More than half the US population is under a wind chill warning as a blast of freezing Arctic air sweeps south and east across the country, bringing the coldest temperatures for decades.

The whirlpool of dense air known as the “polar vortex” has caused a number of deaths, closed schools and businesses, cancelled thousands of flights and left highly-populated cities facing colder temperatures than Siberia.

Around 187 million people could eventually feel the effects of the freezing temperatures – and Americans have been warned their skin could freeze within minutes if they go outside.

The US East Coast is preparing for the cold front moving in from the Midwest on Tuesday and areas as far south as Brownsville, Texas and central Florida are facing record low temperatures.

Temperatures were 11 to 22C (20 to 40F) below average in parts of Montana, North and South Dakota, Minnesota, Iowa, Wisconsin, Michigan and Nebraska and broke records in Chicago, Oklahoma and Texas, according to the National Weather Service.

The US saw colder temperatures than Almaty, Kazakhstan, where it was -22C (8F), Mongolia at -23C (-8F) and Irkutsk, in Siberia, at -33C (-27F).

The National Weather Service has issued life-threatening wind chill warnings for temperatures as low as -51C (-60F) in western and central Dakota and officials in Indiana – hit by high winds and more than a foot (30cm) of snow – urged residents to stay indoors.

Indianapolis Mayor Greg Ballard asked schools and businesses to stay closed for another day and said: “The cold is the real killer here.

“You could be dead in 10 minutes without the proper clothes.”

New York Governor Andrew Cuomo declared a state of emergency, announcing that parts of the New York State Thruway in Western New York would be closed due to extreme winter weather conditions.

The weather has caused chaos for US business and industry, threatening to disrupt oil drilling and fracking and hit livestock and grain shipments across the farm belt, even in the Deep South.

Some 4,392 flights were cancelled and 3,577 delayed on Monday, according to FlightAware.com, which tracks airline activity.

Many airlines could not allow their ground crews to remain outdoors for more than 15 minutes at a time.

There were hundreds of cancellations by airlines including United, Southwest and American at airports across the Midwest and Northeast as supplies of fuel and de-icer froze.

The weather has been blamed for a number of deaths across Michigan, Illinois, Indiana and Ohio.

They included a 48-year-old Chicago man who had a heart attack while shovelling snow on Sunday and an elderly woman who was found outside her Indianapolis home early Monday.

Some states are beginning to turn their focus to recovery, with Illinois Governor Pat Quinn and Indiana Governor Mike Pence issuing disaster declarations, paving the way to request federal aid.

There were, however, some signs of things returning to normal in the affected areas.

etBlue Airways, which stopped all scheduled flights to and from New York and Boston on Monday, plans to resume some flights on Tuesday morning.

Southwest Airlines operations in Chicago resumed on Monday night, even if it was, as a spokesman for the Texas-based airline called it, “a trickle”.

The Minnesota Zoo announced it would reopen to the public on Tuesday and state lawmakers in Indiana plan to open their 2014 legislative session after a day’s postponement.

Warmer temperatures – at least near or above freezing – are in store for the Midwest later in the week.

Indianapolis should reach -3C (27F) on Wednesday, and other parts of the central US could climb above freezing later in the week.

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