Tuesday 24 June 2025
Turbulent flows are a fundamental aspect of many natural and industrial processes, but understanding their behavior can be notoriously tricky. In particular, turbulent pipe flow has long been a thorn in the side of researchers, who have struggled to accurately model its complex dynamics.
One approach to tackling this problem is to use direct numerical simulation (DNS), which involves solving the Navier-Stokes equations for fluid motion on a grid. While DNS can provide incredibly detailed and accurate results, it’s only feasible for relatively simple systems and small scales. For larger or more complex flows, researchers often turn to simplified models that aim to capture the essential features of turbulence.
In recent years, one such model has gained popularity: the Barkley Model (BM), which was developed by Daniel Barkley and his colleagues in 2015. The BM is a low-order model that aims to capture the key dynamics of turbulent pipe flow, including the formation and evolution of turbulent puffs.
However, as researchers have continued to study turbulence in pulsatile pipe flows – where the flow is driven by a periodic pressure gradient – they’ve found that the BM needs some tweaking to accurately capture the behavior. Enter the Extended Barkley Model (EBM), which incorporates new features designed to improve its performance in these complex flows.
The key innovation of the EBM is its ability to account for the effects of pulsation on the mean flow profile, which can be highly nonlinear and oscillatory. By incorporating a new parameter that captures this nonlinearity, the EBM is able to better match the results of DNS simulations, which have become increasingly sophisticated in recent years.
One of the most striking features of the EBM is its ability to reproduce the complex dynamics of turbulent puffs in pulsatile pipe flows. These puffs are localized regions of turbulence that can arise spontaneously from laminar flow and then evolve into more complex patterns as they interact with the surrounding flow. The EBM is able to capture the formation, growth, and decay of these puffs, as well as their interactions with the mean flow profile.
But what about the limitations of the EBM? One major challenge is its sensitivity to the parameter γ, which controls the effect of instantaneous linear instability on turbulence. While this instability plays a key role in many turbulent flows, it’s not always clear how to accurately model its effects – and the EBM may need further refinement to fully capture these dynamics.
Cite this article: “Turbulent Pipe Flow Modeling: The Evolution of the Barkley Model”, The Science Archive, 2025.
Turbulent Flows, Pipe Flow, Direct Numerical Simulation, Navier-Stokes Equations, Simplified Models, Barkley Model, Turbulence, Pulsatile Pipe Flows, Extended Barkley Model, Nonlinear Dynamics
