Ah, the letter thorn (or þorn).
If you use Windows and have the United States-International keyboard enabled, you can type "þ" with right-alt t (hold down right-alt while hitting t).
Otherwise, you can use alt 0254 (hold down alt while entering 0254 on the numeric keypad). If you've got United States-International turned on, then it has to be the left-alt; but, since they numeric keypad is almost always to the right, that's not too big of a deal.
The only exceptions I can think about are rivers that dry up and transition times for rivers that flow in both directions depending on the tide. I'm not sure if they technically count as rivers but people think about them that way. Another person posted here that this word refers to rapids.
Currents are flows of water within another body of water. Streams are usually considered to be a smaller form of rivers, with their own internal currents. Saying a river has no currents doesn't make a lot of sense, but it might be trying to say there are no eddy currents or cross currents.
In American English, we say, "this river doesn't have any current" or "this river has no current at all" or "this river has no current whatsoever." I could understand someone technical, not a common person, but an aquarist, saying currents of they were studying types of current flows or something.