Most words with the spelling au are pronounced with (RP) ɔː. That is what we have in saucer, author, applaud, paunch, Paul, and so on.
There are various other possibilities for au. In cauliflower and sausage the vowel is ɒ. In aunt it is ɑː (AmE æ). In gauge it is eɪ.
In French words it is usually əʊ, as in chauffeur, gauche, mauve and sauté, though I have noticed that in the name De Gaulle, rather than the expected əʊ. it is quite often ɔː (which is actually a closer phonetic fit to French o).
In German words, though, we get aʊ, as in (sauer)kraut, Strauss, Faust(ian) and Gauss(ian). However the trade name Braun usually has ɔː, whilst Audi can go either way.
We also often get aʊ rather than ɔː in a number of scientific words of Greek origin, such as the trauma we started off with, and also glaucoma and tau. But this does not apply to those words of Greek origin that are NOT particularly scientific: autograph, nautical, authentic. The latter have come to us via Latin and/or French, while the former are taken directly from Greek: τραῦμα ‘wound’, γλαύκωμα ‘greyness’. It’s interesting that somehow even non-classicists can tell the difference, and even classicists are not tempted to use Latin-style aʊ in words of direct Latin origin such as augment, auxiliary.
A quite special case is aural, not a Greek word, sometimes pronounced ˈaʊrəl so as to distinguish it aurally (sorry) from oralˈɔːrəl.
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I shall be out of circulation for the next few days. Next posting: 26 Sept.