dorsal/arxiv
View SchemaMultiple Solutions in Fluid Mechanics: Uncertainty of Convection
| Authors | L. S. Yao, S. Ghosh Moulic |
|---|---|
| Categories | |
| ArXiv ID | physics/0612112 |
| URL | https://arxiv.org/abs/physics/0612112 |
| Journal | Int. J. Heat & Mass Transfer, 37, 1713-1721, 1994 |
Abstract
The nonlinear development of finite amplitude disturbances in mixed convection flow in a heated vertical annulus is studied by direct numerical simulation. The unsteady Navier Stokes equations are solved numerically by a spectral method for different initial conditions. The results indicate that the equilibrium state of the flow is not unique, but depends on the amplitude and wavenumber of the initial disturbance. In all cases, the equilibrium state consists of a single dominant mode with the wavenumber kf, and its superharmonics. The range of equilibrium wavenumbers kf was found to be narrower than the span of the neutral curve from linear theory. Flows with wavenumbers outside this range, but within the unstable region of linear theory are found to be unstable and to decay, but to excite another wave inside the narrow band. This result is in agreement with the Eckhaus and Benjamin-Feir sideband instability. The results also show that linearly stable long and short waves can also excite a wave inside this narrow band through nonlinear wave interaction. The results suggest that the selection of the equilibrium wavenumber kf is due to a nonlinear energy transfer process which is sensitive to initial conditions.
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"abstract": "The nonlinear development of finite amplitude disturbances in mixed\nconvection flow in a heated vertical annulus is studied by direct numerical\nsimulation. The unsteady Navier Stokes equations are solved numerically by a\nspectral method for different initial conditions. The results indicate that the\nequilibrium state of the flow is not unique, but depends on the amplitude and\nwavenumber of the initial disturbance. In all cases, the equilibrium state\nconsists of a single dominant mode with the wavenumber kf, and its\nsuperharmonics. The range of equilibrium wavenumbers kf was found to be\nnarrower than the span of the neutral curve from linear theory. Flows with\nwavenumbers outside this range, but within the unstable region of linear theory\nare found to be unstable and to decay, but to excite another wave inside the\nnarrow band. This result is in agreement with the Eckhaus and Benjamin-Feir\nsideband instability. The results also show that linearly stable long and short\nwaves can also excite a wave inside this narrow band through nonlinear wave\ninteraction. The results suggest that the selection of the equilibrium\nwavenumber kf is due to a nonlinear energy transfer process which is sensitive\nto initial conditions.",
"arxiv_id": "physics/0612112",
"authors": [
"L. S. Yao",
"S. Ghosh Moulic"
],
"categories": [
"physics.flu-dyn"
],
"journal_ref": "Int. J. Heat \u0026 Mass Transfer, 37, 1713-1721, 1994",
"title": "Multiple Solutions in Fluid Mechanics: Uncertainty of Convection",
"url": "https://arxiv.org/abs/physics/0612112"
},
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