TURBULENCE AND THE DYNAMICS OF COHERENT STRUCTURES PART I: COHERENT STRUCTURES*

TURBULENCE AND THE DYNAMICS OF COHERENT STRUCTURES PART I: COHERENT STRUCTURES*

OCTOBER 1987 | BY LAWRENCE SIROVICH
The introduction to Parts I-III of the paper by Lawrence Sirovich discusses the recent developments in turbulence theory that have altered the statistical framework established by Taylor. These developments include the existence of coherent structures observed in laboratory experiments and the theoretical suggestion that turbulent flows reside on low-dimensional manifolds or attractors. The paper aims to address both of these issues in a unified manner. A key method used is the orthogonal decomposition of spatial velocity correlations, which has been applied to various flow problems but has been limited by the lack of complete and resolved data. The present work overcomes this limitation by developing methods that can handle fully three-dimensional flows. The Karhunen-Loeve expansion, a classical result in pattern recognition and statistical analysis, is reviewed and further developed within the context of fluid mechanics. The paper also explores the use of symmetries to extend available data and the transformation of coherent structures for use in different geometries. The methodology is demonstrated through numerical examples, showing its usefulness in treating a wide range of turbulent flows.The introduction to Parts I-III of the paper by Lawrence Sirovich discusses the recent developments in turbulence theory that have altered the statistical framework established by Taylor. These developments include the existence of coherent structures observed in laboratory experiments and the theoretical suggestion that turbulent flows reside on low-dimensional manifolds or attractors. The paper aims to address both of these issues in a unified manner. A key method used is the orthogonal decomposition of spatial velocity correlations, which has been applied to various flow problems but has been limited by the lack of complete and resolved data. The present work overcomes this limitation by developing methods that can handle fully three-dimensional flows. The Karhunen-Loeve expansion, a classical result in pattern recognition and statistical analysis, is reviewed and further developed within the context of fluid mechanics. The paper also explores the use of symmetries to extend available data and the transformation of coherent structures for use in different geometries. The methodology is demonstrated through numerical examples, showing its usefulness in treating a wide range of turbulent flows.
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