A seal assembly for a rotary machine is positioned between a rotating component and a stationary component of the rotary machine. The seal assembly includes a seal bearing face that opposes the rotating component and a slide device. The slide device is positioned between different fluid pressure volumes in the rotary machine. The slide device axially moves toward the rotating component responsive to pressurization of the rotary machine. The slide device includes cross-over ports and the seal bearing face includes feed ports. The feed ports extend through the seal bearing face to form an aerostatic portion of a film bearing between the seal bearing face and the rotating component. The seal bearing face and/or the rotating component is a non-planar surface that, during rotating motion of the rotating component, forms an aerodynamic portion of the film bearing between the seal bearing face and the rotating component.