Self-similar gravity currents with variable inflow revisited: Plane currents
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 va...
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | JOUR |
| Materias: | |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00221120_v258_n_p77_Gratton |
| Aporte de: |
| id |
todo:paper_00221120_v258_n_p77_Gratton |
|---|---|
| record_format |
dspace |
| spelling |
todo:paper_00221120_v258_n_p77_Gratton2023-10-03T14:26:33Z Self-similar gravity currents with variable inflow revisited: Plane currents Gratton, J. Vigo, C. 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 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. Fil:Gratton, J. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Vigo, C. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00221120_v258_n_p77_Gratton |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
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 |
| spellingShingle |
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 Gratton, J. Vigo, C. Self-similar gravity currents with variable inflow revisited: Plane currents |
| topic_facet |
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 |
| description |
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. |
| format |
JOUR |
| author |
Gratton, J. Vigo, C. |
| author_facet |
Gratton, J. Vigo, C. |
| author_sort |
Gratton, J. |
| title |
Self-similar gravity currents with variable inflow revisited: Plane currents |
| title_short |
Self-similar gravity currents with variable inflow revisited: Plane currents |
| title_full |
Self-similar gravity currents with variable inflow revisited: Plane currents |
| title_fullStr |
Self-similar gravity currents with variable inflow revisited: Plane currents |
| title_full_unstemmed |
Self-similar gravity currents with variable inflow revisited: Plane currents |
| title_sort |
self-similar gravity currents with variable inflow revisited: plane currents |
| url |
http://hdl.handle.net/20.500.12110/paper_00221120_v258_n_p77_Gratton |
| work_keys_str_mv |
AT grattonj selfsimilargravitycurrentswithvariableinflowrevisitedplanecurrents AT vigoc selfsimilargravitycurrentswithvariableinflowrevisitedplanecurrents |
| _version_ |
1782026295802068992 |