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A low‐order model of coherent structures in the convective atmospheric surface layer
Author(s) -
Zhuang Yahui
Publication year - 1996
Publication title -
quarterly journal of the royal meteorological society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.744
H-Index - 143
eISSN - 1477-870X
pISSN - 0035-9009
DOI - 10.1002/qj.49712253304
Subject(s) - convective boundary layer , turbulence , lagrangian coherent structures , planetary boundary layer , turbulence modeling , boundary layer , convection , physics , galerkin method , ordinary differential equation , mechanics , flow (mathematics) , statistical physics , classical mechanics , mathematical analysis , mathematics , differential equation , nonlinear system , quantum mechanics
Based on a simple application of the dynamical systems theory and experimental evidence of coherent motions in the convective atmospheric surface layer, a low‐order model (15 ordinary differential equations) to study coherent flow dynamics is developed. The model is derived by performing a Galerkin projection of the Navier–Stokes equations on a set of 15 orthogonal functions ϕ ( x, z ), extracted from an ensemble of observed convective plumes (or coherent structures) with the Proper Orthogonal Decomposition method. These orthogonal functions, defined on a two‐dimensional domain (620 m × 150 m), are typical of large‐scale turbulent velocity and temperature fluctuations in the convective atmosphere, and are assumed to have captured enough physics to model the most important aspects of the coherent structures. The effects of the unresolved turbulence on the coherent structures are modelled by the Smagorinsky eddy viscosity closure. The model treats boundary conditions objectively, uses experimental data as the initial conditions, and provides a means to study the dynamics of the coherent structures.