An aircraft wing designer is weighing two options: maintain laminar flow over the full wing surface, or accept transition to turbulent flow at 30% chord. Which statement best describes the engineering trade-off?
ATurbulent flow always reduces total drag and should be preferred at all flight conditions
BLaminar flow produces lower skin friction drag but is more vulnerable to separation under adverse pressure gradients; turbulent flow produces higher skin friction but resists separation — the right choice depends on the pressure distribution
CLaminar flow produces zero drag beyond form drag, making it always superior for efficient flight
DTurbulent flow produces both lower friction drag and lower form drag at typical cruise Reynolds numbers
A laminar boundary layer has the smooth Blasius profile with low wall shear stress, but it separates readily under adverse pressure gradients (near the trailing edge at high angle of attack). Separation causes massive pressure drag. A turbulent boundary layer has higher friction drag per unit area but carries higher near-wall momentum, keeping the flow attached through adverse gradients. On thick airfoils or at high angles of attack, the separation resistance of turbulent flow more than compensates for its higher friction drag. Designers sometimes deliberately trip transition to avoid laminar separation bubbles.
Question 2 Multiple Choice
Why does the mean velocity profile in the log layer of a turbulent boundary layer follow a logarithmic shape (u+ = (1/κ)ln(y+) + B) rather than a linear or power-law shape?
AThe log profile is a purely empirical fit to experimental data with no underlying theoretical derivation
BThe overlap layer is dominated by self-similar eddies — each length scale sees the same local structure — and dimensional analysis of this energy cascade forces the velocity gradient to scale as 1/y, which integrates to a logarithm
CViscous forces dominate in the log layer just as in the viscous sublayer, producing the same functional form via a different constant
DThe 1/7th power law and the log law are equivalent in the overlap layer; the log form is a convenient algebraic approximation
The log law emerges from the physics of an energy cascade in the overlap region. In the log layer, neither viscous nor free-stream effects dominate — only the local friction velocity u_τ and the distance from the wall y matter. Self-similarity of the turbulent structure (each eddy scale looks like any other in non-dimensional form) forces the velocity gradient to be du/dy ∝ u_τ/y. Integrating gives u ∝ ln(y), directly yielding the log law. The 1/7th power law, by contrast, is purely empirical with no theoretical basis and deviates at high Reynolds numbers.
Question 3 True / False
In a turbulent boundary layer, the viscous sublayer is a region where fluid velocity is essentially zero throughout — a stagnant film insulating the wall from the main turbulent flow.
TTrue
FFalse
Answer: False
The viscous sublayer is not stagnant. It is defined as the region where viscous stress dominates over turbulent Reynolds stress (y+ < 5), but within it the mean velocity varies linearly from zero at the wall (no-slip) to a non-negligible value at y+ ≈ 5. The law of the wall gives u+ = y+ in this region, so at y+ = 5, u+ = 5 — the local velocity is 5 times the friction velocity. Turbulent fluctuations also penetrate into the sublayer even though mean turbulent stress is small there. The sublayer governs heat and mass transfer precisely because it is thin but carries a steep velocity gradient.
Question 4 True / False
Transition from laminar to turbulent boundary layer on a flat plate can occur at Reynolds numbers significantly different from Re_x = 5×10⁵ depending on surface and flow conditions.
TTrue
FFalse
Answer: True
Re_x ≈ 5×10⁵ is the transition Reynolds number for a smooth flat plate in a low-turbulence freestream — a textbook baseline, not a universal constant. Surface roughness promotes earlier transition by introducing finite-amplitude disturbances that bypass linear instability. Free-stream turbulence intensity above ~1% can trigger transition far upstream of the smooth-plate value. Favorable pressure gradients stabilize the laminar boundary layer and can push transition well beyond 5×10⁵; adverse gradients trigger earlier transition. These variations are critical for engineering predictions of drag and heat transfer.
Question 5 Short Answer
Why does a turbulent boundary layer resist flow separation better than a laminar boundary layer, even though it produces substantially higher skin friction drag?
Think about your answer, then reveal below.
Model answer: The resistance to separation comes from the turbulent boundary layer's fuller velocity profile. In a laminar Blasius profile, velocity rises gradually from zero at the wall, and near-wall momentum is low. When pressure rises downstream (adverse pressure gradient), this low-momentum near-wall fluid decelerates rapidly and can reverse direction — causing separation. In a turbulent boundary layer, intense turbulent mixing continuously transports high-momentum fluid from the outer flow toward the wall, keeping the near-wall velocity profile steep. This high near-wall momentum resists the adverse pressure gradient: the flow stays attached over much longer stretches before reversing. The same mixing that causes high skin friction (increased momentum transport to the wall equals increased shear stress) is what keeps the boundary layer attached. Drag reduction and separation resistance are inseparably linked.
This trade-off explains why turbulence is deliberately triggered in some applications — dimples on golf balls, vortex generators on aircraft wings — to prevent separation and reduce total (friction + pressure) drag even though it increases friction drag alone.