boundaryLayerThickness
plain-language theorem explainer
Boundary layer thickness in the Tesla turbine is expressed as the gap width divided by the square root of the Reynolds number. Fluid dynamicists modeling bladeless turbines cite this scaling when optimizing disc gaps for minimal flow resistance under laminar conditions. The definition is a direct transcription of the classical approximation for boundary layer growth between parallel plates.
Claim. The boundary-layer thickness satisfies $δ(g, Re) = g / √Re$ for gap width $g ∈ ℝ$ and Reynolds number $Re > 0$.
background
The Tesla turbine module models fluid flow between stacked discs as a φ-scaled logarithmic spiral, with momentum transfer occurring through boundary-layer adhesion. Disc spacing is set proportional to φ times the boundary-layer thickness to achieve a velocity ratio of φ across the gap, thereby minimizing the J-cost of the velocity profile. J-cost is the Recognition Science cost function obeying the composition law J(xy) + J(x/y) = 2 J(x) J(y) + 2 J(x) + 2 J(y). Upstream structures from PhiForcingDerived supply the algebraic properties of this cost, while the SpiralField module defines the underlying log-spiral geometry. This definition provides the fundamental length scale for the engineering parameters enumerated in the module, including optimal disc spacing and spiral pitch.
proof idea
The declaration is a direct definition that implements the standard boundary-layer thickness formula δ = g / √Re for flow between parallel plates at Reynolds number Re.
why it matters
This definition supplies the length scale required to enforce φ-optimal disc spacing in the Tesla turbine, which in turn minimizes J-cost via the Recognition Composition Law. It underpins the module's results on spiral pitch yielding per-turn compression ratio φ and Fibonacci disc counts minimizing distribution cost. The construction links Tesla's 1913 patent geometry to the φ-forcing chain, specifically the J-uniqueness and self-similar fixed point steps. No downstream theorems depend on it directly, leaving its integration into the master certificate as an open implementation step.
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