Date: 201309
Local time of day: 1801-2400
Location: ZZZ.Airport, US
Flight conditions: VMC
Light: Night
Aircraft: MD-83
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Mission: Passenger
Flight phase: Landing
ATC / advisory: Tower ZZZ
Aircraft component: Hydraulic System
Component problem: Failed
Reporter organization: Air Carrier
Reporter function: Captain; Pilot Not Flying
Reporter qualification: Flight Crew Air Transport Pilot (ATP)
Human factors: Troubleshooting; Confusion; Training / Qualification
Second reporter function: First Officer; Pilot Flying
Anomaly: Aircraft Equipment Problem Critical; Deviation / Discrepancy - Procedural Published Material / Policy
Detector: Automation Aircraft Other Automation; Person Flight Crew
When detected: In-flight; Taxi
Result: General Maintenance Action
Contributing factors: Chart Or Publication; Procedure; Manuals; Aircraft
Primary problem: Aircraft

Narrative: Following a normal descent and approach; we landed on Runway XXR. After the nose-wheel touched down the thrust reverser's were deployed. We immediately got a 'Right Reverser Accumulator' light on the overhead that flickered on and off a couple of times. As we decelerated I noticed several other right side hydraulic messages that flickered on and off. After we slowed to a normal taxi speed I turned off the runway and stopped to see what happened. Right hydraulic quantity was at zero and right pressure was at zero. (Left side was normal with 10 quarts and 3;000 PSI). We shut down the right engine driven Hydraulic Pump; and turned off the AUX and Transfer Pumps to protect the good left side. I checked the brake pressure gauge and found that the left side was at 3;000 PSI and the right side was at zero. Braking was normal with the left side powered; and nose-wheel steering was also normal. QRH checklists assumed hydraulic system loss in flight with manual gear extension; and did not pertain to our situation.I taxied cautiously to the gate at a slower than normal speed uneventfully. Upon post-flight inspection we discovered the right hydraulic reservoir was empty and that hydraulic fluid coated the right main gear; the right wheel well; and the aircraft belly aft of the right wheel well. I pulled the CVR circuit breaker this morning when we returned to the aircraft to bring it back to my domicile. I made an info to Maintenance entry in the maintenance logbook regarding the CVR being pulled per FM Part 1 guidance.  There is no QRH procedure for the loss of right system quantity or pressure on the ground. All the checklists assume you lose it in flight and have to manually extend the gear while flying; leaving main gear doors extended following gear free fall. This was not our case as we had extended the gear normally in flight and they automatically lock in the extended position with an over-center linkage. Since we had good pressure on the left side for brakes and steering I felt we were safe to taxi; so we did not declare an emergency on the taxi in. In retrospect it might have been a better option to pin the gear prior to taxi; even though I knew that the gear was down and locked safely following normal procedures that occurred prior to the loss of the Right hydraulic system. A QRH procedure for loss of hydraulics on the ground would be helpful.


Second narrative: [Report narrative contained no additional information].


Synopsis: An MD-83 Right Hydraulic system failed after landing; so the right system pumps were shutdown and the aircraft taxied to the gate on a Left System because no QRH procedure was available for a hydraulic system failure on the ground.