In the spirit of Which journals publish expository work? please advise:
What consistently high quality journals$^1$ today publish results that would otherwise go to a pure mathematics journal if not for the included applied content,$^2$ motivation, and examples?
PNAS (if the paper is short), Lecture Notes in Mathematics (if it's long), Journal of Interdisciplinary Mathematics, SIAM subject journals, Journal of Modern Dynamics, Journal of Mathematical Biology, Bulletin of Mathematical Biology, and International Journal of General Systems (are the last three read by working mathematicians these days?) go without saying. But what about others?
To make the question answerable, please suggest a journal per answer with comments. So that others can vote on it, and an answer can be accepted eventually.
$^1$ Many applied journals are neither read nor refereed by mathematicians primarily working in mathematics. Which makes it difficult to get appropriate referees to advise on submitted papers, at all or in a timely manner. If only because of, for example, notation or terminology lag (APS journals for example). Please only suggest journals that are not especially obscure. (There are many obscure ones, with inconsistent quality. Nothing wrong with obscurity, but as you know ... arXiv by itself is often more widely read in comparison.)
$^2$ Content that is inappropriate in a pure mathematics journal for it contains sufficiently detailed applications. Yet the applications by themselves cannot be coherently published separately from the majority of the paper, which begins with and discusses a problem of primarily mathematical interest and with conventional mathematical rigour.