Penn Engineers have uncovered an unexpected universal pattern in how turbulent airflows behave over natural dune fields, offering insights into one of the most perplexing phenomena in fluid dynamics: the physics of roughness-driven internal boundary layers.
Internal boundary layers form when atmospheric flows encounter roughness transitions; think the interface of land and sea, the boundary of a meadow and forest, a wind farm, or tall city buildings.The inner region of the flow will gradually adjust and develop a new regime of wind velocity and turbulence in response to the dramatic roughness change. This wind pattern determines the transport of sand and dust, and the exchanges of moisture and carbon dioxide between land and the atmosphere. Modeling and predicting this behavior has been an immense challenge due to the complexity of the physics involved.
In a new paper published in the Proceedings of the National Academy of Sciences (PNAS), Justin Cooke, the paper’s lead author and doctoral student in Mechanical Engineering and Applied Mechanics (MEAM) and George I. Park, Assistant Professor in MEAM, discovered that regardless of the dune field geometry, inflow conditions, or streamwise position, the turbulent flow structures within the internal boundary layer exhibit a universal pattern when scaled by the local boundary layer height.
Their work represents an interdisciplinary collaboration combining Cooke’s expertise in turbulence modeling with insights from geophysics by Douglas Jerolmack, Professor in MEAM and in Earth and Environmental Science, who is interested in how wind and water drive the formation of landscape patterns over long timescales. Cooke and Park were able to simulate the full 3D airflow over a dune field geometry matched to the White Sands desert in New Mexico. Their simulations provide the most comprehensive picture yet of how airflow patterns evolve and interact with a full dune field topography.
Jerolmack’s team had previously conducted more than a decade of field work that documented dune dynamics, sand transport, and vertical profiles of wind velocity at White Sands. These data led to the hypothesis that the abrupt roughness transition, from salt flat to dunes, caused large-scale changes in wind flow that forced the dunes to slow down across the 10-kilometer long dune field. “We were never able to see these changes in the wind, however; we could only infer them by their consequences on the landscape,” says Jerolmack. “It’s impossible to collect the 4D (3D + time) wind data needed. What my collaborators have done allows me to actually see a pattern that up to now has only lived in my imagination.”
“This study allows us to fully visualize and quantify the detailed wind patterns and forces involved,” explains Park. The researchers leveraged extreme-scale computational fluid dynamics simulations, computing the airflow over a real dune field geometry from White Sands, New Mexico using an 86 million grid point mesh on thousands of processors. The simulations required thousands of processors over 2-3 months using the large-eddy simulation solver, CharLES. This cutting-edge flow solver was developed from a Stanford-originated technology firm (Cascade Technologies), which is now a part of Cadence Design Systems. Cooke spent significant time iterating on mesh generation, validating inflow conditions against field data measured by Jerolmack’s team, implementing turbulence models, and visualizing the simulated flows.
The payoff was rich 4D flow data elucidating patterns that would be impossible to directly observe in the field. The findings could have widespread implications for not only predicting dune evolution and sand and dust transport, but any scenario involving roughness transitions and internal boundary layer formation, such as atmospheric flows over cities, vegetation canopies, or even engineering surfaces.
A major discovery was that within the internal boundary layer, the turbulent flow structures exhibited a universal vertical profile, when height is scaled by the thickness of the local internal boundary layer. Regardless of streamwise position, important flow quantities describing wind turbulence collapsed onto a self-similar curve. “We were amazed to find these striking universal curves,” says Cooke. “It suggests there’s an underlying structure imprinted by the boundary layer that we’d never anticipated. It opens up new opportunities to model the flow behavior based on this scaling parameter, rather than having to fully resolve the incredibly expensive near-wall regions.”
“This is really groundbreaking work providing insights that just haven’t been possible before through experiments or theory alone,” says Park. “We’re excited to share these results and open up new avenues for modeling and understanding the physics of roughness-driven flows across many systems.” Jerolmack adds, “The complexity of turbulence generated by natural topography required this incredibly sophisticated computational effort. Yet, the surprising self-similar nature of the turbulence implies some deep underlying simplicity – which is satisfying from a scientific point of view, and useful for larger-scale atmosphere and climate simulations that require simplified models of flow at the Earth’s surface”.
The research highlights the power of combining physical insight, modern computational techniques, and access to leadership-class supercomputing facilities to elucidate fundamental processes in fluid mechanics that have remained elusive. Next steps include extending the simulations to capture finer near-wall scale motions and directly coupling the flow data to sediment transport models.
This study was conducted at the University of Pennsylvania School of Engineering and Applied Science. It was supported by the University of Pennsylvania, the National GEM Consortium Fellowship, and NASA (PSTAR Award 80NSSC22K1313). Part of this work used Anvil at Purdue University through allocation MCH230027 from the Advanced Cyberinfrastructure Coordination Ecosystem: Services & Support (ACCESS) program, which is supported by NSF grants #2138259, #2138286, #2138307, #2137603, and #2138296.