We study the dynamics of turbulent boundary layer flow over a heterogeneous topography composed of roughness patches exhibiting relatively high and low correlation in the streamwise and spanwise directions, respectively (i.e. the roughness appears as streamwise-aligned 'strips'). It has been reported that such roughness induces a spanwise-wall normal mean secondary flow in the form of mean streamwise vorticity associated with counter-rotating boundary-layer-scale circulations. Here, we demonstrate that this mean secondary flow is Prandtl's secondary flow of the second kind, both driven and sustained by spatial gradients in the Reynolds-stress components, which cause a subsequent imbalance between production and dissipation of turbulent kinetic energy that necessitates secondary advective velocities. In reaching this conclusion, we study (i) secondary circulations due to spatial gradients of turbulent kinetic energy, and (ii) the production budgets of mean streamwise vorticity by gradients of the Reynolds stresses. We attribute the secondary flow phenomena to extreme peaks of surface stress on the relatively high-roughness regions and associated elevated turbulence production in the fluid immediately above. An optimized state is attained by entrainment of fluid exhibiting the lowest turbulent stresses -from above -and subsequent lateral ejection in order to preserve conservation of mass.

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In studies of turbulent boundary layers at high Reynolds number, the term “roughness transition” is generally an implicit reference to the case of a streamwise step-change in roughness length (whether the roughness length is associated with surface fluxes of momentum, temperature, humidity, or some other quantity). This roughness configuration and flow response has received broad attention. Here, in contrast, we consider turbulent wall-bounded flows over transverse roughness transitions using large-eddy simulation. This is accomplished simply by aligning the boundary layer freestream direction parallel to momentum roughness length transitions, instead of perpendicular. In the present cases, the bounding surface is composed of two “high roughness” strips placed between three “low roughness” strips. The influences of two parameters are evaluated: (1) λ, the ratio of the high roughness length to the low roughness length; and (2) Ls, the width of the high roughness strips. In the immediate vicinity of the roughness change, the abrupt wallstress variation induces transverse turbulent mixing which is the source of a δ-scale secondary flow, recently described as a low momentum pathway (LMP) by Mejia-Alvarez et al. [“Structural attributes of turbulent flow over a complex topography,” Coherent Flow Structures at the Earth's Surface (Wiley-Blackwell, 2013), Chap. 3, pp. 25–42] and Mejia-Alvarez and Christensen [“Wall-parallel stereo PIV measurements in the roughness sublayer of turbulent flow overlying highly-irregular roughness,” Phys. Fluids, 25, 115109]. LMPs are spatially stationary and flanked by δ-scale counter-rotating vortices which serve to pump fluid vertically from the wall, ultimately leading to a spanwise variation in the boundary layer depth (for flows over surface roughness with a converging-diverging riblet pattern, spanwise variation of δ was also found in recent experiments by Nugroho et al. [“Large-scale spanwise periodicity in a turbulent boundary layer induced by highly ordered and direction surface roughness,” Int. J. Heat Fluid Flow 41, 90–102 (2013)]. Mean velocity and transverse Reynolds stresses are used to determine the mixing length associated with transverse mixing. In general, we find that variations in Ls and λ have a strong and mild impact on the secondary flow pattern, respectively.

Many flows especially in geophysics involve turbulent boundary layers forming over rough surfaces with multiscale height distribution. Such surfaces pose special challenges for large-eddy simulation (LES) when the filter scale is such that only part of the roughness elements of the surface can be resolved. Here we consider LES of flows over rough surfaces with power-law height spectra Eh(k) ~ kβs (−3 ≤ βs < −1), as often encountered in natural terrains. The surface is decomposed into resolved and subgrid-scale height contributions. The effects of the unresolved small-scale height fluctuations are modelled using a local equilibrium wall model (log-law or Monin–Obukhov similarity), but the required hydrodynamic roughness length must be specified. It is expressed as the product of the subgrid-scale root-mean-square of the height distribution and an unknown dimensionless quantity, α, the roughness parameter. Instead of specifying this parameter in an ad hoc empirical fashion, a dynamic methodology is proposed based on test-filtering the surface forces and requiring that the total drag force be independent of filter scale or resolution. This dynamic surface roughness (DSR) model is inspired by the Germano identity traditionally used to determine model parameters for closing subgrid-scale stresses in the bulk of a turbulent flow. A series of LES of fully developed flow over rough surfaces are performed, with surfaces built using random-phase Fourier modes with prescribed power-law spectra. Results show that the DSR model yields well-defined, rapidly converging, values of α. Effects of spatial resolution and spectral slopes are investigated. The accuracy of the DSR model is tested by showing that predicted mean velocity profiles are approximately independent of resolution for the dynamically computed values of α, whereas resolution-dependent results are obtained when using other, incorrect, α values. Also, strong dependence of α on βs is found, where α ranges from α ~ 0.1 for βs = −1.2 to α ~ 10−5 for βs = −3.

