"Imperial Japanese Navy" or "Japanese Imperial Navy"?

Although @tchrist has given an excellent explanation for why it ought to be "Japanese Imperial Navy", searching for "Japanese Imperial Navy" auto-corrects to "Imperial Japanese Navy"... and even if you override that and re-correct to "Japanese Imperial Navy", the first hit is http://en.wikipedia.org/wiki/Imperial_Japanese_Navy. Even the pages further down in the results, whose titles include "Japanese Imperial Navy", revert to "Imperial Japanese Navy" in their actual body text. Further, the official (English) abbreviation is "IJN", not "JIN".

As for why, I suspect that the answer is twofold:
- originally, an arbitrary choice on the part of some translator or other - perhaps employed by the Imperial court - that "stuck" and became official usage
- in modern usage, to distinguish between the Japanese Navy of Imperial days and the modern navy, known as the Japan Maritime Self-Defense Force.

It’s “Japanese Imperial Navy”, not the other way around. This is due to adjective ordering restrictions.

See this paper by Alexandra Teodorescu for details various and sundry.