A weak surface front and dryline is advancing slowly Southeast into Oklahoma at this time. You can see part of the boundary on the above radar image taken from the Tulsa area radar just a moment ago. It is indicated by the very thin blue line extending from near Bartlesville to the immediate West of Tulsa, and on back to the East/Southeast of the Oklahoma City metro area.
Thunderstorms are expected to develop along and immediately ahead of this boundary during the next couple of hours. Any thunderstorm that developes will be capable of producing large hail & damaging winds. Isolated tornadoes also cannot be ruled out.
This activity will move East/Northeastward into adjacent portions of Missouri and Arkansas during the evening hours. Activity may also back-build southwestward as far as portions of northeast Texas.
I would expect a Tornado Watch to be issued for this region between now and 4pm.
Once the above boundary moves East of any given location, the threat of severe weather development will end for that particular point. For example, the boundary is likely to move through the Tulsa Metro area between 3 and 4 pm, based on current movement. If activity does not form before the boundary passes through, then Tulsa will be in the clear, with the severe threat shifting off to the East.