We propose that turbulent mixing layers are common in the interstellar
medium (ISM) of our Galaxy and selected external galaxies, with many
layers per kiloparsec along typical lines of sight. Initiated by shear
flows at the boundaries of hot and cold gas, these mixing layers prod
uce intermediate-temperature gas at TBAR almost-equal-to 10(5.0)-10(5.
5) K that radiates strongly in the optical, ultraviolet, and extreme u
ltraviolet. Expanding on the idea of Begelman & Fabian, we have modele
d these layers under the assumptions of rapid mixing and mean steady f
low. By including the effects of nonequilibrium ionization and self-ph
otoionization of the gas as it cools after mixing, we predict the inte
nsities of numerous optical, infrared, and ultraviolet emission lines,
as well as absorption column densities of C IV, N V, Si IV, and O VI.
Mixing layers can produce the line ratios [S II]/Halpha almost-equal-
to 0.5, [N II]/Halpha almost-equal-to 0.3-0.7, and [O II]/[O III] almo
st-equal-to 2-3, in good agreement with observations of diffuse ionize
d gas and ''interstellar froth'' in Magellanic irregular galaxies and
some edge-on spiral galaxies, and with the extended component of diffu
se ionized gas in the Seyfert galaxy NGC 1068. Mixing layers also prov
ide a transfer mechanism from hot to cold gas for reradiation of the e
nergy deposited in the hot interstellar gas by supernovae and stellar
winds. The line intensities from a mixing layer are proportional to th
e gas pressure. In the Galaxy, at a pressure P/k(B) almost-equal-to 30
00 cm-3 K, the layers can account for (1) between 2% and 10% of the di
ffuse Halpha in the Galactic disk; (2) a significant fraction (possibl
y >30%) of the diffuse Halpha at high latitude, with correct line rati
os of [S II], [N II], [O II], and [O III]; (3) all of the high-latitud
e C IV lambda1550 emission observed by Martin & Bowyer with the observ
ed ratios of O III] lambda1663 to C IV lambda1549 emission and C IV em
ission to absorption; and (4) the observed column density ratios of th
e highly ionized species C IV, N V, O VI, and Si IV if one posits some
grain depletion. Some approximately 20% of the supernova power and 75
M. yr-1 may be processed through mixing layers. Thus, these processes
could have dramatic effects on the energy budget of the Galactic foun
tain. Further observations of the emission lines O III] lambda1663, [O
III] lambda5007, and O VI lambdalambda1032, 1038 at high latitude are
important to test our models and to understand the nature of ''frothy
'' diffuse ionized gas in the ISM.