Landed on a runway after a rainfall, this particular base rarely experienced rain. As soon as the reversers were deployed we were traveling sideways down the runway. There was nothing in our training to account for this unusual manuver...
Our Flight Handbook addresses the issue in the "Wet/Slippery Runway Landings" section. Initial training includes discussion and pictures with appropriate vector diagrams.
The reverse thrust side force and a crosswind can cause the aircraft to drift to the downwind side of the runway if the aircraft is allowed to weathervane into the wind. As the aircraft starts to weathervane into the wind, the reverse thrust side force component adds to the crosswind component and drifts the aircraft to the downwind side of the runway. Main gear tire cornering forces available to counteract this drift will be reduced when the anti-skid system is operating at the maximum braking effectiveness for existing conditions.
To correct back to the centerline, reduce reverse thrust to reverse idle and release the brakes. This will minimize the reverse thrust side force component without the requirement to go through a full reverser actuating cycle, and provide the total tire cornering forces for realignment with the runway centerline. Use rudder, steering and differential braking as required to prevent overcorrecting past the runway centerline. When re-established on the runway centerline, reapply steady brakes and reverse thrust as required to stop the aircraft.