Session R35: Turbulence: Planetary Boundary Layer

Modeling turbulent flows in the atmospheric boundary layer of Mars: application to Gale crater, Mars, landing site of the Curiosity rover.

Mars is a dry planet with a thin atmosphere. Aeolian processes -- wind-driven mobilization of sediment and dust -- are the exclusive mode of landscape variability on Mars. Craters are common topographic features on the surface of Mars, and many craters on Mars contain a prominent central mound (NASA's \textit{Curiosity} rover was landed in Gale crater). Using density-normalized large-eddy simulations, we have modeled turbulent flows over crater-like topographies that feature a central mound. We have also run one simulation of flow over a digital elevation map of Gale crater. Resultant datasets suggest a deflationary mechanism wherein vortices shed from the upwind crater rim are realigned to conform to the crater profile via stretching and tilting. This was accomplished using three-dimensional datasets (momentum and vorticity) retrieved from LES. As a result, helical vortices occupy the inner region of the crater and, therefore, are primarily responsible for aeolian morphodynamics in the crater. We have also used the immersed-boundary method body force distribution to compute the aerodynamic surface stress on the crater. These results suggest that secondary flows -- originating from flow separation at the crater -- have played an important role in shaping landscape features observed in craters (including the dune fields observed on Mars, many of which are actively evolving).   

Turbulent transitions in the stable boundary layer: Couette and Poiseuille flow

The stable boundary layer (SBL) can be classified into two distinct regimes. The weakly stable regime (WSBL) which occurs in the presence of moderate to strong pressure gradients or cloudy skies and is characterized by continuous turbulent mixing, and the very stable regime (VSBL) which occurs in the presence of weak pressure gradients or clear skies and turbulence weakens to the point of collapse. Modelling and observational results indicate that transitions from the WSBL to the VSBL occur when the maximum sustainable heat flux (MSHF), or shear capacity, is exceeded. The collapse of turbulence in the SBL is investigated using a one dimensional model of Couette flow with a constant heat flux. We show that the MSHF framework for predicting turbulent collapse is qualitatively robust to the choice of turbulence parameterization and extend these earlier stability analyses by numerically determining the unstable modes along the unstable branch. To explore transitions between the VSBL and the WSBL we extend the model to include a horizontal pressure gradient and a surface radiation scheme. Analysis of the Poiseuille flow demonstrates how the idealized energy/momentum budget model with parameterized turbulence can reproduce the regime transitions present in atmospheric data.   

Reduced-Basis Determination of Planetary Boundary-Layer Flow Statistics for a Novel Turbulence Model

Uncertainty in climate modeling and weather forecasting can largely be attributed to the omission or inaccurate representation of oceanic and atmospheric subgrid processes. Existing subgrid turbulence models are built on assumptions of isotropy, homogeneity, and the locality of correlations. Direct statistical simulation (DSS) using expansion in equal-time cumulants is a novel approach to subgrid modeling that does not make these assumptions. In prior work, a second-order closure, CE2, was shown to capture important vertical turbulent transports in Langmuir turbulence and Rayleigh-B\'{e}nard convection, but to run efficiently, this approach to turbulence modeling requires a drastic reduction in dimensionality. The present work addresses how accurately these systems can be represented with a truncated principal orthogonal decomposition (POD). The representation of turbulent transports by truncated POD bases are studied by static projection of fully resolved statistics and dynamical evolution of a reduced model. Results indicate the projected truncated turbulent statistics in these flows are less sensitive to flow details, like mixed-layer depth, than the truncated basis itself. The question of whether POD is an optimal truncation technique for these purposes is considered.   

Physics-based Enrichment of Planetary Boundary Layer LES

A new multiscale simulation methodology is introduced to facilitate efficient simulations of very high Reynolds number wall bounded flows such as the PBL. The two-simulation, one-way coupled, scale splitting methodology combining a) Non-linear wave space model using the Gabor Transform and spectral eddy-viscosity, b) Representation of the subfilter fields via a set of random modes, and c) Large Eddy Simulation using a robust subgrid scale model, is introduced. The viability of the methodology is investigated using 3 increasingly sophisticated idealizations for the PBL. In the first idealization, the surface layer is approximated using a uniform shear and a positive (stable) temperature gradient which makes the problem homogeneous. The second idealization models the PBL as a constant pressure gradient driven half channel thus introducing inhomogeneity in the vertical direction. The high latitude Stable PBL used in GABLS1 intercomparison study (Beare et. al. BLM 2006) serves as the third idealization for the PBL and it further introduces Coriolis and Stratification effects. These idealizations help validate the two-simulation methodology, where comparisons are made in terms of statistics such as space-time correlations, k-omega spectra and profiles of second order correlations.   

Flow within and above heterogeneous and homogeneous canopies.

