A framework for identifying turbulence periods with the relative financial Reynolds number: case study on six construction projects

Abstract

This study proposes a framework for identifying financial turbulence in construction project cash flows using the Relative Financial Reynolds Number (Re(t)). Inspired by fluid mechanics, the indicator captures transitions between stable, high-risk, and turbulent financial regimes and provides an early-warning mechanism for identifying liquidity stress in construction projects. Daily cash flow data from six residential construction projects in Izmir, Türkiye, were analyzed. The Relative Financial Reynolds Number was calculated as the ratio between cumulative cash flow and its daily rate of change, following an analogy derived from Bernoulli-type financial flow models. Financial regimes were classified using statistical boundaries based on the mean and standard deviation of Re(t). The empirical performance of the indicator was evaluated through ROC analysis, lead-time analysis, and Monte Carlo simulation. The results show that Re(t) captures financial turbulence periods more sensitively than conventional S-curves. ROC analysis yielded AUC values between 0.49 and 0.78 across projects, with a pooled AUC of 0.64, indicating moderate classification capability. Lead-time analysis suggests that turbulence signals appear approximately 2–3 weeks before liquidity stress events on average. Monte Carlo simulations further indicate a 60-day stress probability ranging between 0.75 and 0.90 across projects. The empirical analysis is limited to six projects within a single national context. Future research should test the model across different countries and project types and explore additional statistical validation techniques to strengthen the theoretical foundations of the approach. The six-project analysis demonstrates that Re(t), compared to conventional S-curves, more distinctly differentiates stable periods, risk clusters, and extreme turbulence regimes. It provided early indications of the impact of macroeconomic shocks (interest rate hikes, currency crises, political transitions) on project financing, while also capturing legal, parcel-based, and site-specific disruptions directly in the time series. As such, Re(t) functions as an effective early-warning mechanism for project managers, offering insights that cumulative S-curves alone cannot provide. These results strongly support the study’s main hypothesis that Re(t) serves as a more sensitive and responsive indicator of financial risks in construction projects. The primary contribution is the demonstration of the applicability of Re(t), derived from a hydraulic analogy, to project finance. This approach enables project managers to monitor not only cumulative progress but also daily volatilities and critical boundary exceedances. Thus, Re(t) can serve as a signal detection mechanism contributing to risk management.Secondly, project managers should integrate Re(t) into daily or weekly reporting to detect risks more quickly. Re(t) boundary exceedances should be carefully monitored, especially during interest rate shocks, currency crises, and liquidity shortages. Integration of the Re(t) algorithm into project finance software could facilitate practical applications. The study introduces an interdisciplinary analytical framework that connects fluid mechanics and construction finance. By conceptualizing cash flow dynamics through the Relative Financial Reynolds Number, the proposed method provides a practical early warning tool for monitoring financial turbulence in construction projects.