The standard equilibrium for radiation-dominated accretion disks has long been known to be viscously, thermally, and convectively unstable, but the nonlinear development of these instabilities—and hence the actual state of such disks—has not yet been identified. By performing local two-dimensional hydrodynamic simulations of disks, we demonstrate that convective motions can release heat sufficiently rapidly as to substantially alter the vertical structure of the disks. If the dissipation rate within a vertical column is proportional to its mass, the disk settles into a new configuration that is thinner than the standard radiation-supported equilibrium by a factor of 2. If, on the other hand, the vertically integrated dissipation rate is proportional to the vertically integrated total pressure, the disk is subject to the well-known thermal instability. Convection, however, biases the development of this instability toward collapse. The end result of such a collapse is a gas-pressure-dominated equilibrium at the original column density.
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