How do you notate a score that doesn't have a continuous tempo, but ebbs and flows? How can you communicate the rhythmic intentions of the composer to future players? What I was lectured that you need to feel the beat. I feel that there's a change in the beat structure mathematically it's still stays on the tempo but the feeling is different.
Without more information, I would guess that at least four things could be going on:
- Rubato: An intentional fluctuation of tempo, with an expressive goal, used in music since Romanticism. This would feel most as 'ebbs and flows' to me. Because rubato is supposed to be only a temporary deviation of the original tempo.
- Changing meter: The number of beats in a measure can temporarily change. For example, a piece or a song can go from a 3/4 meter to a 2/4 meter for just one measure and then return to 3/4. It can also be more structural: every 4/4 measure is followed by a 3/4 measure, for example.
- Syncopation: There are many kinds of syncopation, see the Wikipedia article for that, but often it feels like a missed beat or a note that is suspended over the bar line. Most popular, jazz and rock music is syncopated which can make it difficult to transcribe rhytmically for an untrained ear, especially if there isn't a clear beat played underneath it.
- Triplets or tuplets: three or more notes are played or sung in the space of one beat. Sometimes this can give a feeling of a temporary temposwitch.
It's difficult to know what you are dealing with but I would read up on those three and see if one of them qualifies.