The spectral velocity tensor for homogeneous boundary-layer turbulence

Abstract

We have postulated a simple model for the spectral tensor Q,(k) of an anisotropic, but homogeneous turbulent velocity field. It is a simple generalization of the spectral tensor @$"(k) for isotropic turbulence and we show how in the limit of isotropy, @Jk) becomes equal to Q?(k). Whereas @j"(k) is determined entirely by one scalar function of k = (kl, namely the energy spectrum, we need three independent scalar functions of k to specify Qij(k). We show how it is possible by means of the three stream-wise velocity component spectra to determine the three scalar functions in aij(k) by solving two uncoupled, ordinary linear differential equations of first and second order. The analytic form of the component spectra each has a set of three parameters: the variance and the integral length scale of the velocity component and a dimensionless parameter, which governs the curvature of the spectrum in the transition domain from the inertial subrange towards lower wave numbers. When the three sets of parameters are the same, the three spectra correspond to isotropic turbulence and they are all interrelated and related to the energy spectrum. We show how it is possible to obtain these spectral forms in the neutral surface layer and in the convective boundary layer from data reported in the literature. The spectral tensor is used to predict the lateral coherences for all three velocity components and these predictions are compared with coherences obtained in two experiments, one using three masts at a horizontally homogeneous site in Denmark and one employing two aircraft flying in formation over eastern Colorado. Comparison shows reasonable agreement although with considerable experimental scatter.

Turbulent structure and scaling of the inertial subrange in a stratocumulus-topped boundary layer observed by a Doppler lidar

“…1. The spectral model by Kristensen et al (1989), also applied by Lothon et al (2009), is used to identify the transition wavelength, an example of which is also shown in Fig. 1.…”

Modelagem Matemática em Turbulência Atmosférica

“…Entretanto, o espectro na Eq. (3.6.55)é 3-D. O espectro 3D pode ser obtido de um espectro 1D usando uma formulação proposta por Kristensen et al [52] (a dedução dos principais resultados do artigo [52]é desenvolvida em detalhes na tese de doutorado de Charles R. P. Szinvelski [79]). …”

“…Nunes et al [59] usaram dois modelos para representar as variâncias turbulentas: a parametrização de Kristensen et al [52] (M1) e a parametrização de Degrazia et al [30] (M2). Os modelos e variâncias baseados em [52] e em [30] (respectivamente: M1 e M2) tem resultados similares em quase todos os níveis da GCL e reproduzem bem os resultados de LES, exceto próximo ao topo da GCL, onde o modelo baseado na teoria de Taylor [59] tem um desempenho muito melhor.…”

A heuristic model of three-dimensional spectra of temperature inhomogeneities in the stably stratified atmosphere

“…The spectrum of temperature inside such¯ows is strictly speaking a function of the three independent variables: k x Y k y , and k z . Turbulence in similar¯ows was studied by Kristensen et al (1987).…”

“…Some properties of the LAS turbulence were considered (Sreenivasan and Narasimha 1978;Kristensen et al, 1983;George and Hussein, 1991), mainly for the case of small deviations in the velocity ®eld properties from the LI. The properties of the spectral tensor were considered for a more degenerative case of symmetry of the boundarylayer velocity ®eld when the symmetry exists both with respect to the horizontal plane and with respect to the vertical plane parallel to the direction of mean wind velocity (Kristensen et al, 1987).…”