@WeedeaterDM - you're right, i was thinking that normally the solid line is on the outside of the turn lane.
@Nigel - yes, they are meant for traffic going either direction. they are dedicated left turn lanes, usually on roads where there are too many driveways on either side to have a raised median with individual turn lanes for each direction. often seen in areas with a lot of retail/commercial. the intention is you should slow down before entering the turn lane for that very reason - you never know if someone may enter from the opposite direction. the highest speed limit i've ever seen this kind of turn lane on was only 45 mph so it's generally not a big problem. of course there's always morons out there, but that's just part of defensive driving.
i was taught to treat them a lot like regular turn lanes in respect to how long you should actual travel in one - just long enough to come to a stop where you want to make your turn, then wait for a break in oncoming traffic to make your turn.
most of the crashes i've seen with this type of turn lane are T-bone wrecks, not head-on. obviously you'll get T-bones with a normal turn lane too. i have had to jam on my brakes or swerve back into the mainlanes once or twice when entering because someone else entered at the same time from the other way, but it's pretty rare. it seems most of the time, they try to stagger the driveways people would want to turn into so as to minimize the chances of a head-on.
that said, FM1960/TX-6 used to have one of these center turn lanes for most of its length in the congested areas of town (about 20 miles, best guess). apparently there were enough wrecks that they installed medians and curbs to create dedicated turn lanes, and specifically limit the areas people could make turns. now it means a lot more U-turns to get to many stores, and now waiting for a traffic light instead of just waiting for a break in traffic, but i'm sure they wouldn't have spent that much money changing the road for no reason. it certainly doesn't LOOK better, since they didn't plant anything in the medians other than grass. trees would have been nice.
here's a section of 1960 that hasn't been changed yet, as they're now working on a huge overpass that will skip several traffic lights and go over US290.
https://www.google.com/maps/@29.9199448,-95.6092901,268m/data=!3m1!1e3 slide the map east a little bit and you'll come to Eldridge pkwy. notice how on the eastbound side, the yellow lines disappear for a bit, then a solid white one appears, making it a dedicated turn lane for eastbound traffic turning onto Eldridge. also notice that on the westbound side, for the length of the EB-to-Eldridge turn lane, the solid/dashed yellow turns to a double solid yellow, meaning DO NOT CROSS.