B737 CREW FLEW WITH AN MEL'ED INOP YAW DAMPER.

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ACFT DISPATCHED WITH MEL'ED YAW DAMPER INOP (NO RESTRS) LAX-SEA. FILED FOR FL350; WE STAYED AT FL310 (CAPT'S DECISION). WE WERE THE ONLY ACFT THAT RPTED LIGHT TURB. WE HAD AN UNCOMFORTABLE RIDE -- DUTCH ROLL WITH ACFT NOSE MOVING R-L. ENDED UP AT FL280 FOR BETTER CTL. INTO SEA INSIDE NEEAL TO RWY 34R FLAPS 10 DEGS; 170 KTS AND 2700 FT MSL; AT 4 MI IN TRAIL OF COMPANY B737; ENCOUNTERED WAKE TURB. R WING STARTED TO DROP. PUT IN COUNTER AILERON; ADDED PWR; STOPPED DSCNT. WENT AT 1 DOT HIGH ON GS (ACFT STILL ROLLING TO R; NOW AT 10-15 DEGS R WING DOWN). ADDED MORE PWR; MORE L AILERON; PLUS A VERY SMALL (JUST A TOUCH) OF L RUDDER -- SPD NOW 190 KTS; R WING AT 25-30 DEGS DOWN BEFORE ACFT RESPONDED! ASKED FOR RWY 34L (DUE TO CLOSURE; 190 KTS). I WOULD HAVE HOPED FOR AN IMMEDIATE RESPONSE FROM ACFT! TALKED TO MAINT ON THE GND. ALL PROCS WERE ACCOMPLISHED BY MAINT FOR YAW DAMPER INOP. PASSED ON INFO TO OUTBOUND CREW. GUESS I JUST HIT WINGTIP VORTICES/WAKE TURB PERFECTLY. HIT HIS L WING TURB; FOLLOWED BY HIS R WING TURB. WX WAS CLR; SURFACE WIND AT 350 DEGS 9 KTS AT XA15.