Fluid-dynamical basis of the embryonic development of left–right asymmetry in vertebrates: Supplementary information about the model

where ρ is the fluid density, p the pressure, u is the velocity, ν is the viscosity, and f is the external force. For a steady (time-independent) flow the first partial derivative vanishes. The character of a steady viscous flow depends strongly on the relative magnitudes of the terms (u · ∇)u and ν∇u in the equation of motion. In order to compare them, we must put the equation into a dimensionless form. To do this, we redefine the variables u, t, p, and f , dividing them by a characteristic scale length L of the flow, a characteristic velocity U , a characteristic pressure P , and a characteristic force F . The Navier–Stokes equation then reads