The Met Office has issued weather warnings over the tail end of the ex-hurricane.
Amber “be prepared” weather warnings covering Dumfries and Galloway, Lothian and Borders and Strathclyde warn of “potential for injuries and danger to life” from flying debris and high waves as wind gusts up to 80mph are expected.
A yellow “be aware” warning is in place for Central, Tayside, Fife, the Highlands and Western Isles.
Motorists on the M77 faced lengthy tailbacks on Monday as a lorry overturned in high winds at about 8.30am and blocked the southbound lane for more than a hour.
The accident happened near junction two.
Meanwhile, several flights from Scottish airports were cancelled due to the storm.
Glasgow Airport advised customers to check with their airline due to flight cancellations caused by high winds, including Aer Lingus departures to Dublin, Cork and Donegal.
Ryanair flights to Dublin, Warsaw, Frankfurt and London Stansted were also cancelled.
The airport said in a statement: “We are open and operating as normal but some flights have been cancelled due to Ophelia and we expect more disruption later today, so please check with your airline for specific flight information.”
Aer Lingus flights from Edinburgh to Dublin were also cancelled as were Flybe departures to Belfast from Edinburgh and Aberdeen.
Loganair passengers booked on some west-coast routes have been offered free flight changes, including those on flights from Glasgow to Barra, Benbecula, Campbeltown and Tiree.
Loganair managing director Jonathan Hinkles said: “Weather forecasts indicate that high winds and rain will impact the west of Scotland from Monday afternoon through to Tuesday lunchtime.
“The possibility of weather disruption to our flights is increased and we’re therefore offering customers booked to travel on certain routes on Monday and Tuesday the opportunity to voluntarily rearrange their travel without charge.”
The storm has also hit ferry routes, with Calmac sailings from Oban to Barra and Colonsay and the Uig to Tarbert route among those cancelled due to forecast high winds.
Northlink Ferries warned of delays to the Northern Isles sailings.
An Edinburgh Airport spokesman said: “Due to the weather, the only disruption we are currently experiencing is to our Irish flights.
“Aer Lingus have cancelled the rest of their flights for Monday, Ryanair, EasyJet and FlyBe are also experiencing some cancellations.
“We would advise passengers flying to Ireland to check with their airline in advance of coming to the airport. All other flights are currently operating as normal to and from Edinburgh Airport.”