The organizing principle for nonlinear pulsatile flow

Dataset and computational outputs for “The organizing principle for nonlinear pulsatile flow: Ginzburg–Landau universality and the structure of steady streaming in compliant tubes” This dataset contains the numerical outputs generated by the accompanying Google Colab notebook for the weakly nonlinear analysis of pulsatile flow in a compliant tube. The computations evaluate the first-order compliant-Womersley fields, the second-order steady-streaming response, the complex Ginzburg–Landau (CGL) coefficient diagnostics, and the Benjamin–Feir–Newell (BFN) instability-occupancy diagnostic over the sampled parameter domain. The control parameters are the Womersley number alpha and the prescribed real dimensionless wavenumber q = |k-hat|. The final expanded computational grid spans 3 <= alpha <= 30 and 0.5 <= |k-hat| <= 50. The archive manuscript_figures.zip contains the publication-ready figures and LaTeX table files generated by the notebook, including the primary CGL bifurcation diagram, the normalized second-order transport-intensity map, the validated BFN instability-occupancy diagnostic, the maps of mean wall shear and net streaming flux, the kinematic displacement profiles derived from the second-order mean streaming velocity, the wavenumber-dependent mean streaming velocity profiles, and the compact LaTeX table summarizing the BFN diagnostic, finite-value coverage, denominator-conditioning information, and finite-difference step-halving checks. The archive data.zip contains the numerical data files used to generate the figures and diagnostic summaries. These include grid_results.csv, which stores the main parameter-grid output containing alpha, |k-hat|, CGL coefficient components, normalized wall shear, normalized streaming flux, quality-control flags, and pointwise timing information; bfn_fd_results.csv, which stores the finite-difference BFN diagnostic output including reconstructed xi, beta, pointwise BFN values, and BFN classification flags; and bfn_occupancy_by_alpha.csv, which stores reduced BFN occupancy statistics as a function of alpha, including all finite BFN points and denominator-filtered sensitivity curves. The numerical workflow proceeds by defining the physical parameter grid in (alpha, |k-hat|), constructing the radial finite-difference discretization, evaluating the analytical first-order compliant-Womersley fields, assembling the second-order Reynolds-stress forcing, solving the mean-flow boundary-value problem using a fixed LU factorization of the radial mean-flow operator, computing the normalized second-order observables <tau_w-hat> and <Q_stream-hat>, evaluating the CGL coefficient diagnostics, reconstructing the finite-difference BFN diagnostic, reducing the pointwise BFN result to an instability-occupancy statistic, and exporting the manuscript figures, diagnostic tables, and reproducibility CSV files. The raw pointwise BFN ratio can become ill-conditioned where xi_r beta_r is small. For this reason, the dataset includes the full finite-difference BFN diagnostic values, but the manuscript figures report the BFN result primarily as an instability-occupancy statistic. The dataset also includes denominator-filtered sensitivity curves and finite-difference step-halving diagnostics to support transparent interpretation of the BFN calculation. Please cite the associated manuscript when using this dataset. If citing the computational output directly, cite this Zenodo record and the accompanying notebook. Suggested keywords: Complex Ginzburg–Landau equation; pulsatile flow; compliant tubes; Womersley flow; steady streaming; Benjamin–Feir–Newell criterion; weakly nonlinear analysis; fluid–structure interaction; scientific computing; hemodynamics.