The Kadomtsev Pinch Revisited for Sheared-Flow-Stabilized Z-Pinch Modeling

Crews, Daniel W; Datta, Iman_A M; Meier, Eric T; Shumlak, Uri

doi:10.1109/TPS.2024.3383312

Although bubble pinch-off is an archetype of a dynamical system evolving toward a singularity, it has always been described in idealized theoretical and experimental conditions. Here, we consider bubble pinch-off in a turbulent flow representative of natural conditions in the presence of strong and random perturbations, combining laboratory experiments, numerical simulations, and theoretical modeling. We show that the turbulence sets the initial conditions for pinch-off, namely the initial bubble shape and flow field, but after the pinch-off starts, the turbulent time at the neck scale becomes much slower than the pinching dynamics: The turbulence freezes. We show that the average neck size, d ¯ , can be described by d ¯ ∼ ( t − t 0 ) α , where t 0 is the pinch-off or singularity time and α ≈ 0.5 , in close agreement with the axisymmetric theory with no initial flow. While frozen, the turbulence can influence the pinch-off through the initial conditions. Neck shape oscillations described by a quasi–2-dimensional (quasi-2D) linear perturbation model are observed as are persistent eccentricities of the neck, which are related to the complex flow field induced by the deformed bubble shape. When turbulent stresses are less able to be counteracted by surface tension, a 3-dimensional (3D) kink-like structure develops in the neck, causing d ¯ to escape its self-similar decrease. We identify the geometric controlling parameter that governs the appearance of these kink-like interfacial structures, which drive the collapse out of the self-similar route, governing both the likelihood of escaping the self-similar process and the time and length scale at which it occurs.

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