In the capital, winds are likely to rise as high as 45mph, bringing torrential rain overnight.
Forecasters also say there is a "danger to life" from beach material being thrown up onto the coast.
The storm is expected to pass quickly through the emerald isle before hitting Britain, where winds can be expected to hit 80mph.
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At 6pm on Tuesday, Met Eireann warned of increasingly strong winds and gusts that are battering the country..
Later this afternoon they will also be looking to issue Flood Warnings for areas along the coast where we forecast potential flooding of properties.
A wind warning is in place for Dublin, Galway, Clare, Carlow, Kildare, Laois, Longford, Louth, Wicklow, Offaly, Westmeath, Meath, Limerick and Tipperary.
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With Storm Eleanor now in full force, it said that a gust of 139km/h was recorded at Mace Head Galway at 5pm.
The Environment Agency warned earlier that strong winds and high tides could bring coastal flooding from Tuesday until Thursday. If you are in areas affected by the flood warnings please be prepared and where necessary take action to protect property, friends and family.
Dan Harris, its deputy chief forecaster, added: "Later in the week and over the weekend there are signs of a trend to colder conditions, especially in the north, with clearer skies for many and a return of the risk of frost, ice and wintry showers".
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"Our frontline teams are on the ground, checking defences and may close coastal flood gates".