Immiscible Rayleigh-Taylor turbulence using mesoscopic lattice Boltzmann algorithms

Validation and application of the lattice Boltzmann algorithm for a turbulent immiscible Rayleigh–Taylor system

“…Also, numerical anisotropy of the Shan-Chen force generates spurious currents [33,34] within thin diffuse interfaces, which do not affect most of our measurements but may interfere with the results for enstrophy. We note that, in the companion article [21], we apply the proposed numerical scheme for the investigation of the long-time behaviour of RT systems and verify a series of phenomenological predictions.…”

“…This model approximates the Boussinesq system for the immiscible RT systems [21] considered at scales much larger than l int with the surface tension σ = 0.0059 obtained from pressure measurements for large bubbles. Similarly, one recovers the miscible Boussinesq approximation for the miscible RT systems [21] in the continuous limit for small gradients of the order parameter. The diffusion coefficient can be [43,47].…”

“…In this section, we describe the two-component lattice Boltzmann method for simulating immiscible and miscible RT systems in Boussinesq approximation; we refer to [25,26] and especially [21] for more details. In this method, spatial coordinates and time take values on the lattice with spacings x and t, and the system is described by the interactions between two species of particles A and B.…”

“…Fewer works have been dedicated to the immiscible two-dimensional (2D) viscous case [1,[13][14][15][16][17][18][19][20], and most of them are devoted to the early stages of the instability with little information about the state of developed turbulence. Only recently, the 2D immiscible RT instability was simulated for high Reynolds numbers [17,18,[21][22][23]. To the best of our knowledge, only [21] simulated a statistically homogeneous fully developed turbulent mixing layer compatible with classical phenomenological theories for immiscible RT turbulence [6,24].…”

“…Only recently, the 2D immiscible RT instability was simulated for high Reynolds numbers [17,18,[21][22][23]. To the best of our knowledge, only [21] simulated a statistically homogeneous fully developed turbulent mixing layer compatible with classical phenomenological theories for immiscible RT turbulence [6,24]. One of the reasons for this is the highly complicated pattern formed by the interfaces that appear in the immiscible case, originating high gradients and singularities in the solutions.…”