Pore pressure in a wind‐swept rippled bed below the suspension threshold

Abstract

Toward elucidating how a wavy porous sand bed perturbs a turbulent flow above its surface, we record pressure within a permeable material resembling the region just below desert ripples, contrasting these delicate measurements with earlier studies on similar impermeable surfaces. We run separate tests in a wind tunnel on two sinusoidal porous ripples with aspect ratio of half crest‐to‐trough amplitude to wavelength of 3% and 6%. For the smaller ratio, pore pressure is a function of streamwise distance with a single delayed harmonic decaying exponentially with depth and proportional to wind speed squared. The resulting pressure on the porous surface is nearly identical to that on a similar impermeable wave. Pore pressure variations at the larger aspect ratio are greater and more complicated. Consistent with the regime map of Kuzan et al. (), the flow separates, creating a depression at crests. Unlike flows on impermeable waves, the porous rippled bed diffuses the depression upstream, reduces surface pressure gradients, and gives rise to a slip velocity, thus affecting the turbulent boundary layer. Pressure gradients within the porous material also generate body forces rising with wind speed squared and ripple aspect ratio, partially counteracting gravity around crests, thereby facilitating the onset of erosion, particularly on ripples of high aspect ratio armored with large surface grains. By establishing how pore pressure gradients scale with ripple aspect ratio and wind speed, our measurements quantify the internal seepage flow that draws dust and humidity beneath the porous surface.

Basal Pressure Variations Induced by a Turbulent Flow Over a Wavy Surface

“…Weakly non-linear developments [9,62] and measurements [10] suggest that kζ 0.2 is an upper bound for validity of the linear theory. In recorded pressure profiles, we clearly discern weakly non-linear effects, especially in Musa et al (Supplementary Figure S4), whose pressure is lower than expected on bed crests and troughs, although this effect may be due to an interaction with the porous bed underneath [29]. In addition, non-linearities also raise the effective bed roughness on a scale comparable to λ, with a first corrective term in (kζ) 2 [9].…”

“…7), whose pressure is lower than expected on bed crests and troughs, although this effect may be due to an 1. interaction with the porous bed underneath [29]. In addition, non-linearities also raise the effective bed roughness on a scale comparable to λ, with a first corrective term in (kζ) 2 [9].…”

“…Our objective is to review articles reporting pressure measurements on wavy surfaces subject to a turbulent flow. As we will discuss, existing data [29,36,37,47,56] suggest that the anomalous transition in shear stress may also arise in the pressure response. However, we recognize that the corresponding experiments, which were not designed to address this question, do not support a definitive conclusion.…”

Sediment suspension and bed morphology in a mean shear free turbulent boundary layer

“…At present, we do not have direct measurements to support or negate this, though we hypothesize a dynamic pressure field above the bed would likely show similar correlation length scales as the integral length scale of the turbulence, due to the inextricably linked velocity fluctuations and dynamic pressure gradients. Spatial pressure gradients within the bed, as described in Musa et al (2014), can reinforce ripple evolution, as the internal pressure field within a ripple induces upward seepage at the crest and a downward flux at the trough. Indeed, when examining the ripple fields produced with the 8 × 8 RASJA at low levels of sediment suspension, implications of this type of phenomenon are apparent as coarse grained material ejected from the ripple is often found at the crests whereas dark, finer sediments that may be pulled into the bed from the flow are found in the troughs.…”

“…Even in the complete absence of mean shear, local and intermittent turbulent events can generate strong shear stresses that contribute to sediment pick-up (Heathershaw & Thorne 1985). Furthermore, pressure gradients and fluctuations associated with these flows can cause fluidization of the bed and sediment motion not expected by shear alone (Foster et al 2006;Musa et al 2014).…”