scholarly journals SPECTRA AND BISPECTRA OF OCEAN WAVES

1974 ◽  
Vol 1 (14) ◽  
pp. 16
Author(s):  
Ole Gunnar Houmb
Keyword(s):  
Power Spectrum ◽  
Water Waves ◽  
Surface Displacement ◽  
Ocean Waves ◽  
Higher Order ◽  
Order Effects ◽  
Two Dimensional ◽  
Wave Surface ◽  
Linear Superposition ◽  
Breaking Energy

The two dimensional (directional) power spectrum gives an adequate description of water waves that may be regarded as a linear superposition of statistically independent waves. In such cases the sea surface is linear to the first order and the surface displacement is represented by CO n(t) = Z an sm(u> t + n) n=l where an are the amplitudes of individual waves and is a Tn randomly distributed phase angle, and the process is stationary. Under such circumstances the wave surface is Gaussian, which means that ordinates measured from MWL are normally distributed rf they are sampled at constant intervals of time. It is equally important that the wave heights are Rayleigh distributed. This formulation of the wave surface is widely used e.g. in wave forecasting. There are, however, phenomena such as wave breaking, energy transfer between wave components and surf beat which can only be described by higher order effects of wave motion (1, 2, 3, 4). In this case the two dimensional power spectrum fails to give an accurate description of the wave surface. This means that the first and second order moments (mean and covariance) no longer give all the probability information, and we have to consider higher order moments (5, 6, 7).

A new equation describing travelling water waves

2013 ◽  
Vol 717 ◽  
pp. 514-522 ◽  
Author(s):  
Katie Oliveras ◽  
Vishal Vasan
Keyword(s):  
Water Waves ◽  
Water Wave ◽  
Single Equation ◽  
Travelling Wave ◽  
Higher Order ◽  
Stokes Wave ◽  
Two Dimensional ◽  
Wave Surface ◽  
New Equation ◽  
New Formulation

AbstractA new single equation for the surface elevation of a travelling water wave in an incompressible, inviscid, irrotational fluid is derived. This new equation is derived without approximation from Euler’s equations, valid for both a one- and two-dimensional travelling-wave surface. We show that this new formulation can be used to efficiently derive higher-order Stokes-wave approximations, and pose that this new formulation provides a useful framework for further investigation of travelling water waves.

Mass transport in two-dimensional water waves

1991 ◽  
Vol 231 ◽  
pp. 395-415 ◽  
Author(s):  
Mohamed Iskandarani ◽  
Philip L.-F. Liu
Keyword(s):  
Mass Transport ◽  
Water Waves ◽  
Surface Displacement ◽  
Flow Region ◽  
Two Dimensional ◽  
Governing Equations ◽  
Free Surface Displacement ◽  
Inhomogeneous Flow ◽  
Flow Domain ◽  
Transport Flow

Mass transport in various kind of two-dimensional water waves is studied. The characteristics of the governing equations for the mass transport depend on the ratio of viscous lengthscale to the amplitude of the free-surface displacement. When this ratio is small, the nonlinearity is important and the mass transport flow acquires a boundary-layer character. Numerical schemes are developed to investigate mass transport in a partially reflected wave and above a hump in the seabed. When the mass transport is periodic in the horizontal direction, a spectral scheme based on a Fourier–Chebyshev expansion, is presented for the solution of the equations. For the ease of a hump on the seabed, the flow domain is divided into three regions. Using the spectral scheme, the mass transport in the uniform-depth regions is calculated first. and the results are used to compute the steady flow in the inhomogeneous flow region which encloses the hump on the seabed.

On the dynamics of unsteady gravity waves of finite amplitude Part 2. Local properties of a random wave field

1961 ◽  
Vol 11 (1) ◽  
pp. 143-155 ◽  
Author(s):  
O. M. Phillips
Keyword(s):  
Kinetic Energy ◽  
Wave Field ◽  
Root Mean Square ◽  
Surface Displacement ◽  
Higher Order ◽  
Random Wave ◽  
Order Effects ◽  
Mean Square ◽  
Local Properties ◽  
The Mean

Expressions in closed form are derived for a number of local properties of a random, irrotational wave field. They are: (i) the mean potential and kinetic energies per unit projected area; (ii) the energy balance among the processes of energy input from the surface pressure fluctuations, rate of growth of potential and kinetic energy and horizontal energy flux; and (iii) the partition between potential and kinetic energy. These expressions are mainly in terms of quantities measured at the free surface, which are therefore functions of only two spatial variables (x, y) and of time t.Approximations for these expressions can be found simply by subsequent expansion methods; the fourth order being the highest for which the assumption of irrotational motion is appropriate in a real fluid. It is shown that the mean product of any three first-order quantities is of fourth or higher order in the root-mean-square wave slope, and this result is applied in estimating the magnitude of some higher order effects. In particular, the skewness of the surface displacement is of the order of the root-mean-square surface slope, which has been confirmed observationally by Kinsman (1960).

