Exchange of stabilities in stress-free convection
= Exchange of stabilities in stress-free convection
{title2=$\sigma_c=0$}
In nonrotating <Rayleigh-Bénard convection> with fixed-temperature, <stress-free boundary conditions>, the <stress-free convection growth-rate polynomial> has real roots on the destabilizing side. Consequently the first instability is stationary, rather than oscillatory. Minimizing the <free-slip convection neutral curve> selects $\lambda_c=\pi/\sqrt2$ and $\mathrm{Ra}_c=27\pi^4/4$.