viscousRate
plain-language theorem explainer
viscousRate supplies the viscous dissipation scale as nu divided by h squared for lattice-based Navier-Stokes estimates. Workers on discrete fluid models cite it when establishing that advection is dominated by viscosity under the sub-Kolmogorov condition. The definition is a direct quotient with no additional lemmas or reductions.
Claim. The viscous dissipation rate is defined by $nu / h^2$, with $nu$ the kinematic viscosity and $h$ the lattice spacing.
background
The Vortex-Stretching module provides zero-sorry estimates for vortex stretching and viscous dissipation in discrete Navier-Stokes, drawing on published results from Thapa & Washburn (2026) on finite-volume rigidity, Washburn & Zlatanovic (2026) on reciprocal cost uniqueness, and Pardo-Guerra et al. (2026) on coherent comparison. viscousRate appears inside the OneStepData structure that packages nu, h, dt, and gradMax for a single time step on a finite lattice. It quantifies the contraction strength from viscosity at the grid scale. This rate is compared directly against advection bounds to enforce dissipation dominance.
proof idea
The declaration is a one-line definition that returns the quotient of the viscosity parameter nu by the square of the lattice spacing h. It is applied verbatim in downstream theorems without further manipulation.
why it matters
This definition is invoked by the advection_dominated_by_viscosity and gradient_nonincreasing theorems in the DiscreteMaximumPrinciple module, which establish contraction of the gradient maximum under the sub-Kolmogorov condition. It completes the viscous component of the analytic gap closures listed in the module documentation for the Navier-Stokes discretization. Within Recognition Science it supports the discrete operator framework that interfaces with the eight-tick octave and phi-ladder structures.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.