'Awrah is mainly any part of the human body that should be hidden or covered from the sight of foreigners -so called non-Mahrams- according to Islam. This is a behavior which was quoted in the qur'an and the same verse tell the women who are their mahrams -the people who might be allowed to see more of their body-:
And tell the believing women to reduce [some] of their vision and guard their private parts and not expose their adornment except that which [necessarily] appears thereof and to wrap [a portion of] their headcovers over their chests and not expose their adornment except to their husbands, their fathers, their husbands' fathers, their sons, their husbands' sons, their brothers, their brothers' sons, their sisters' sons, their women, that which their right hands possess, or those male attendants having no physical desire, or children who are not yet aware of the private aspects of women. And let them not stamp their feet to make known what they conceal of their adornment. And turn to Allah in repentance, all of you, O believers, that you might succeed. (24:31)
Due to the fact that hijab should cover the hair for a woman it doesn't matter what hair style you have or how it looks when it comes to the order of hiding it from foreign sight.
You may find this fatwa on islamqa: #6244 helpful.