
F. Di Carolo ◽  
J. Vasco-Olmo ◽  
F. A. Diaz ◽  
...  
Keyword(s):  
Crack Tip ◽  
Thermoelastic Stress ◽  
Qualitative Evaluation ◽  
Second Order ◽  
Order Effects ◽  
Mean Stress ◽  
Thermoelastic Effect ◽  
Crack Tips ◽  
The Mean ◽  
Second Order Effects

Abstract Background The Stress Intensity Factor (SIF) is used to describe the stress state and the mechanical behaviour of a material in the presence of cracks. SIF can be experimentally assessed using contactless techniques such as Thermoelastic Stress Analysis (TSA). The classic TSA theory concerns the relationship between temperature and stress variations and was successfully applied to fracture mechanics for SIF evaluation and crack tip location. This theory is no longer valid for some materials, such as titanium and aluminium, where the temperature variations also depend on the mean stress. Objective The objective of this work was to present a new thermoelastic equation that includes the mean stress dependence to investigate the thermoelastic effect in the proximity of crack tips on titanium. Methods Westergaard’s equations and Williams’s series expansion were employed in order to express the thermoelastic signal, including the second-order effect. Tests have been carried out to investigate the differences in SIF evaluation between the proposed approach and the classical one. Results A first qualitative evaluation of the importance of considering second-order effects in the thermoelastic signal in proximity of the crack tip in two loading conditions at two different loading ratios, R = 0.1 and R = 0.5, consisted of comparing the experimental signal and synthetic TSA maps. Moreover, the SIF, evaluated with the proposed and classical approaches, was compared with values from the ASTM standard formulas. Conclusions The new formulation demonstrates its improved capability for describing the stress distribution in the proximity of the crack tip. The effect of the correction cannot be neglected in either Williams’s or Westergaard’s model.

Seismic Waves in a Laterally Inhomogeneous Layered Medium, Part II: Analysis

1997 ◽  
Vol 64 (1) ◽  
pp. 59-65 ◽  
Author(s):  
Ruichong Zhang ◽  
Liyang Zhang ◽  
Masanobu Shinozuka
Keyword(s):  
Half Space ◽  
Ground Motion ◽  
Scattered Wave ◽  
Wave Number ◽  
Dislocation Source ◽  
Wave Fields ◽  
Seismic Dislocation ◽  
Body Forces ◽  
The Mean ◽  
Layered Half Space

Seismic wave scattering representation for the layered half-space with lateral inhomogeneities subjected to a seismic dislocation source has been formulated in the companion paper with the use of first-order perturbation (Born-type approximation) technique. The total wave field is obtained as a superposition of the mean and the scattered wave fields, which are generated, respectively, by a series of double couples of body forces equivalent to the seismic dislocation source and by fictitious body forces equivalent to the existence of the lateral inhomogeneities in the layered half-space. The responses in both the mean and the scattered wave fields are found with the aid of an integral transform technique and wave propagation analysis. The characteristics of the scattered waves and their effects on the mean waves or corresponding induced ground and/or underground mean responses are investigated in this paper. In particular, coupling phenomena between P-SV and SH waves and wave number shifting effects between the mean and the scattered wave responses are presented in detail. With the lateral inhomogeneities being assumed as a homogeneous random field, a qualitative analysis is provided for estimating the effects of the lateral inhomogeneities on the ground motion, which is related to a fundamental issue: whether a real earth medium can or cannot be approximately considered as a laterally homogeneous layer. The effects of the lateral inhomogeneities on the ground motion time history are also presented as a quantitative analysis. Finally, a numerical example is carried out for illustration purposes.

Determination of Combined and Second Order Factor Effects for Simultaneous Optimization of Physical and Mechanical Properties of NR/BR Blend System

2014 ◽  
Vol 42 (4) ◽  
pp. 290-304
Author(s):  
Rajarajan Aiyengar ◽  
Jyoti Divecha
Keyword(s):  
Physical And Mechanical Properties ◽  
Second Order ◽  
Simultaneous Optimization ◽  
Order Effects ◽  
Elongation At Break ◽  
Five Factors ◽  
Rubber Compounds ◽  
Polybutadiene Rubber ◽  
Contour Plots

