The kernel_task process in question is likely your process running.
You can try freeing up "inactive memory" with the purge command in Terminal, just type purge and hit return when the inactive memory gets to be a good percentage of the used memory.
You can also try running your process without the gui, or without the window server running. This will free up memory and processor resources.
Set your login window to require name and password from the accounts control panel in system preferences, turn off auto login if enabled.
Then reboot to free up memory.
from the login window (if set as username/password) type >console in the name field, hit enter, and when the window server quits...
log in at the console, shortname & enter password when prompted
type screen and hit return
screen man page - so you can have another term to watch with top; will use less resources than running gui. control-a then c to create new terminal, control-a then n to move between the two scrreens
run your process in one, run top -u -s5 to run a utility like activity monitor so you can monitor your process
when done, just exit out of both screens, and then exit out of the console to launch the window server and return the login window and back to gui
I've seen this ever since Safari 8 on OS X 10.9.5, OS X 10.10.x all versions with Safari 8 and sadly in Safari 9 on all El Capitan betas to date, too. The Safari memory leak in my case is severe and Safari has to be completely quit & restarted often. It only seems to happen if you tend to have a few windows open a lot, which you "reuse"; but overall, Safari just grows and grows (by many GB).
Suggestions about "putting in more memory" are absurd. I've a 16GB Macbook Pro laptop which is the maximum configuration of soldered-on ("pro" my rear-end!) memory which Apple provide. It simply isn't possible to add more. Memory pressure and slowdown tend to get critical when Safari exceeds 10GB. I did once persist to the point where it was using over 13GB. When restarted with all tabs manually revisited to ensure all pages are loaded, it'll go back to about 2.5Gb. A leak of that size is utterly indefensible.
This is a stark change in behaviour from Safari 7, which behaved basically fine in this regard - yet there are surprisingly few reports of it online. It isn't a subtle problem and Safari 8 has been around for ages. Others would have noticed, yet few report it.
I see it on my 10.9.5 machine, 10.10 home laptop, 10.11 test laptop and even, more recently, a 10.10 laptop at work. My conclusion is that this must be Safari screwing up when particular bookmark, cookie, cache and/or other data is present and this data must be part of the stuff it shares over iCloud - otherwise I would not have expected my independently clean-installed-by-IT-vendor work laptop to exhibit exactly the same behaviour.
Bottom line is that this seems to be a user data thing. Taking a deep breath and doing a complete Safari reset - ditching your iCloud bookmarks, emptying everything from every Safari instance on the iCloud account, deleting ~/Library/Safari and so-on - might work according to the Developer Forums. But as ever with Apple since roughly OS X 10.7, its a heisenbuggy mess and no amount of psuedorandom chicken slaying will be guaranteed to fix your issue.
Closed tab stray processes might just be down to a "bad extension", but that's no excuse - extensions are under Safari control, and a bad extension should never be able to break the browser. It's just JavaScript code executing completely under the browser's oversight. Still, we know that Safari must have very poor code for extension support given the problematic history, so that's always worth investigating if you haven't already.
Best Answer
That's actually not a lot of memory for usernoted, Finder, or Dock. "usernoted" is a known process and is installed with OS X. Do you mind telling how much memory you have, as well as what OS version? Also note that you clicked on the Compressed Memory column, rather than regular memory, which is a more accurate way of showing memory usage. Don't forget to show all processes (not just your processes).