act of flowing in.
an inflow (opposed to outflux ): an influx of tourists.
the place at which one stream flows into another or into the sea.
the mouth of a stream.

1620–30; < Neo-Latin or Medieval Latin influxus, verbal noun of Latin influere to flow in. See in-2, flux

2. incursion, inpouring, entry. Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2014.
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World English Dictionary
influx (ˈɪnˌflʌks)
1.  the arrival or entry of many people or things
2.  the act of flowing in; inflow
3.  the mouth of a stream or river
[C17: from Late Latin influxus, from influere; see influence]

Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
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Word Origin & History

1626, from L.L. influxus "a flowing in," from influere "to flow in" (see influence). Originally of rivers, air, light, spiritual light, etc.; used of people from 1652.
Online Etymology Dictionary, © 2010 Douglas Harper
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Example sentences
Warmer waters could also alter the flow of ocean currents and initiate an
  influx of cooler water in certain areas.
But for many local residents, the influx of energy developers has not been so
Sleep was what happened when you turned out the lights and stopped the influx
  of sensation.
One of the reasons driving this undoubtedly will be the influx of e-readers.
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