Equations for the propagation of finite local disturbances in vector fields of physics and mechanics
| Autor: | Robert C. Costen |
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| Rok vydání: | 1979 |
| Předmět: | |
| Zdroj: | Journal of Mathematical Physics. 20:1439-1445 |
| ISSN: | 1089-7658 0022-2488 |
| Popis: | The purpose of this theoretical investigation is to determine the propagation velocities of local disturbances that may occur in the curl and divergence of a vector field v that satisfies the equation ∂v/∂t+f=0, where f is a general vector field. Equations of this form frequently occur in physics and mechanics. A disturbance in the curl v (div v) field is defined by ∂curl v/∂t≠0 (∂div v/∂t≠0). Such a disturbance is termed a local disturbance if it is surrounded by a quiescent layer of finite thickness. Equations are derived for the velocity U(r,t) of curl v lines and the velocity W(r,t) of div v elements. These velocities conserve, respectively, the circulation of v about arbitrary circuits and the efflux of v through arbitrary closed surfaces. These conservation conditions are not sufficient to completely specify the two velocity fields, and each contains an arbitrary term. More convenient for three‐dimensional applications than the circulation is the gyration G (spatial integral of curl v); and U is fou... |
| Databáze: | OpenAIRE |
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