Publication Abstracts

Toomre et al. 1982

Toomre, J., D.O. Gough, and E.A. Spiegel, 1982: Time-dependent solutions of multimode convection equations. J. Fluid Mech., 125, 99-122, doi:10.1017/S0022112082003279.

Truncated modal equations are used to study the time evolution of thermal convection. In the Boussinesq approximation these nonlinear equations are obtained by expanding the fluctuating velocity and temperature fields in a finite set of planforms of the horizontal coordinates. Here we report on numerical studies dealing with two or three modes with triad interactions. We have found rich time dependence in these cases: periodic and aperiodic solutions can be obtained, along with various steady solutions. Three-mode solutions reproduce the qualitative appearance of spoke-pattern convection as observed in experiments at high Prandtl numbers. Though the values of the periods of the time-dependent solutions do not agree with those of the experiments, their variation with Rayleigh number compares favourably. Except at the highest Rayleigh number we have considered (107), the theoretical Nusselt numbers agree well with experiment.

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BibTeX Citation

@article{to09000j,
  author={Toomre, J. and Gough, D. O. and Spiegel, E. A.},
  title={Time-dependent solutions of multimode convection equations},
  year={1982},
  journal={J. Fluid Mech.},
  volume={125},
  pages={99--122},
  doi={10.1017/S0022112082003279},
}

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RIS Citation

TY  - JOUR
ID  - to09000j
AU  - Toomre, J.
AU  - Gough, D. O.
AU  - Spiegel, E. A.
PY  - 1982
TI  - Time-dependent solutions of multimode convection equations
JA  - J. Fluid Mech.
VL  - 125
SP  - 99
EP  - 122
DO  - 10.1017/S0022112082003279
ER  -

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