AN ACR FLC CLOSES WITHIN 2000 FT INTRAIL OF AN ACR B737 AND ENCOUNTERS THE WAKE. THE TRAILING FLC EXPECTED THE B737 TO CONTINUE ITS DEP CLB.

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UPON DEP FROM DFW; WE WERE ON RADAR VECTORS AT 4000 FT OVER DAL WHEN A B737 DEPARTED DAL. THE B737 WAS ASSIGNED 4000 FT AS WELL. WE WERE LEVEL WITH AIRSPD AT 240 KTS COMING UP ON THE B737 AT HIS 6 O'CLOCK POS. DUE TO THE LONG DUTY DAY AND MINIMAL TIME BTWN FLTS; MY COPLT PLACED THE TCASII SWITCH IN 'TA ONLY.' IF THE TCASII HAD BEEN SET NORMALLY WE WOULD HAVE RECEIVED AN RA AND AVOIDED SOME NASTY WAKE TURB. I FEEL THE CTLR WAS NEGLIGENT IN PLACING A 240 KT LEVEL ACFT BEHIND A CLBING B737; EVEN THOUGH HE HAD JUST LEVELED; HIS SPD WAS LESS THAN OURS. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTR SAID THAT HE DID NOT ANTICIPATE THAT THE B737 WOULD NOT BE CONTINUING ITS CLB. INSTEAD THIS WAS A MAINT FERRY THAT HAD LEVELED AT 4000 FT FOR THE SHORT; LOW SPD CRUISE TO THE MAINT BASE. THE RPTR ALSO SAID THAT THE FLC WAS FATIGUED AND COMPLACENT MAKING SEVERAL SMALL PROCEDURAL ERRORS PRIOR TO THIS. THE WAKE ENCOUNTER WAS A WAKEUP CALL. THE EVENT ONLY LASTED A COUPLE OF SECONDS ACCORDING TO THE CAPT; BUT HE AND HIS FO TALKED ABOUT IT FOR 2 DAYS. JUST PRIOR TO HITTING THE WAKE THE CAPT SAID THAT HE TOLD HIMSELF THAT HE WAS PROBABLY GOING TO; THEN DID. HE DISCONNECTED THE AUTOPLT; ADVANCED THE THROTTLES AND FLEW OUT OF THE WAKE. THE CAPT SAID THAT HE HAD HAD SOME EXPERIENCE WITH FORMATION FLYING BEFORE THIS.