They are smoke rocket trails. Before each test blast, technicians fired these rockets up in the air, leaving large smoke trails that rose well above the bomb's mushroom.
When the atomic blast's shockwave arrived, they moved the trails. Scientists at observation stations could instantly see the effect of the shockwave, hitting, moving and deforming the smoke columns. They were able to measure the speed of the shockwave, as well as the shape and the pressure in relation to the space.