Data Assimilation in Large-Prandtl Rayleigh-B\'enard Convection from Thermal Measurements
SIAM Journal on Applied Dynamical Systems, 19:1, 510-540 (2020) This work applies a continuous data assimilation scheme---a particular framework for reconciling sparse and potentially noisy observations to a mathematical model---to Rayleigh-B\'enard convection at infinite or large Prandtl numbe...
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04.03.2019
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Abstract | SIAM Journal on Applied Dynamical Systems, 19:1, 510-540 (2020) This work applies a continuous data assimilation scheme---a particular
framework for reconciling sparse and potentially noisy observations to a
mathematical model---to Rayleigh-B\'enard convection at infinite or large
Prandtl numbers using only the temperature field as observables. These Prandtl
numbers are applicable to the earth's mantle and to gases under high pressure.
We rigorously identify conditions that guarantee synchronization between the
observed system and the model, then confirm the applicability of these results
via numerical simulations. Our numerical experiments show that the analytically
derived conditions for synchronization are far from sharp; that is,
synchronization often occurs even when the conditions of our theorems are not
met. We also develop estimates on the convergence of an infinite Prandtl model
to a large (but finite) Prandtl number generated set of observations. Numerical
simulations in this hybrid setting indicate that the mathematically rigorous
results are accurate, but of practical interest only for extremely large
Prandtl numbers. |
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AbstractList | SIAM Journal on Applied Dynamical Systems, 19:1, 510-540 (2020) This work applies a continuous data assimilation scheme---a particular
framework for reconciling sparse and potentially noisy observations to a
mathematical model---to Rayleigh-B\'enard convection at infinite or large
Prandtl numbers using only the temperature field as observables. These Prandtl
numbers are applicable to the earth's mantle and to gases under high pressure.
We rigorously identify conditions that guarantee synchronization between the
observed system and the model, then confirm the applicability of these results
via numerical simulations. Our numerical experiments show that the analytically
derived conditions for synchronization are far from sharp; that is,
synchronization often occurs even when the conditions of our theorems are not
met. We also develop estimates on the convergence of an infinite Prandtl model
to a large (but finite) Prandtl number generated set of observations. Numerical
simulations in this hybrid setting indicate that the mathematically rigorous
results are accurate, but of practical interest only for extremely large
Prandtl numbers. |
Author | Whitehead, J. P Martinez, V. R Glatt-Holtz, N. E Farhat, A McQuarrie, S. A |
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BackLink | https://doi.org/10.48550/arXiv.1903.01508$$DView paper in arXiv https://doi.org/10.1137/19M1248327$$DView published paper (Access to full text may be restricted) |
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Snippet | SIAM Journal on Applied Dynamical Systems, 19:1, 510-540 (2020) This work applies a continuous data assimilation scheme---a particular
framework for... |
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Title | Data Assimilation in Large-Prandtl Rayleigh-B\'enard Convection from Thermal Measurements |
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