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Understanding check: This is the difference you'd get between consecutive readings by sticking your thermometer in a single spot of a moving fluid.

E.g. you put a thermometer at The Point, let the rivers flow for a day, then put the thermometer at The Point again, and the difference is the material derivative.


@ak-47 If you replace "day" with "yoctosecond," then yes. This is the instantaneous change in the temperature due both to the fact that the fluid may be heating up/cooling down, and the fact that it may be moving.