Atmospheric turbulence

Swirling air moves heat and pollutants. How can its mixing be predicted when hills, buildings, temperature layers and changing winds all matter? Consider a city in a mountain valley: carbon dioxide can build up near the surface overnight, while sustained winds down from the mountains can mix and replace that air. Measurements in Innsbruck document this contrast. The challenge is to predict transport across changing conditions, rather than assume one mixing rule works everywhere.[1] [2]

A mountain valley can retain near-surface emissions overnight, yet a sustained downslope wind can bring strong mixing and suppress the usual carbon-dioxide buildup. What transport laws can predict the effects of these changing flows, their temperature layering and their terrain?

Turbulent eddies carry momentum, heat and substances across a model’s resolved grid. A closure represents the effects of motions that the model does not explicitly resolve. Classical Monin–Obukhov similarity relates near-surface turbulent statistics using common scales under assumptions including steady conditions and flat, horizontally uniform terrain. Strongly stable layering—where buoyancy resists vertical displacement—can weaken vertical motions, while intermittent turbulence and other wave-like motions complicate their separation. Higher grid resolution by itself does not establish that an unresolved-motion rule is valid.

Stiperski and Calaf’s 2023 study adds turbulence anisotropy, the unequal strength of fluctuations in different directions, to similarity scaling and compares measurements across flat and mountainous sites. It improves the relations for its studied statistics and conditions; predicting anisotropy itself remains a needed step for general model use. The 2025 workshop synthesis also identifies gaps for changing, uneven and very stable flows.

Ward and colleagues’ 2022 Innsbruck study supplies a concrete transport example: sustained foehn, a downslope wind, maintained mixing into the night and reduced the usual carbon-dioxide accumulation. Some events reached the valley floor only intermittently or at different places. This observed city/flow case illustrates why wind regime and transport matter alongside emissions; it is not a rule that every downslope wind clears every pollutant everywhere.[1] [2] [3]

Measurements and models explain simpler conditions. Their rules do not reliably cover every complicated atmospheric flow.[1] [3]

Idealized similarity laws and simulations provide substantial progress. Higher resolution alone does not validate closures across real conditions; this physical modeling target differs from mathematical Navier–Stokes regularity.[1] [3]

The same emissions can produce different near-surface concentrations when air mixes differently. Predicting that transport helps interpret air-quality conditions; turbulent heat exchange also affects surface temperatures and weather.[1] [2]

Turbulent transport turns small-motion statistics into larger-scale heat budgets and concentration patterns. Testing where a closure or similarity relation works helps prevent a simulation from attributing a transport error to surface heating or emissions instead.[1] [2] [3]