Linear adiabatic wave equation

• Favors deep, thin cells
• Isothermal case: pressure scale height as length scale

Linear non-adiabatic wave equation (including radiation)

• The is a horizontal scale with maximum growth rate
• Mode with maximum growth rate smaller than granules (Böhm, 1963)
• New-born downdrafts go through linear phase (and are rather small)
• Positive effect of radiation: vertical: convective instability enhanced
• Negative effect of radiation: horizontal: temperature/density fluctuations suppressed