Shark Skin Riblets — Turbulent Drag Reduction

Riblet Geometry

Riblet spacing s 30 µm

Height / spacing ratio h/s 0.50

Flow

Flow speed U 5.0 m/s

Reference length L 2.0 m

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Riblet spacing s⁺

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Friction velocity u_τ

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Skin-friction drag change ΔC_f

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Wall shear stress τ_w (smooth → riblet)

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How it works

Shark denticles carry parallel microscopic ridges ("riblets") aligned with the flow. They don't reduce drag by being smooth — they reduce it by controlling the streamwise vortices that dominate turbulent skin friction. The grooves pin those vortices above the ridge tips, shrinking the wetted area they can drag momentum across.

Turbulent flat-plate friction (Schlichting fit):
  Re_L = U·L / ν            C_f0 = 0.074 · Re_L^-0.2
  u_τ  = U · sqrt(C_f0 / 2)  (friction velocity)

Riblet spacing in wall units:
  s⁺ = s · u_τ / ν

Drag response (fit to Bechert et al. 1997 towing-tank data,
peak reduction ≈ 8% near s⁺ ≈ 15, crossing back to drag-increasing past s⁺ ≈ 30):
  ΔC_f/C_f0 (%) = 8 · [ 1 − ((s⁺ − 15) / 15)² ]

  τ_w = C_f · ½ρU²   (ρ = 1000 kg/m³ for water)

Riblet spacing s — the physical groove pitch in micrometres; real shark denticles and coated ship hulls sit in the 20–100 µm range.
Height/spacing ratio h/s — sharper, taller grooves (~0.5, close to nature) pin vortices best; very flat or very tall ridges lose the effect.
Flow speed U & reference length L — set the Reynolds number, which sets the friction velocity u_τ and therefore how large the physical spacing s reads out in dimensionless wall units s⁺ — the number that actually governs whether the riblets help or hurt.
Below s⁺ ≈ 15 the grooves are too small to matter much; near s⁺ ≈ 15 they reach peak drag reduction; above s⁺ ≈ 30 they start protruding into the high-speed flow and increase drag instead — exactly what the particle streaks over the two plate halves are meant to show.

Real-world relevance: riblet films modelled on shark skin have flown on Olympic swimsuits and Airbus wing panels, and are being trialled as low-friction hull coatings for cargo ships.

Fast / low-friction streak Slow / high-friction streak Riblet surface (right)

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