## torsdag 28 november 2019

### Role of Shear Layer: No-Slip vs Slip

The book Computational Turbulent Incompressible Flow (Chap 36) describes in theory and computation the transition to turbulence in parallel shear flow such as Couette flow between two parallel plates and in a laminar boundary layer. The basic mechanism is the action of streamwise vorticity, generated from perturbations in incoming flow, which slowly redistributes the shear flow transversally into high and low speed streamwise flow streaks with increasing transversal velocity gradients, which trigger turbulence when big enough.

The transition is a threshold phenomenon based on the product of perturbation growth (scaling with Reynolds number and shear strength) and perturbation level, which if large enough triggers transition to turbulence through the above mechanism acting in a shear layer. See this picture from the book:

In particular, without shear the transition to turbulence does not get triggered. This closely connects to the discussion in recent posts on a no-slip vs a slip boundary condition on a solid wall: With no-slip there is a boundary shear layer, while with slip there is no shear layer. In other words:
• A no-slip laminar shear boundary layer may turn into a no-slip turbulent boundary layer.
• Laminar flow with slip does not develop a turbulent boundray layer.
This makes a difference for skin friction, where no-slip connects to large skin friction of a turbulent boundary layer, while slip is seen as a bypass limit of a laminar boundary layer with small skin friction.

Standard CFD is calibrated to large skin friction from tripped flat plate experiments forcing transition to a turbulent boundary layer, which then attributes most of drag to skin friction for a streamlined body like an airplane wing.

DFS with slip computes drag of all bodies including streamlined bodies (for Reynolds numbers bigger than $10^6$ beyond the drag crisis) in accordance with observations, thus as form/pressure drag with no skin friction.  This gives strong evidence that flow beyond drag crisis acts as effectively satisfying a slip boundary with small skin friction, and thus that calibration to tripped flat plate experiments has led CFD in a wrong direction.

The real catch: With slip there are no thin laminar or turbulent boundary layers to resolve computationally, and this makes DFS computable while standard CFD with boundray layers is not.

DFS supports the following conceptual understanding:
• bluff body flow = potential flow with 3d rotational slip separation into a turbulent wake.
In particular, turbulence is not generated by tripping the flow by no-slip in boundary layers, but instead from 3d rotational slip separation in the back (with small damped contribution from flow attachment in the front). This is a radical step away from Prandtl's scenario which has paralysed CFD by asking for computational resolution of very thin boundary layers beyond any forseeable computer power.