A number of recent studies have demonstrated the existence of so-called large- and very-large-scale motions (LSM, VLSM) that occur in the logarithmic region of inertia-dominated wall-bounded turbulent flows. These regions exhibit significant streamwise coherence, and have been shown to modulate the amplitude and frequency of small-scale inner-layer fluctuations in smooth-wall turbulent boundary layers. In contrast, the extent to which analogous modulation occurs in inertia-dominated flows subjected to convective thermal stratification (low Richardson number) and Coriolis forcing (low Rossby number), has not been considered. And yet, these parameter values encompass a wide range of important environmental flows. In this article, we present evidence of amplitude modulation (AM) phenomena in the unstably stratified (i.e. convective) atmospheric boundary layer, and link changes in AM to changes in the topology of coherent structures with increasing instability. We perform a suite of large eddy simulations spanning weakly ($-z_{i}/L=3.1$) to highly convective ($-z_{i}/L=1082$) conditions (where$-z_{i}/L$is the bulk stability parameter formed from the boundary-layer depth$z_{i}$and the Obukhov length $L$) to investigate how AM is affected by buoyancy. Results demonstrate that as unstable stratification increases, the inclination angle of surface layer structures (as determined from the two-point correlation of streamwise velocity) increases from$\unicode[STIX]{x1D6FE}\approx 15^{\circ }$for weakly convective conditions to nearly vertical for highly convective conditions. As$-z_{i}/L$increases, LSMs in the streamwise velocity field transition from long, linear updrafts (or horizontal convective rolls) to open cellular patterns, analogous to turbulent Rayleigh–Bénard convection. These changes in the instantaneous velocity field are accompanied by a shift in the outer peak in the streamwise and vertical velocity spectra to smaller dimensionless wavelengths until the energy is concentrated at a single peak. The decoupling procedure proposed by Mathiset al.(J. Fluid Mech., vol. 628, 2009a, pp. 311–337) is used to investigate the extent to which amplitude modulation of small-scale turbulence occurs due to large-scale streamwise and vertical velocity fluctuations. As the spatial attributes of flow structures change from streamwise to vertically dominated, modulation by the large-scale streamwise velocity decreases monotonically. However, the modulating influence of the large-scale vertical velocity remains significant across the stability range considered. We report, finally, that amplitude modulation correlations are insensitive to the computational mesh resolution for flows forced by shear, buoyancy and Coriolis accelerations.

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Recent studies have demonstrated that large-and very-large-scale motions in the logarithmic region of turbulent boundary layers 'amplitude modulate' dynamics of the near-wall region (Marusic et al.prompted development of a predictive model for near-wall dynamics (Mathis et al., J. Fluid Mech., vol. 681, 2011, pp. 537-566) that has promising implications for large-eddy simulations of wall turbulence at high Reynolds numbers (owing to the presence of smaller scales as the wall is approached). Existing studies on the existence of amplitude modulation in wall-bounded turbulence have addressed smooth-wall flows, though high Reynolds number rough-wall flows are ubiquitous. Under such conditions, the production of element-scale vortices ablates the viscous wall region and a new near-wall layer emerges: the roughness sublayer. The roughness sublayer depth scales with aggregate roughness element height, h, and is typically 2h ∼ 3h. Above the roughness sublayer, Townsend's hypothesis dictates that turbulence in the logarithmic layer is unaffected by the roughness sublayer (beyond its role in setting the friction velocity and thus inducing a deficit in the mean streamwise velocity known as the roughness function). Here, we present large-eddy simulation results of turbulent channel flow over rough walls. We follow the decoupling procedure outlined in Mathis et al. (J. Fluid Mech., vol. 628, 2009a, 311-337) and present evidence that outer-layer dynamics amplitude modulate the roughness sublayer. Below the roughness element height, we report enormous sensitivity to the streamwise-spanwise position at which flow statistics are measured, owing to spatial heterogeneities in the roughness sublayer imparted by roughness elements. For y/h 1.5 (i.e. above the cubes, but within the roughness sublayer), topography dependence rapidly declines.

Crater basins on Mars host thick sedimentary sequences, which record the environments of early Mars. These basin fills commonly exhibit mound morphologies thought to arise from aeolian erosion of initially crater filling strata. This study presents transport‐based models explaining how mounds could be carved by wind. Wind tunnel experiments generated morphologies similar to those observed on Mars, and numerical modeling of flow over a crater using large‐eddy simulation (LES) demonstrated a positive feedback between topographic focusing of flow and erosion potential. Observations of yardangs, dunes, and wind streaks, all proxies for wind direction, largely agree with model results. Where mound strata origins have been interpreted, basal subaqueous deposits are overlain by aeolian deposits. This stratigraphic progression, culminating in wind‐driven excavation, is consistent with a global desiccation event. The occurrence of sedimentary mounds only on Noachian terrain argues that this event was related to late Noachian climatic change.