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to advance on; to close in; to march on; to descend on (the enemy); to move towards; to surge forward (crowd, wave of nostalgia, wave, etc.); to rush for (the door); to inundate; to overwhelm; to push aside
大勢のファンがコンサート会場に押し寄せた。
A large crowd of fans surged toward the concert venue.
津波が海岸に押し寄せて大きな被害をもたらした。
The tsunami surged toward the coast, causing major damage.
年末になると様々な仕事が一度に押し寄せてくる。
At year-end, various tasks come rushing in all at once.