ABSTRACT The blends of natural rubber (NR), polybutadiene rubber (BR), and other forms of rubbers are widely used for enhancing the mechanical and physical properties of rubber compounds. Lots of work has been done in conditioning and mixing of NR/BR blends to improve the properties of its rubber compounds and end products such as tire tread. This article employs response surface methodology designed experiments in five factors; high abrasion furnace carbon black (N 330), aromatic oil, NR/BR ratio, sulfur, and N-oxydiethylene-2-benzothiazole sulfenamide for determination of combined and second order effects of the significant factors leading to simultaneous optimization of the NR/BR blend system. One of the overall optimum of eight properties existed at carbon 44 phr, oil 6.1 phr, NR/BR 78/22 phr with the following values of properties: tensile strength (22 MPa), elongation at break (528%), tear resistance (30 kg/mm), rebound resilience (67%), moderate hardness (68 International rubber hardness degrees) with low heat buildup (17 °C), permanent set (12%), and abrasion loss (57 mm3). More optimum combinations can easily be determined from the NR/BR blend system models contour plots.

scholarly journals A Note on the Strong Maximum Principle for Fully Nonlinear Equations on Riemannian Manifolds

2021 ◽  
Author(s):  
Alessandro Goffi ◽  
Francesco Pediconi
Keyword(s):  
Maximum Principle ◽  
Riemannian Manifolds ◽  
Mean Curvature ◽  
Strong Maximum Principle ◽  
Second Order ◽  
Fully Nonlinear Equations ◽  
Nonlinear Operators ◽  
Fully Nonlinear ◽  
Second Order Equations ◽  
Curvature Type

AbstractWe investigate strong maximum (and minimum) principles for fully nonlinear second-order equations on Riemannian manifolds that are non-totally degenerate and satisfy appropriate scaling conditions. Our results apply to a large class of nonlinear operators, among which Pucci’s extremal operators, some singular operators such as those modeled on the p- and $$\infty $$ ∞ -Laplacian, and mean curvature-type problems. As a byproduct, we establish new strong comparison principles for some second-order uniformly elliptic problems when the manifold has nonnegative sectional curvature.

scholarly journals Weighted statistical binary patterns for facial feature representation

2021 ◽  
Author(s):  
Hung Phuoc Truong ◽  
Thanh Phuong Nguyen ◽  
Yong-Guk Kim
Keyword(s):  
Comprehensive Evaluation ◽  
Facial Feature ◽  
Input Image ◽  
Feature Representation ◽  
Illumination Variation ◽  
Straight Line ◽  
Mean And Variance ◽  
The Mean ◽  
Face Datasets ◽  
Degraded Images

AbstractWe present a novel framework for efficient and robust facial feature representation based upon Local Binary Pattern (LBP), called Weighted Statistical Binary Pattern, wherein the descriptors utilize the straight-line topology along with different directions. The input image is initially divided into mean and variance moments. A new variance moment, which contains distinctive facial features, is prepared by extracting root k-th. Then, when Sign and Magnitude components along four different directions using the mean moment are constructed, a weighting approach according to the new variance is applied to each component. Finally, the weighted histograms of Sign and Magnitude components are concatenated to build a novel histogram of Complementary LBP along with different directions. A comprehensive evaluation using six public face datasets suggests that the present framework outperforms the state-of-the-art methods and achieves 98.51% for ORL, 98.72% for YALE, 98.83% for Caltech, 99.52% for AR, 94.78% for FERET, and 99.07% for KDEF in terms of accuracy, respectively. The influence of color spaces and the issue of degraded images are also analyzed with our descriptors. Such a result with theoretical underpinning confirms that our descriptors are robust against noise, illumination variation, diverse facial expressions, and head poses.

scholarly journals Groups and Individuals: Optical Flow Patterns of Broiler Chicken Flocks Are Correlated with the Behavior of Individual Birds

Animals ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 568
Author(s):  
Sabine G. Gebhardt-Henrich ◽  
Ariane Stratmann ◽  
Marian Stamp Dawkins
Keyword(s):  
Optical Flow ◽  
Broiler Chicken ◽  
Average Length ◽  
Flow Patterns ◽  
Group Level ◽  
Positive Correlation ◽  
Water Test ◽  
Mean And Variance ◽  
The Mean

Group level measures of welfare flocks have been criticized on the grounds that they give only average measures and overlook the welfare of individual animals. However, we here show that the group-level optical flow patterns made by broiler flocks can be used to deliver information not just about the flock averages but also about the proportion of individuals in different movement categories. Mean optical flow provides information about the average movement of the whole flock while the variance, skew and kurtosis quantify the variation between individuals. We correlated flock optical flow patterns with the behavior and welfare of a sample of 16 birds per flock in two runway tests and a water (latency-to-lie) test. In the runway tests, there was a positive correlation between the average time taken to complete the runway and the skew and kurtosis of optical flow on day 28 of flock life (on average slow individuals came from flocks with a high skew and kurtosis). In the water test, there was a positive correlation between the average length of time the birds remained standing and the mean and variance of flock optical flow (on average, the most mobile individuals came from flocks with the highest mean). Patterns at the flock level thus contain valuable information about the activity of different proportions of the individuals within a flock.

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