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Abstract:

We use shallow-water theory to study the self-similar gravity currents that describe the intrusion of a heavy fluid below a lighter ambient fluid. We consider in detail the case of currents with planar symmetry produced by a source with variable inflow, such that the volume of the intruding fluid varies in time according to a power law of the type f. The resistance of the ambient fluid is taken into account by a boundary condition of the von Karman type, that depends on a parameter β that is a function of the density ratio of the fluids. The flow is characterized by β, α, and the Froude number F0 near the source. We find four kinds of self-similar solutions: subcritical continuous solutions (Type I), continuous solutions with a supercritical-subcritical transition (Type II), discontinuous solutions (Type III) that have a hydraulic jump, and discontinuous solutions having hydraulic jumps and a subcritical-supercritical transition (Type IV). The current is always subcritical near the front, but near the source it is subcritical (F0 < 1) for Type I currents, and supercritical (F0 > 1) for Types II, III, and IV. Type I solutions have already been found by other authors, but Type II, III, and IV currents are novel. We find the intervals of parameters for which these solutions exist, and discuss their properties. For constant-volume currents one obtains Type I solutions for any β that, when β > 2, have a ‘dry’ region near the origin. For steady inflow one finds Type I currents for 0 < β < ∞ and Type II and III currents for any 8, if is sufficiently large. © 1994, Cambridge University Press. All rights reserved.

Registro:

Documento: Artículo
Título:Self-similar gravity currents with variable inflow revisited: Plane currents
Autor:Gratton, J.; Vigo, C.
Filiación:Departamento de Física, Universidad de Buenos Aires, Pabellón I., Ciudad Universitaria, 1428 Buenos Aires, Argentina
Palabras clave:Boundary value problems; Density (specific gravity); Gravity waves; Hydraulic jump; Froude number; Power law; Self similar gravity currents; Shallow water theory; Supercritical subcritical transition; Variable inflow; Flow interactions; Currents; Gravity Flow; Inflow; density flow; plane currents; shallow-water theory
Año:1994
Volumen:258
Página de inicio:77
Página de fin:104
DOI: http://dx.doi.org/10.1017/S0022112094003241
Título revista:Journal of Fluid Mechanics
Título revista abreviado:J. Fluid Mech.
ISSN:00221120
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00221120_v258_n_p77_Gratton

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Citas:

---------- APA ----------
Gratton, J. & Vigo, C. (1994) . Self-similar gravity currents with variable inflow revisited: Plane currents. Journal of Fluid Mechanics, 258, 77-104.
http://dx.doi.org/10.1017/S0022112094003241
---------- CHICAGO ----------
Gratton, J., Vigo, C. "Self-similar gravity currents with variable inflow revisited: Plane currents" . Journal of Fluid Mechanics 258 (1994) : 77-104.
http://dx.doi.org/10.1017/S0022112094003241
---------- MLA ----------
Gratton, J., Vigo, C. "Self-similar gravity currents with variable inflow revisited: Plane currents" . Journal of Fluid Mechanics, vol. 258, 1994, pp. 77-104.
http://dx.doi.org/10.1017/S0022112094003241
---------- VANCOUVER ----------
Gratton, J., Vigo, C. Self-similar gravity currents with variable inflow revisited: Plane currents. J. Fluid Mech. 1994;258:77-104.
http://dx.doi.org/10.1017/S0022112094003241