First of all you need to read up on it more... because everything out there that isnt for 5th graders will tel you that time is not a normal medium and thus does not "travel" in "waves". Time is a quantized standard that is present reguardless of state or action or "situation" as you put it. There is no way to manipluate time in the manner in which you speak about it.
1. Right off the bat, TIME TRAVEL requires an object to move at a rate faster than the speed of light, this requires an object that is composed of matter have infinate acceleration to propel itself at a rate faster than the speed of light. So, since there is absolutely NO way possible to have something with infinate acceleration, the outlook on TIME TRAVEL is dim. And please dont come back with your lame anti-matter solution. Because, simply put, you or any other thing that humans could ever manufacture, will always be made of normal matter, so putting your normal matter ass on a time-ship comprised of anit-matter is just moronic.
2. I really already addressed this issue with the first statement, but just to bring extra attention to it, time travel into the past would never ever ever ever ever ever be possible past the initial frame of reference (when the "time machine" was built). There is no magical way to make time go backwards and transport you to a differnent "time" but not make it go backwards completely.
2.5 The only really 100% true Time Travel that is theoretically possible is time travel through worm-holes. but their existence is sketcky and traveling through one is 1) (debatably) impossible and 2) Even if you COULD travel through one, you would have no idea where you would come out in space-time, nor would you be able to get back to where you were before the space-time jump through the wormhole.
3. The only possible solutions to controlled "time travel" are Faster Then Light Travel and Time Dilation. However, neither of these are true time travel, they take advantage of the breakdown of time as velocity increases and they are simply manipulations of space-time that give the same end result as true time travel.
Faster than light travel means that your time-ship itself is not moving FTL, but the space around the ship is, this is accomplished through compressing the space ahead of the ship with a large gravity force, and expanding the space fabric behind the ship with Anti-matter / Phontons / Whatever they are thinking we could use. Again this is not TRUE time travel as the ship's velocity is NOT FTL, only the velocity of the warp bubble around said ship is moving FTL.
Time Dilation occurs all the time, astronauts and the space shuttle actually experience a (very small) Time Dilation during the lauch, this is evident in the fact that the mission clock @ NASA and the clock on the shuttle dont match, need I remind you that we are talking about NANO-MILLI seconds of difference here, not even noticeable to anyone but the scientists. but Time Dilation is a slowing of the passing of time as the velocity of an object made of matter approaches the speed of light. as an object is accelerated, the time dilation starts to become more and more evident, there is not miracle magic to it, it just simply happens. Time Dilation, coupled with suspended animation is the future for the human race, traveling at FTL speeds MAY be a possiblility somewhere in the distant future, but for the forseeable furture, we must rely on near FTL, and suspended animation to zoom about the cosmos.