On the inapplicability of Navier–Stokes equations to interpreting the turbulence

The experimental data are compared with the results of numerical integration of the Navier–Stokes equations for the problem on flow around a fixed solid sphere obtained during the recent decade. It is ascertained that the qualitative rebuilding of flow, i.e., the transition from the stable regime into the unstable one, is followed by the appearance of explicit discrepancies between the calculations and the experiments. The experiments demonstrate the retention of the flow axial symmetry after the stability loss at the critical value of the Reynolds number Re∗. What this means is as follows. At Re>Re∗, the axisymmetric flow loses its stability because the weak axisymmetric fluctuations generated by the medium begin to grow. Nevertheless, both at ReRe∗ the weak non-axisymmetric fluctuations fade out, and their fading out is the cause of the retention of the flow axial symmetry. The results of all the calculations without exception are directly opposite. Namely, the stability loss is followed by the loss of the flow axial symmetry, i.e., both at ReRe∗ the weak axisymmetric disturbances fade out. At the same time, the weak non-axisymmetric disturbances begin to grow at Re>Re∗, and their growing is the cause of the loss of the flow axial symmetry. The cause of the Navier–Stokes equations failure is pointed out.