What do the following phrases mean from "Ode to the West Wind"?"Thou dirge of the dying year", "Cleave themselves into chasms", "The tumult of thy mighty harmonies."
One of the techniques that is used in this poem repeatedly is apostrophe, as Shelley personifies the wind and the speaker addresses it. Thus your first phrase, "Thou dirge of the dying year," is an example of this and points towards the way that the wind represents the mourning song of the dying year, as it comes always during autumn, representing the move into winter and the "death" of the "dying year."
The second quote occurs in the third section of the poem, which describes the might and power of the West Wind and how, in response to it, nature is shown to give way in fear and respect. The Atlantic itself with its "level powers" are subject to this response, as these "powers" are shown to "Cleave themselves into chasms," dividing themselves up into different channels against the onslaught of the mighty wind.
Lastly, the final quote which comes in the last section of the poem points towards the speaker's desire to be inspired and used by this powerful elemental force of nature, that is able to produce such a strong and beautiful music, captured in the phrase "The tumult of thy mighty harmonies." The West Wind is shown to be able to metaphorically inspire great music, which is why of course the speaker begs to be the wind's instrument.