Caf\'{e} Latte: Spontaneous layer formation in laterally heated double diffusive convection: Numerical simulations

The experiments of N. Xue et al., Nat. Commun., 8, 1960 (2017) have shown that the well-known layer formation in Caf\'{e} Latte is due to double diffusive convection, with the hot milk injected into the coffee cooling down to the side. Here we perform a corresponding numerical investigation of laterally cooled double diffusive convection where the fluid flow is driven by a horizontal temperature difference and stabilized by a vertical concentration difference.~ When the stabilization caused by the concentration field is too weak, the flow behaves like standard vertical convection in which there is a large-scale circulation throughout the domain. However, upon increasing stabilization, one observes the spontaneous formation of layers where there are several vertically-stacked circulations and every circulation forms a well-mixed layer. As time evolves, the two neighbouring layers can merge into one layer whenever there is strong enough flow that can break the interface in between. Finally, we analytically calculate the average initial height of the layers and find good agreement with our numerical data.