This idea is over the top! I love it. Even if no appreciable results could be observed, it would be cool to be able to say you were able to do it.
Thanks for the links, I tried to find info on this subject, and struck out.
A couple of questions..
Would you need the short pulses in the alternating tides? I thought the tide itself was pretty much similar to a river coming/going- a continuous flow (that does increase/decrease relative to time), with the random flow coming from wave action, which is caused by the winds flowing onto shore. Maybe add a Gyre to your existing setup for the random flow? And have it programmed to slow down at night?
Another area I have unsuccessfully tried to find info on is the temp variances between the tides. It would seem to be that the waters being pushed up with the incoming tide would be cooler than the same water going back out with the tide. What that variance would be, I have no clue. I'm sure there would be more of a variance in a tidal flat in the middle of a sunny afternoon than there would be 20ft down on a reef at night. But again, I think that variance, however slight it may be, could possibly have an impact on coral health and growth. I would think there would be some way to program an Apex to vary the temp on a cycle, even taking into account the time of day/night.
As far as the tide in relation to bringing up/in food- have you looked into this? I know the majority of plankton migrates up at night to feed, but I would think there has to be some that is caught in the incoming tides. It wouldn't be too hard to set a dosing system to coincide with the "incoming" tide, dosing some during the day, and even more at night. I've considered setting up my next tank with.. (here comes the blasphemy) .. an under gravel filter

that reverses the flow at night


.
(Before anyone chimes in and derails this thread, I am not looking at it as a source of filtration, but as a source of food. My lps all go crazy any time I stir the sandbed. I figure I should be able to use this to my advantage. Not to mention, if done properly, I should be able to avoid any anaerobic zones within the bed.)
Speaking of derailing... Sorry. But this thread is the only one I've seen that seems to be thinking along the same lines as I am.
Have you posted this question over in the Neptune forum? If anyone can figure out how to accomplish this, it would be the gurus over there.