On the NOAA surface analysis (
https://www.wpc.ncep.noaa.gov/#page=sfc) for 24 hours ago, they have drawn the situation as a quasi-stationary waving front stretching from north Texas east-north-eastwards towards Kentucky and Virginia, then out into the western Atlantic.
In reality, there is tropical air of high moisture content covering the southern half of the USA. The jet stream is overhead the boundary between the tropical air and the cooler air to its north. It looks as if some active short wave upper troughs ran along the jet stream during the past couple of days, and ascent ahead of these created heavy rain. This would likely have been analysed as waves on the aforementioned front. Essentially it was uplift of the tropical air that caused the rain.