Velocities for moving random surfaces

Baxevani, Anastassia; Podgórski, Krzysztof; Rychlik, Igor

doi:10.1016/s0266-8920(03)00029-8

Cited by 43 publications

(44 citation statements)

References 14 publications

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“…In a classical paper [7] LonguetHiggins has introduced velocities to study movements of random surfaces. There are several definitions of velocities proposed in the literature, see [8]. Here we will use velocity in a fixed direction θ, say.…”

Section: Velocity Of a Wind Stormmentioning

confidence: 99%

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Probabilistic Model for Wind Speed Variability Encountered by a Vessel

Rychlik¹,

Mao²

2014

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As a result of social awareness of air emission due to the use of fossil fuels, the utilization of the natural wind power resources becomes an important option to avoid the dependence on fossil resources in industrial activities. For example, the maritime industry, which is responsible for more than 90% of the world trade transport, has already started to look for solutions to use wind power as auxiliary propulsion for ships. The practical installation of the wind facilities often requires large amount of investment, while uncertainties for the corresponding energy gains are large. Therefore a reliable model to describe the variability of wind speeds is needed to estimate the expected available wind power, coefficient of the variation of the power and other statistics of interest, e.g. expected length of the wind conditions favorable for the wind-energy harvesting. In this paper, wind speeds are modeled by means of a spatio-temporal transformed Gaussian field. Its dependence structure is localized by introduction of time and space dependent parameters in the field. The model has the advantage of having a relatively small number of parameters. These parameters have natural physical interpretation and are statistically fitted to represent variability of observed wind speeds in ERA Interim reanalysis data set.

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Section: Velocity Of a Wind Stormmentioning

confidence: 99%

“…see [8] for proof. The speeds in directions θ and θ − 90˚ will be denoted by v θ , , , cos 2π 2π cos 2π …”

Section: Velocity Of a Wind Stormmentioning

confidence: 99%

Probabilistic Model for Wind Speed Variability Encountered by a Vessel

Rychlik¹,

Mao²

2014

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“…This spatio-temporal variability is due only to different velocities at different locations and times and thus is dictated by the underlying flow. Analysis of the velocity distributions of these fields can be performed by a method of [5] and it is observed that velocities are centered at the value that is the sum of the flow velocity and an additional term that is due to the non-isotropic character of the underlying stochastic field.…”

Section: 2mentioning

confidence: 99%

“…There is no unique approach to this problem and for a comprehensive treatment we refer to [5], [8], and [11]. Below we focus on a conceptually simple surface velocity that was first introduced in the pioneering work of Longuet-Higgins [8], and allows us to investigate the field dynamics or the lack thereof.…”

Section: Velocities Of a Random Field Defining Motion Of A Surface Imentioning

confidence: 99%

Dynamically evolving Gaussian spatial fields

2010

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Abstract. We discuss general non-stationary spatio-temporal surfaces that involve dynamics governed by velocity fields. The approach formalizes and expands previously used models in analysis of satellite data of significant wave heights. We start with homogeneous spatial fields and by applying an extension of the standard moving average construction we arrive to stationary in time models. The obtained surface although changing in time can be considered dynamically inactive since its velocities when sampled across the field have distributions centered at zero. We introduce a dynamical evolution to such a field by composing it with a dynamical flow governed by a given velocity field. This leads to non-stationary models that are extensions of the previous discretized auto-regressions accounting for a local velocity of traveling surface. For such a surface we demonstrate that its dynamics is a combination of dynamics introduced by the flow and the dynamics resulting from the covariance structure of the underlying stochastic field. We extend this approach to fields that are only locally stationary and have their parameters varying over a larger spatio-temporal horizon.

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“…Other approaches to the same problem have been proposed in Podgórski et al (2000) and Baxevani et al (2003), where several notions of velocity were introduced, including the one used here: 'velocity in the direction of the gradient'. Our results are different in the sense that we look at the two components of the gradient, while the cited authors expressed their results in terms of the joint distribution of the modulus and the angle.…”

Section: Speed Of Crossings and Contoursmentioning

confidence: 99%