Footage from the plane showed travellers clapping as it finally touched down in Glasgow after the terrifying 45-minute ordeal.
Those on board the flight said "everyone was chalk white" as the plane "felt like was going to turn 180 degrees".
Deadly Storm Ali has already claimed the lives of two people after the country was battered with 102mph winds.
Jamie Shuttleworth, who was travelling home from Ibiza with his girlfriend and her mum, told Glasgow Live: "My girlfriend's mum was crying because she was so scared."
The 26-year-old said the pilot took two attempts to land the TUI flight.
He added: "The pilot said over the tannoy 'I know a lot of you will have been sick, so just leave those behind on your seats.' The smell was awful."
Warnings have been issued for the whole of the UK today and tomorrow as the storm lingers and winds whip up once more.
The south of the UK will get a hammering today, after the north, Scotland and Ireland took the brunt of the storm yesterday.
What we know so far:
- Storm Ali crashed into the UK on Wednesday bringing 102mph winds, flying debris and travel chaos
- Two people died – a woman killed after her caravan was blown over a cliff in County Galway, named locally as a Swiss tourist, and a man who crushed by a tree in Northern Ireland
- An amber 'danger to life' warning was issued in Northern Ireland, northern parts of England and southern Scotland, but ended on Wednesday night
- The rest of the UK has a yellow weather warning in place with the Storm lasting until Friday
- More than a quarter of a million homes have been left without power in the UK and Ireland
- Schools were closed across the country with some parents warned to pick their children up
Ali claimed its first two victims yesterday after a woman, named locally as Swiss tourist Elvira Ferraii, died after the caravan she was sleeping in was blown off a cliff near Cliffden in Co Galway.
And an engineer, aged in his 20s, was then killed by a falling tree in Slieve Gullion Forest Park in Newry, Northern Ireland.
A woman in Cheshire was seriously injured when a tree fell onto her car in the high winds – fire crews eventually freed the woman before she was taken to hospital by air ambulance.
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