The Rebels used "Lightmaker" - a "Hammerhead Corvette" aka "Corvette Five" - to push the damaged Destroyer into (through?) the other one and forced the one they were pushing into the gate. Note the trajectory of the ship being pushed and the proximity to the gate:
From "The Battle of Scarif":
...Along with four of his squad mates, Vander launched multiple ion torpedoes at a Star Destroyer, disabling it. Noticing the disabled capital ship, Admiral Raddus contacted a Hammerhead corvette and explained his plan to break open the shield.
Lightmaker, commanded by Kado Oquoné, evacuated all non-essential personnel, leaving a skeleton crew behind before Oquoné gave the order, sending his ship into the side of the disabled ship, sending it on a collision course for another one. As the two Star Destroyers collided, they broke apart and fell towards Scarif, crashing into the orbital docking station that controlled the deflector shield, disabling it. With the shield down, Erso and Andor were able to successfully transmit the Death Star plans to the Alliance flagship above Scarif.
In the film it didn't really "fall" or per your comment, "sink" - it was pushed really hard - note the thrusters on the hammerhead. The damaged Destroyer was "dead in the water" with no thrust of it's own. The inertial trajectory from the hammerheads thrusters was powerful enough to tear through the other Destroyer and carry the damaged one to its target. I don't explicitly see the Hammerhead fly away, so possibly this was a suicide mission?
Visual effects supervisor John Knoll mentioned there was much back-and-forth about whether the crew survived; cutting to shots of escape pods were deemed distracting by Gareth Edwards, so ILM merely implied they survived by not having the pods present during the collision of the disabled Star Destroyer with the Shield Gate. However, given the Death Star fires on the position where the pods would land, it's still unlikely any of the Lightmaker's crew survived.
Some additional info one the Hammerhead history and the Battle of Scarif: