Which term describes water rushing into an area due to a rise in sea level as a tide crest approaches?

The term that describes water rushing into an area due to a rise in sea level as a tide crest approaches is indeed "Flood Current." When the tide is on the rise, water moves in from the ocean toward the shore, leading to an increase in water level in coastal regions, estuaries, and rivers. This incoming flow is characterized by the water "flooding" into these areas, which is where the term "Flood Current" originates.

This phenomenon is especially notable in tidal regions, where the dynamic interplay between the gravitational pull of the moon and sun influences sea level changes. As the tide rises, it can create strong currents that push water upstream into rivers and estuaries.

Conversely, slack water refers to the moment of calm water when the tide is neither rising nor falling, while ebb current describes the outgoing water flow during a falling tide. A tidal bore refers to a specific type of wave that travels upriver against the current caused by an incoming tide, but it is not a general term for all rising tides like flood current is.