Dynamical property and triadic interaction of Beltrami-type rotating waves

What is it about?

This work deepens previous investigations on the dynamics of the perturbations that occur in an ideal fluid with uniform rigid rotation. From a rotating reference system, solidary to the flow, it is verified that the vorticity of the perturbations is parallel to the velocity at each point, which is called Beltrami flow. The dynamics of this flow is that of a progressive rotating wave which verifies that two rotating waves with equal phase velocity do not exchange energy. We have called these two characteristics the dynamic property of the Beltrami flow. This property allows us to classify the waves, taking the phase velocity as a parameter. When the phase velocities are different, the waves exchange energy. One of the forms of this interaction is the resonant triadic interaction for which the frequency of one of the waves is equal to the sum of the frequencies of the other two and the same with the axial and azimuthal wave numbers. Under these conditions we study the linear and nonlinear stability of some resonant triadic interactions between different combinations of co-rotating (rotation in the same direction as that of the base flow) and counter-rotating (rotation in the opposite direction) waves and find criteria of stability or instability in both cases. These criteria can be interpreted as the interplay between rotation and helicity, which is a constant of motion that is a central aspect of this dynamics.

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Photo by Espen Bierud on Unsplash

Photo by Espen Bierud on Unsplash

Why is it important?

This issue is important because this type of flow occurs, for example, in atmospheric vortices such as tornadoes and rotating storms. Appear in turbomachinery where there are flows with rigid rotations that are disturbed when going through an expansion or contraction in a tube such as in dam turbines. In astrophysical plasmas such as loops and prominences in the solar corona, in the formation of highly collimated jets in accretion disks. And in magnetohydrodynamics when perturbing uniform rigid rotating base flow together with a base magnetic field of toroidal type.

Perspectives