Exact asymmetric slope distributions in stochastic Gauss–Lagrange ocean waves

Lindgren, Georg

doi:10.1016/j.apor.2009.06.002

Cited by 14 publications

(23 citation statements)

References 14 publications

(27 reference statements)

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“…All calculations and simulations were performed in MATLAB using the WAFO toolbox (see http:www.maths.lth.se/matstat/wafo/). A discussion on the theoretical results in this paper in relation to empirical wave studies is to be found in [10]. The theory presented in this paper works for two-dimensional time waves, i.e.…”

Section: Front-back Asymmetric Lagrange Time Wavesmentioning

confidence: 99%

“…The examples of front-back asymmetry in the following section are based on one orbital spectrum. A discussion of the relations to real wave data and observed asymmetry measures can be found in [10].…”

Section: If L(t) = L(t X 0 ) Is the Lagrange Time Wave And L(t) Is Imentioning

confidence: 99%

“…For the time waves, the situation is more complex, since we need to keep track of what particle is presently located at the measure station. Therefore, the relevant conditional slope distributions will have a much more complicated distribution; see [10].…”

Section: Crossing Related Wave Characteristicsmentioning

confidence: 99%

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Slope distribution in front-back asymmetric stochastic Lagrange time waves

Lindgren

2010

Adv. Appl. Probab.

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The stochastic Lagrange wave model is a realistic alternative to the Gaussian linear wave model, which has been successfully used in ocean engineering for more than half a century. In this paper we present the slope distributions and other characteristic distributions at level crossings for asymmetric Lagrange time waves, i.e. what can be observed at a fixed measuring station, thereby extending results previously given for space waves. The distributions are given as expectations in a multivariate normal distribution, and they have to be evaluated by simulation or numerical integration. Interesting characteristic variables are the slope in time, the slope in space, and the vertical particle velocity when the waves are observed close to instances when the water level crosses a predetermined level. The theory has been made possible by recent generalizations of Rice's formula for the expected number of marked crossings in random fields.

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Section: Front-back Asymmetric Lagrange Time Wavesmentioning

confidence: 99%

Section: If L(t) = L(t X 0 ) Is the Lagrange Time Wave And L(t) Is Imentioning

confidence: 99%

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Slope distribution in front-back asymmetric stochastic Lagrange time waves

Lindgren

2010

Adv. Appl. Probab.

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“…where α m = ξ/W 2 m and ξ is the parameter that donates the relation between the horizontal acceleration of water particles and vertical displacement and more detailed description can be find in [31,32]. K ave is the average wavenumber defined as…”

Section: Nonlinear Fractal Sea Surface Modelmentioning

confidence: 99%

“…A one-dimensional nonlinear fractal sea surface model has been established based on the narrow-band Lagrange model in this paper, in which the vertical and horizontal skewnesses are both considered [30][31][32]. In fact, this model has been used to study the Doppler spectrum of sea surface by Wang et al in [32], but the method used in [32] is twoscale method, which can not calculate the scattering field directly from linear and nonlinear sea surfaces.…”

Section: Introductionmentioning

confidence: 99%

Investigation on the Scattering From One-Dimensional Nonlinear Fractal Sea Surface by Second-Order Small-Slope Approximation

Luo¹,

Min²

2013

PIER

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Abstract-In this paper, a one-dimensional nonlinear fractal sea surface model has been established based on the narrow-band Lagrange model, which takes into account the vertical and horizontal skewnesses for the sea surface. By using the method of second-order small-slope approximation (SSA-II), the normalized radar cross section (NRCS) and Doppler spectrum of linear and nonlinear fractal sea surface are calculated. The calculated NRCS of the nonlinear fractal sea surface is larger than the linear surface for backscattering, especially for large incidence angles, which indicates the nonlinear surface has stronger scattering echoes. And the result of nonlinear fractal sea surface is also larger than the linear fractal sea surface for bistatic case, which is characterized as the discrepancies being small near specular direction, while the discrepancies becoming larger as the scattering angles departing from the specular direction. For the Doppler spectrum of sea surface, the nonlinearity of sea surface effects greatly enhances the Doppler shift and the Doppler spectrum bandwidth at large incidence angles, which are attributed the fact that the nonlinear-wave components propagate faster than the linear-wave components and the nonlinear fractal sea surface corrects the phase velocities by adding the horizontal and vertical skewness. And also, all the results can indicate the validity of this nonlinear model.

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