Kolmogorov flow in two dimensional strongly coupled Yukawa liquid: A molecular dynamics study

The transition from laminar to turbulent flows in liquids remains a problem of great interest despite decades of intensive research. Here, we report an atomistic study of this transition in a model Yukawa liquid using molecular dynamics simulations. Starting from an thermally equilibrated Yukawa liquid, for a given value of coupling parameter Γ (defined as ratio of potential energy to kinetic energy per particle) and screening length κ, a subsonic flow of magnitude U₀ is superposed and transition to an unstable regime is observed eventually leading to turbulent flow at sufficiently high Reynolds numbers. We have performed a parametric study for a range of Reynolds number R and found that the flow is neutrally stable for $R<Rc(Γ)$⁠, while a transition from laminar to turbulent flow occurs for $R>Rc(Γ)$⁠, where R_c is the critical value of Reynolds number. Strong molecular shear heating is observed in all cases studied here. It is found that the coupling parameter Γ decreases because of molecular shear heating on a time scale comparable to the instability time scale. Irrespective of the initial value of coupling parameter Γ, the average heating rate is found to be sensitive to the ratio of equilibrium flow speed to the thermal speed, say, $α=U0vth$⁠, where $vth=2Γ$⁠. Our results reported here are expected to be generic and should apply to a wide variety of strongly coupled systems such as laboratory dusty plasma, molten salts, and charged colloidal systems.