Where is the laminar sub-layer and why does it exist?

Next to the wall in a turbulent boundary layer, because the wall damps the eddies

At the edge of the laminar boundary layer, due to free stream

Far from the wall, due to low velocity

What governs shear stress in the laminar sub-layer?

Viscosity only: tau = mu du/dy, with a nearly linear profile

Which is correct for a turbulent boundary layer compared with a laminar one?

Fuller velocity profile, higher wall shear and better resistance to separation

Parabolic profile and lower wall shear

Lower wall shear and separates more easily

Thinner layer that grows more slowly

How does thickness grow in the two boundary layers?

Laminar: delta = 5x/sqrt(Re_x); turbulent: delta = 0.37x/Re_x^0.2, growing faster

Laminar: 0.37x/Re^0.2; turbulent: 5x/sqrt(Re)

Both stay constant along the plate

2078 Bhadra · 2+2 marks

Laminar sub-layer; laminar vs turbulent BL

Short answer

The laminar sublayer is a very thin viscous layer next to the wall beneath a turbulent boundary layer, where velocity varies linearly and shear is purely viscous. Laminar boundary layers have orderly flow, lower thickness (δ ∝ √x), and separate easily; turbulent layers have random eddies, greater thickness (δ ∝ x^0.8), higher shear, and resist separation better.

What is laminar Sub-layer? Differentiate between the characteristics of laminar and turbulent boundary layer.

Laminar sub-layer

In a turbulent boundary layer, a very thin layer next to the solid surface still has laminar flow, because the wall damps out the eddies there. In this layer the velocity changes almost linearly with $y$ and the shear is purely viscous, $\tau_0 = \mu\,(du/dy)$ . Its thickness is

\delta' = \frac{11.6\,\nu}{u_*},\qquad u_* = \sqrt{\tau_0/\rho}

It is only a small fraction of the total boundary layer thickness, but it controls wall shear and heat transfer, and decides whether a surface is hydraulically smooth or rough.

Laminar vs turbulent boundary layer

Point	Laminar BL	Turbulent BL
Flow	Smooth, orderly layers	Random eddies and mixing
Where	Near leading edge, $Re_x < 5\times10^5$	Downstream, $Re_x > 5\times10^5$
Shear stress source	Viscosity only	Viscosity plus turbulent (Reynolds) stress
Velocity profile	Parabolic type, gradual	Fuller, steeper at wall ( $\approx 1/7$ power law)
Thickness	$\delta = 5x/\sqrt{Re_x}$ , grows slowly	$\delta = 0.37x/Re_x^{0.2}$ , grows faster
Wall shear	Lower	Higher
Separation	Separates easily under adverse pressure gradient	Resists separation better

✓ Answer checked by Claude Opus 5.5 (high effort)

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