The flow development above and within homogeneous and heterogeneous canopies was studied using planar and stereo PIV in a refractive-index-matching open channel. The homogeneous model is constituted of elements of height h arranged in staggered configuration; whereas the heterogeneous canopy consisted of elements of two heights h1 $=$ h $+$ 1/3 h and h2 $=$ h - 1/3 h alternated every two rows. Both canopies had the same roughness density, element geometry, and mean height. The flow was studied under three submergences H/h $=$ 2, 3, 4, where H denotes the flow depth. Turbulence statistics complemented with quadrant analysis and proper orthogonal decomposition reveal richer flow dynamics induced by height heterogeneity. Topography-induced spatially-periodic mean flows are observed for the heterogeneous canopy. In contrast to the homogeneous case, non-vanishing vertical velocity is maintained across the entire length of the heterogeneous canopy with increased levels at lower submergence depths. The results indicate that heterogeneous canopies exhibit greater vertical turbulent exchange at the canopy interface, suggesting a potential for greater scalar exchange and greater impact on channel hydraulic resistance.   

Flow over a model boreal forest canopy and its dependence on canopy density

Deforestation occurs due to the rapidly growing population demand for more space and resources. Effects on the canopy density are observed via a wind tunnel experiment.~ The flow field of the boreal forest canopy is obtained via particle image velocimetry where mean velocities and Reynolds stresses are evaluated.~ A scaled model that includes the traits of vegetative structures is used to represent a boreal forest within the test section of the wind tunnel.   

A study of the role of convective stratification and rates of aeolian activity on arid landscapes.

Aeolian activity -- wind-driven mobilization of sediment and dust -- is driven by aerodynamic surface stress. Existing models for aeolian activity scale mass flux on shear velocity to an exponent that exceeds unity, which demonstrates the role of turbulence in mobilizing sediment and dust. Large-eddy simulation (LES) was used to model neutrally stratified atmospheric boundary layer flows; a computational domain with very long streamwise extent was used to capture large- and very-large-scale motions. A time-series of local surface stress was used to generate a probability density function of stress, which was used to guide the selection of conditional-sampling thresholds. Results show that high stress events are caused by the passage of large scale inclined coherent structures composed of uniform momentum excesses, which are flanked on either side by low-stress regions (the opposite is true when conditioned on low stress events). Since surface heating during the daytime induces buoyancy fluxes that result in additional turbulence production (this is, in addition to production via mechanical shear), we have repeated the aforementioned simulations with convective heating. Parameters of LES cases are set to mimic flat, arid landscape with different heat flux forcing. The variation of structural inclination angle displays good general agreement with previously reported results, varying systematically with the Monin-Obukhov stability parameter under different stability conditions.   

Numerical and experimental study of flow over stages of an offset merger dune interaction.

Results of unidirectional turbulent flows over barchan dunes at high Reynolds number are presented. In order to capture the inertial-dominated dynamics typical of these environmental flows, complementary large-eddy simulations (LES) and experimental measurements have been used. A series of dune field topographies have been considered wherein a small dune is positioned at different positions upflow of a large dune, from a spanwise-offset position. The smaller dune is geometrically similar, but one-eighth the volume of the larger dune, thus replicating instantaneous realizations during actual dune interactions in laboratory or natural settings. Experimental measurement and LES are both used to study these configurations, with strong agreement reported between resultant datasets. We report that flow channeling in the interdune space induces a mean flow heterogeneity -- termed ``wake veering'' -- in which the location of maximum momentum deficit in the dune wake is spanwise-displaced. Elevated turbulent stresses are observed in the shear layers flanking the channeling flow. Finally, spatial distributions of surface stress from LES have been used to identify locations of elevated erosion, predicting bedform migration patterns. Results show that locations of minimal erosion -- whether associated with upflow sheltering or with vanishing spatial gradients of dune height -- constitute spatial ``junctions'' of coalescing, proximal dunes.   

Refractive index matched PIV measurements of flow around interacting barchan dunes.

Barchan dunes are crescent shaped bedforms found in both Aeolian and subaqueous environments, including deserts, river beds, continental shelves, and even the craters of Mars. The evolution of and dynamics associated with these mobile bedforms involve a strong degree of coupling between sediment transport, morphological change, and flow, the last of which represents the weakest link in our current understanding of barchan morphodynamics. Their three-dimensional geometry presents experimental challenges for measuring the full flow field, particularly around the horns and in the leeside of the dunes. In this study we present measurements of the turbulent flow surrounding fixed barchan dune models in various configurations using particle image velocimetry in a refractive index matching flume environment. The refractive index matching technique opens the door to making measurements in wall-parallel planes surrounding the models, as well as wall-normal plane measurements in the leeside region between the horns. While fixed bed experiments are unable to directly measure sediment transport, they allow us to focus solely on the flow physics and full resolution of the turbulent flow field in ways that are otherwise not possible in mobile bed experiments.