It was named by the Met Office over the weekend and is expected to arrive tomorrow.
Barra follows hot on the heels of Storm Arwen, which brought widespread disruption at the end of November.
The Met Office has warned that it will bring gusts of up to 55mph to Portsmouth.
Storm Barra will hit on Tuesday, following on from wet and windy weather on Sunday night and throughout today.
While the west of Ireland will receive the worst of the storm, yellow wind weather warnings are in place across England, Wales and Northern Ireland. Yellow snow warnings are also in place in southern and western Scotland.
A yellow weather warning is in place for Portsmouth and the rest of Hampshire from 9am tomorrow until 11.59pm.
Heavy rain is also expect for much of the day in the city.
According to the latest Met Office forecast, the winds will be strongest in Portsmouth between 2pm and 4pm tomorrow – reaching speeds of 55mph.
A fresh weather warning has now been issued for between midnight and 6pm on Wednesday.
The Met Office adds that is could cause ‘potential travel disruptions’.
On its website the Met Office said: ‘Strong winds are expected to affect much of the UK on Tuesday, with potential travel disruption in places.
‘Some delays to road, rail, air and ferry transport are likely.
‘Probably some bus and train services affected, with some journeys taking longer.
‘Delays for high-sided vehicles on exposed routes and bridges likely.
‘Some short term loss of power and other services is possible.
‘It’s likely that some coastal routes, sea fronts and coastal communities will be affected by spray and/or large waves.’