Empirical orthogonal function analysis of coherent structures in a neutral atmospheric surface layer

1 Introduction

Coherent structures in the form of near-surface streaks are ubiquitous features of large-eddy simulations (LES) of the planetary boundary layer (PBL) in which shear plays an important role in the dynamics [2,8,4,1]. In [1], simulated flow patterns near the ground show so-called streaks, regions near the surface of alternating high and low speed fluid organized into nearly linear bands, with horizontal spacing of several hundred meters, oriented up to 30° relative to the geostrophic wind, that evolve through a continuous cycle of generation, growth, decay and re-formation. Their existence also received recent support from field observations [3]. Beyond this qualitative observations, there is a need for a quantitative analysis of their individual structure as well as their role in the dynamics and energetics of the flow. There have been theoretical attempts to interpret streaks in terms of optimal linear perturbations of an Ekman layer [5,4]. Another way is to extract from a numerical simulation the most recurrent structures and to analyze their contribution to the simulated dynamics.

One extraction method is Empirical orthogonal function (EOF) analysis, also known as proper orthogonal decomposition (POD). Such a correlation technique was initially applied to turbulence by Lumley and others in classical flows (pipe, channel, boundary layer) [6,7]. However the lack of datasets having sufficient coverage and resolution prevented until recently this type of analysis in the planetary boundary layer. Wilson and Wyngaard performed an EOF analysis of a weakly convective atmospheric boundary layer, extracting EOFs some of which could be identified as gravity waves or boundary-layer rolls [9]. Nevertheless a reliable representation of near-ground structures such as streaks requires a higher resolution which could be achieved only very recently.

In this work, three-dimensional empirical orthogonal functions (EOFs) representing the statistically most energetic structures are extracted from a high resolution large-eddy simulation of a neutral atmospheric boundary layer [1] and their energetics analyzed. abstract.html#Deardorff72

2 EOFs and their energetics

The simulation runs the non-hydrostatic LES model Méso-NH in a horizontally periodic box with size 1km x 3km x 750m and cubic mesh cell of side 6.25m. Forcing by a large-scale pressure gradient produces a time-averaged wind following a deformed Ekman spiral continued by a log-layer near the surface. Streaky structures roughly aligned with the ground wind are observed in the first 100m  [1]. Our set of realizations consists in 14 snapshots of the whole velocity field taken at different instants. Thus we extract the recurrent spatial flow patterns and drop any temporal or dynamical information from the signal. Due to horizontal homogeneity the EOFs are horizontally sinusoidal flows. EOFs that explain a significant (>50% ) energy fraction in their Fourier mode have their phase lines closely parallel to the streaks observed qualitatively. Based on horizontal scale, EOFs likely corresponding to streaks are displayed (left). The quadratic terms of the budget of turbulent kinetic energy (TKE) are decomposed at each altitude into contributions by each EOF (right). While shear production globally compensates viscous dissipation, this balance does not hold on a single EOF, stressing the importance of interscale energy transfers. Bibliography

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