Von Kármán constant

The dimensionless proportionality constant in the logarithmic mean-velocity law for turbulent wall-bounded flow.

Version

v1 · 2026-09-08 · History

Domain-specific #

7440

Origin domain

turbulence

Subdomain

turbulence

Aliases

Kármán constant

Core Idea

Its approximately 0.4 value is empirical and convention-sensitive, the log law applies only in an overlap region under appropriate flow conditions, and universality across roughness Reynolds number and pressure gradients remains a qualified claim. Matching the inner shear-dominated layer with an outer inertial layer yields a mean velocity gradient inversely proportional to wall distance; integration places the constant in the slope of the log profile. The abstraction is therefore identified by a declared carrier, a transformation or constraint over that carrier, and an invariant that tells an analyst whether the named structure is genuinely present.

Scope of Application

Von Kármán constant belongs to turbulence and is useful where the analyst can specify the typed turbulence carrier, including objects, relations, parameters, conventions, evidence, boundaries, and comparison targets, then evaluate the wall-bounded flow and geometry, no-slip boundary and wall distance, density viscosity and wall shear stress, friction velocity, inner and outer scaling, logarithmic overlap region, mean velocity profile and additive intercept, definition and estimated value of kappa, roughness and Reynolds-number conditions, uncertainty and limits of universality are explicit.

Clarity

The abstraction clarifies a crowded vocabulary by making the wall-bounded flow and geometry, no-slip boundary and wall distance, density viscosity and wall shear stress, friction velocity, inner and outer scaling, logarithmic overlap region, mean velocity profile and additive intercept, definition and estimated value of kappa, roughness and Reynolds-number conditions, uncertainty and limits of universality are explicit the center of the account. A claim should name the carrier, the governing operation or relation, the applicable assumptions, and the recognition test.

Manages Complexity

Without the abstraction, an analyst must reason directly over many local details: the carrier roles, admissibility assumptions, competing conventions, derived invariants, boundary cases, and proof or validation obligations specific to Von Kármán constant. Von Kármán constant compresses them into the roles in the structural signature. That compression permits comparison across instances without erasing the variables that determine validity. It also exposes which details may be varied safely and which are constitutive.

Abstract Reasoning

1. Identify the carrier. State what the elements, states, objects, or observations are: the typed turbulence carrier, including objects, relations, parameters, conventions, evidence, boundaries, and comparison targets. Reject examples whose alleged carrier belongs to a different problem. 2. Lock the constitutive rule. Express the wall-bounded flow and geometry, no-slip boundary and wall distance, density viscosity and wall shear stress, friction velocity, inner and outer scaling, logarithmic overlap region, mean velocity profile and additive intercept, definition and estimated value of kappa, roughness and Reynolds-number conditions, uncertainty and limits of universality are explicit independently of one notation or implementation.

Knowledge Transfer

Knowledge transfers strongly among subfields of turbulence because they reuse the typed turbulence carrier, including objects, relations, parameters, conventions, evidence, boundaries, and comparison targets, Matching the inner shear-dominated layer with an outer inertial layer yields a mean velocity gradient inversely proportional to wall distance; integration places the constant in the slope of the log profile., and type the carrier, state every parameter and convention in the definition, test that the wall-bounded flow and geometry, no-slip boundary and wall distance, density viscosity and wall shear stress, friction velocity, inner and outer scaling, logarithmic overlap region, mean velocity profile and additive intercept, definition and estimated value of kappa, roughness and Reynolds-number conditions, uncertainty and limits of universality are explicit, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.

Relationships to Other Abstractions

Current abstraction Von Kármán constant Domain-specific

Parents (1) — more general patterns this builds on

• Von Kármán constant is a kind of Relation Prime

  The proposed strict upward parent is prime:relation.

Hierarchy path (1) — routes to 1 parentless root

• Von Kármán constant → Relation

Neighborhood in Abstraction Space

Von Kármán constant sits in a moderately populated region (58^th percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.

Family — Fluid Flow & Transport (27 abstractions)

Nearest neighbors

• Relative wind stress — 0.88
• Kármán vortex street — 0.88
• Acoustic streaming — 0.88
• Thermal wind — 0.87
• Stefan adhesion — 0.87

Computed from structural-signature embeddings · 2026-09-08