JIRA search in one tab or browser should not affect searches in other tabs or browsers

This is just one example but I run into weirdnesses like this quite a bit where one search interferes with another.

1. Login to our project and go to JIRA
2. Search 1 -> Search for issues on something that results in several pages of issues
3. Search 2 -> In another tab or browser search on something that displays multiple pages of a different set of issues
4. In the original tab or browser hit the Next or '2' link to get to page 2

Expected: Results 51-100 from Search 1
Actual: Results 51-100 from Search 2

Note: Is it possible/bad if the search criteria is in the URL so it can be copied or saved as favorites instead of having to save every one as filters when may only want them temporarily or don't want to share them? Will create a separate bug if needed.