There is a question related to this one right here but I'm more interested in the danger of those vortices. Are they very dangerous to cause a wake turbulence for the aircraft that comes behind this? Can it cause an accident or so?
The wing does a great job in straightening the propeller swirl, but adds its own vortex. Wake turbulence is dominated by the flow field around the wing.
While @Peter Kämpf 's answer is great and sufficient to answer the question, I would like to add a clarification (which should be a posted as a comment, but is too long for this format).
In the image in the question, there are visible streams of condensed water vapor from the atmosphere. These streams are only present at the blade tips. The question seems to assume that these streams depict the wake from the propellers. They don't, or more accurately there are only a very small part of the wake volume.
1. Images of tip vortices from different devices
1a, tip vortex from a propeller
Condensed water forms because the change of pressure is adiabatic, in simple terms it occurs with little exchange of heat with the neighboring regions. It occurs first where the pressure difference is large and the transition quick. (By the way, note the 8 rockets used to assist for takeoff.)
1b, tip vortex from a wing
1c: tip vortex from a rotor
There is not doubt the rotors spin in opposite direction.
tip vortex from a wind turbine
Notice: Actually after looking at oddities on this image (the direction of the wind), I realized that this is an experimental turbine used by the US DoE and the NREL to study winds. The white stream is actually smoke released from the blade. Probes are visible on the leading edge to measure speed at different locations of the blade. I keep the image as it's a good one.
2. Full wake turbulence
Contrary to the previous images, the ones below show the whole turbulence created by the same airfoils. While the tip vortices are materialized by condensed water vapor created by a transition from high to low pressure at the tip of the devices, the whole wake is visible only if air is not clear.
2a, turbulence from a propeller
Principle (no photo found, do you have one?)
2b, turbulence from a wing
2c: turbulence from a rotor
2d, turbulence from a wind turbine
3. Images where both effects are combined
Note that regardless of whether they are visible or not, both the tip vortices and full wake always exist. Their visibility greatly depends, like contrails, on the air moisture and temperature.
As explained by @Peter, the energy of the tip vortices is diluted in the energy of the actual wake turbulence:
4. Complexity of the wake
Wake from a wind turbine, mixing all sources of turbulence:
The tip vortex is initially a very small part of the wake, created by the high pressure air escaping from the low side of the wing. The whole wake volume grows in length and diameter as the airfoil moves. The vertex diameter grows, until there is no more energy left and air stops moving (see images in §3):
See this question for details: How does an aircraft form wake turbulence?