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Do you have any green matter mixed in with those leaves? If not you may want to add some to help the process along. Also as oregonwoodsmoke says, you are gonna have to be able to turn that pile every so often. Can that be done with your setup. If not follow his suggestion on adding a perforated pipe down the center to get some air thru it. If all is good, black gold is in your future!
Or.... if all your garden debris fits in that relatively small container, why not just till the debris into the soil and let it do it's thing naturally in situ. Nothing comes out of a compost pile that you didn't put in it in the first place. It's not magic.
Composting is for gathering organic material from far & wide, concentrating it and then augmenting a much smaller area (your garden plot) with the nutrients. Using only the proceeds of the garden only recycles what originally came out of it and doesn't actually "improve" the soil (except for texture).
Is the compost pile near the neighbor's property (I see the fence)? My city has a 5' setback for many things, so I comply just out of caution and civility.
I like your open air design a lot but I don't think it's going to break down into compost in the same manner as a compacted pile that gets cooking and steaming hot in the middle. However, I think with your design you can still convert it into really good organic material suitable for the gardens with the help of earth worms if you add some.
I don't know how much rain you get where you are but if you don't get a lot you can always sprinkle it with a hose or watering can from time to time. Don't pack it down too tight, water it and let it pack down naturally. Once the leaves have softened and started to break down and go mushy from the moisture you can speed up the process by throwing a few hands full of earth worms into it to break it down further. Just drop the worms down the middle of that chimney and scattered about near the top just under the top layer of leaves so birds don't take them.
The earth worms will start working their way through it and eating the softened leaves and convert them into worm castings. It will be a smorgasbord for them so they will likely stay at all levels in the leaves rather than going down into the ground unless you get below freezing temperatures for an extended time. If that happens they will go down into the ground beneath the pile where it is warmer. You could cover the whole thing over with a tarp or big sheet of plastic if you get extended freezing temperatures. That will help it to stay warmer and protect your worker worms.
(If I was going to try a design like that here where I live and where it's a lot colder climate, I would definitely have to protect it from the cold and winds by covering and wrapping it with a tarp or heavy plastic throughout the entire winter.)
When you go to open it up to turn it later remember to spread a tarp on the ground in front and around of it first to catch the stuff that falls out when you open up the two mesh overlaps. Makes it so much easier to gather it up on the tarp and dump it back in when you're finished turning it.
Good luck with this design, I look forward to an update on this thread after you turn the contents.
I've found the easiest and best system so far to be four pallets with the back and sides tied together with wire twine, and the front leaned to, to keep domestic pets out. The front can easily be moved aside to get in there and turn it.
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I look forward to an update on this thread after you turn the contents. 
