Which makes for some very confusing situations when the river is twisty. There are different places in New Orleans where the West Bank is south of you, west of you, and east of you.

Ironically that city's four cardinal directions of "Uptown," "Downtown," "Lakeside," and "Riverside" are completely unambiguous.

That's exactly because they didn't follow the convention. If they called it the Right Bank, it would always be clear which side that was if you could identify the flow of the river.

Rail uses “up” and “down main” where up is in the direction of the port or main terminus.

In Germany it's just direction "a" (kilometrage increasing) and direction "b" (kilometrage decreasing), though I think that usage isn't quite as prominent as Up/Down is in the UK and UK-influenced countries. In Romania AFAIK they're calling them direction "X" and direction "Y" instead.

> In geography left and right banks of a river are always in the direction of the flow

Isn't there some river where the flow goes either way depending on tide? I'm thinking it might be in Alaska, but there might be more than one.

There are surely more than one, but this happens only close to the sea and the general flow of the river is still into the sea.

The Hudson River is tidal up past Poughkeepsie.

Farther than that! It's tidal past Albany and only fully stops at the dam in Troy. https://en.wikipedia.org/wiki/Hudson_River

The Thames is tidal in London so the water does 'flow' both ways, but I'm fairly sure you'd say it flows towards the river but London is on a tidal section.

Tides coming in is normal, but there are rivers that change direction for other reasons. The Chicago River and the Mississippi can change direction due to storm surges, for example (for the Chicago River, that temporarily returns it to its flow direction, into Lake Michigan (https://en.wikipedia.org/wiki/Chicago_River#Course))

A better example is https://en.wikipedia.org/wiki/Tonl%C3%A9_Sap#Geography:

“As the monsoon rain begins, the water level of the river begins to rise. As the water level continues to rise, the flow of the river reverses. The water level of the Tonlé Sap increases by about 10 metres (33 ft), the flow of the Mekong gradually decreases at the end of the rainy season, and the flow of the Tonlé Sap then reverses and began to replenish the flow of the Mekong.”

Even where it happens (it's common, the cases I know personally are Nantes or Antwerp) it's still obvious which side is right and which side is left, it's simply according to the main flow of the river.

Although in this instance, I think it's more common to talk about north/island/south in Nantes rather than left/right banks. While Antwerp's part on the left bank is literally called "left bank" (Linkeroever).

When kayaking, I'd have referred to the banks as "river left" and "river right" to mean the same thing.

In one of Tim Snyders Yale lectures on Ukrainian history, goes overboard about the left bank/right bank in respect of the Dniepro. The river runs north to south, so the right bank is basically the west. I strongly suspect he has trouble telling his left from his right; I've read an essay in which there is a map with a small patch of Russia (coloured red) in the bottom-left, but the caption says it's bottom-right.

I suspect the reason he made a meal of this subject (and the reason he insists on using the left/right terminology) is because he finds it challenging.

I learned it with the Seine, in Paris: the left bank is to the south of the right bank. It's also where the bulk of the 1968 political protest happened; the protestors were leftists. The Seine generally flows south to north, emptying into the English Channel.