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The approximations implicit in Bénard convection have been modified to include viscous dissipation. It is shown that both the influence of an adiabatic temperature gradient and of viscous dissipation are governed by the same dimensionless parameter Di = α gh / c p . Numerical calculations of finite amplitude convection are given for finite values of Di. It is found that increasing Di decreases flow velocities and finally stabilizes the flow.
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Turcotte et al. (1974) studied this question.
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