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- Brian J. Cantwell
- Department of Aeronautics and Astronautics, Stanford University, Stanford, California 94305
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<jats:p>The velocity gradient tensor satisfies a nonlinear evolution equation of the form (dAij/dt)+AikAkj− (1/3)(AmnAnm)δij=Hij, where Aij=∂ui/∂xj and the tensor Hij contains terms involving the action of cross derivatives of the pressure field and viscous diffusion of the velocity gradient. The homogeneous case (Hij=0) considered previously by Vielliefosse [J. Phys. (Paris) 43, 837 (1982); Physica A 125, 150 (1984)] is revisited here and examined in the context of an exact solution. First the equations are simplified to a linear, second-order system (d2Aij/dt2)+(2/3)Q(t)Aij=0, where Q(t) is expressed in terms of Jacobian elliptic functions. The exact solution in analytical form is then presented providing a detailed description of the relationship between initial conditions and the evolution of the velocity gradient tensor and associated strain and rotation tensors. The fact that the solution satisfies both a linear second-order system and a nonlinear first-order system places certain restrictions on the solution path and leads to an asymptotic velocity gradient field with a geometry that is largely but not wholly independent of initial conditions and an asymptotic vorticity which is proportional to the asymptotic rate of strain. A number of the geometrical features of fine-scale motions observed in direct numerical simulations of homogeneous and inhomogeneous turbulence are reproduced by the solution of the Hij=0 case.</jats:p>
収録刊行物
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- Physics of Fluids A: Fluid Dynamics
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Physics of Fluids A: Fluid Dynamics 4 (4), 782-793, 1992-04-01
AIP Publishing
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詳細情報 詳細情報について
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- CRID
- 1362544420555382784
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- NII論文ID
- 30015996615
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- NII書誌ID
- AA00773996
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- DOI
- 10.1063/1.858295
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- ISSN
- 08998213
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