Anisotropic random wave models

Abstract : Let d be an integer greater or equal to 2 and let k be a d-dimensional random vector. We call random wave model with random wavevector k any stationary random field defined on R^d with covariance function t ∈ R d → E[cos(k.t)]. The purpose of the present paper is to link properties that concern the geometry and the anisotropy of the random wave with the distribution of the random wavevector. For instance, when k almost surely belongs to the unit sphere in R^2 and the random wave model is nothing but the anisotropic version of Berry's planar waves, we prove that the expected length of the nodal lines is decreasing as the anisotropy of the random wavevector is increasing. Also, when k almost surely belongs to the Airy surface in R^3 and the associated random wave serves as a model for the sea waves, we prove that the direction that maximises the expected length of the static crests is not always orthogonal to what we call favorite direction of the random wavevector.
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Pré-publication, Document de travail
MAP5 2018-07. 2018
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Anne Estrade, Julie Fournier. Anisotropic random wave models. MAP5 2018-07. 2018. 〈hal-01745706v2〉

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