Phase-averaged equation for water waves

2013 ◽  
Vol 718 ◽  
pp. 280-303 ◽  
Author(s):  
Odin Gramstad ◽  
Michael Stiassnie
Keyword(s):  
Kinetic Equation ◽  
Time Scale ◽  
Water Waves ◽  
Order Effects ◽  
Two Dimensional ◽  
Spectral Evolution ◽  
Weakly Nonlinear ◽  
Averaged Equations ◽  
Numerical Solver ◽  
Fast Field

AbstractWe investigate phase-averaged equations describing the spectral evolution of dispersive water waves subject to weakly nonlinear quartet interactions. In contrast to Hasselmann’s kinetic equation, we include the effects of near-resonant quartet interaction, leading to spectral evolution on the ‘fast’ $O({\epsilon }^{- 2} )$ time scale, where $\epsilon $ is the wave steepness. Such a phase-averaged equation was proposed by Annenkov & Shrira (J. Fluid Mech., vol. 561, 2006b, pp. 181–207). In this paper we rederive their equation taking some additional higher-order effects related to the Stokes correction of the frequencies into account. We also derive invariants of motion for the phase-averaged equation. A numerical solver for the phase-averaged equation is developed and successfully tested with respect to convergence and conservation of invariants. Numerical simulations of one- and two-dimensional spectral evolution are performed. It is shown that the phase-averaged equation describes the ‘fast’ evolution of a spectrum on the $O({\epsilon }^{- 2} )$ time scale well, in good agreement with Monte-Carlo simulations using the Zakharov equation and in qualitative agreement with known features of one- and two-dimensional spectral evolution. We suggest that the phase-averaged equation may be a suitable replacement for the kinetic equation during the initial part of the evolution of a wave field, and in situations where ‘fast’ field evolution takes place.

Higher Order Effects of Interactions in Two-Dimensional Weakly Localized Regime

1983 ◽  
Vol 52 (1) ◽  
pp. 16-17 ◽  
Author(s):  
Hidetoshi Fukuyama ◽  
Yoshimasa Isawa ◽  
Hiroshi Yasuhara
Keyword(s):  
Higher Order ◽  
Order Effects ◽  
Two Dimensional ◽  
Higher Order Effects

Time after time: support for memory accounts of temporal preparation.

2019 ◽  
Author(s):  
Joe Butler ◽  
Samuel Ngabo ◽  
Marcus Missal
Keyword(s):  
Response Times ◽  
Reaction Times ◽  
Evidence Base ◽  
Higher Order ◽  
Order Effects ◽  
Previous Trial ◽  
Adaptive Responses ◽  
Temporal Preparation ◽  
Subsequent Trial ◽  
Higher Order Effects

Complex biological systems build up temporal expectations to facilitate adaptive responses to environmental events, in order to minimise costs associated with incorrect responses, and maximise the benefits of correct responses. In the lab, this is clearly demonstrated in tasks which show faster response times when the period between warning (S1) and target stimulus (S2) on the previous trial was short and slower when the previous trial foreperiod was long. The mechanisms driving such higher order effects in temporal preparation paradigms are still under debate, with key theories proposing that either i) the foreperiod leads to automatic modulation of the arousal system which influences responses on the subsequent trial, or ii) that exposure to a foreperiod results in the creation of a memory trace which is used to guide responses on the subsequent trial. Here we provide data which extends the evidence base for the memory accounts, by showing that previous foreperiod exposures are cumulative with reaction times shortening after repeated exposures; whilst also demonstrate that the higher order effects associated with a foreperiod remain active for several trials.

Two-Dimensional Local Deep-Level Transient Spectroscopy Imaging Using Super-Higher-Order Scanning Nonlinear Dielectric Microscopy

2016 ◽  
Author(s):  
N. Chinone ◽  
Y. Cho ◽  
R. Kosugi ◽  
Y. Tanaka ◽  
S. Harada ◽  
...  
Keyword(s):  
Deep Level Transient Spectroscopy ◽  
Deep Level ◽  
Higher Order ◽  
Trap Density ◽  
New Technique ◽  
Two Dimensional ◽  
Nonlinear Dielectric ◽  
Annealing Conditions ◽  
Transient Spectroscopy ◽  
A New Technique

Abstract A new technique for local deep level transient spectroscopy (DLTS) imaging using super-higher-order scanning nonlinear dielectric microscopy is proposed. Using this technique. SiCVSiC structure samples with different post oxidation annealing conditions were measured. We observed that the local DLTS signal decreases with post oxidation annealing (POA), which agrees with the well-known phenomena that POA reduces trap density. Furthermore, obtained local DLTS images had dark and bright areas, which is considered to show the trap distribution at/near SiCVSiC interface.

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