Towards an impulse-based Lagrangian model of boundary layer turbulence

We describe a numerical model of near-wall flow in R2 which is based on the kinematics of sheet elements of impulse. This model is developed from Kuz’min’s [Phys. Lett. A 96 (1983) 88–90] decomposition of the velocity field, which we interpret to be a constitutive relationship. Lagrangian elements are formed from partitioning thin sheets of impulse which are created at a solid wall in response to viscous boundary conditions. We investigate numerically the case of flow over an infinite flat plate. This case is geometrically simple in the sense that boundary conditions can be imposed through the use of images. We examine the velocity fluctuation field which is established by the macroscopic effect of an ensemble of doublet elements. It is demonstrated numerically how such a field may be characterized using standard turbulence measures. We conjecture that two complementary modes of impulse creation, taken in superposition, provide insight into the underlying physical mechanisms of boundary layer turbulence.