Turbulence Coherence Within Canonical and Realistic Aeolian Dune-Field Roughness Sublayers

Abstract

Large-eddy simulation has been used to study the formation and spatial nature of inertia-dominated turbulent flows responding to aeolian sand dunes. The former is recovered from simulations initialized with a Reynolds-averaged flow, without any small-scale features, which highlights the emergence of salient structures within the dune-field roughness sublayer (RSL). The latter is based upon computation of integral lengths. In the interest of generality, these exercises are based upon flow over canonical dune geometries—which serve as a comparative benchmark—and flow over a section of the White Sands National Monument aeolian dune field in southern New Mexico. These cases, thus, capture a vast range of complexity. In both applications, we report the emergence of mixing-layer-like processes—as per results for other canopy flows—although the distinct geometric nature of the dunes shows the prevalence of a persistent interdune roller, which is aligned most closely with the streamwise direction. In order to demonstrate underlying similarities in the processes occuring above idealized and natural dune fields, we normalize the integral lengths by characteristic length scales: vorticity thickness, attached-eddy-hypothesis mixing length, and dissipation length. This exercise reveals a distinct growth and collapse pattern that is robust across all considered dune arrangements. Herein, ‘growth’ refers to the stage of downflow thickening of vortices produced via vortex shedding off the upflow dune; growth is regulated by the lesser of the distance to the wall or distance to the upflow dune, where the latter marks the beginning of the ‘collapse’ stage. Both are compliant with the notion of wall-attached eddies. In the RSL, we demonstrate that the integral lengths exhibit an optimal collapse when normalized by vorticity thickness, while inertial layer scaling is attained as close as one dune height above the top of the dune canopy. These results help to establish dune-field RSL dynamics within the broader context of canopy turbulence, which is important given the relatively greater efforts devoted to flows over vegetative canopies and urban environments.

Appendix 1

In order to establish resolution insensitivity, we show here selected results for the cases summarized in Table 1. Figure 14 shows vertical profiles of plane- and Reynolds-averaged streamwise velocity for flow over the WSNM DEM (panel a), and the idealized DEMs (panels b to e, where panel annotations denote corresponding case). Profiles are shown for the relatively high- and low-resolution cases summarized in Table 1. For all panels, the elevation, $\mathrm {max}(h)/H$, is shown for perspective. The WSNM DEM represents a ‘field’, and as such the vertical profile exhibits an inflection, a distinctive attribute of canopy flows and responsible for the continual production of Kelvin–Helmholtz eddies. Although the idealized DEMs are also part of a field of identical interactions—by virtue of the periodic boundary conditions—the spatial extent of the computational domain minimizes the emergence of field-like conditions. As such, a pronounced inflection is not recovered. Nevertheless, it is apparent that resolution insensitivity has been attained for all cases, at least within the context of the plane- and Reynolds-averaged streamwise velocity component.

To demonstrate resolution insensitivity in a higher-order turbulence statistic, we show profiles of the integral length normalized by $l_\omega$ against $x^\prime /s_x$ for the idealized (Fig. 15a) and natural (Fig. 15b) dune field. The profiles are shown for relatively low- and high-resolution LES, where Table 1 summarizes the simulation attributes. There is no discernible or systematic resolution sensitivity in the profiles.