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

Abstract

Turbulent flows over wavy surfaces give rise to the formation of ripples, dunes and other natural bedforms. To predict how much sediment these flows transport, research has focused mainly on basal shear stress, which peaks upstream of the highest topography, and has largely ignored the corresponding pressure variations. In this article, we reanalyze old literature data, as well as more recent wind tunnel results, to shed a new light on pressure induced by a turbulent flow on a sinusoidal surface. While the Bernoulli effect increases the velocity above crests and reduces it in troughs, pressure exhibits variations that lag behind the topography. We extract the in-phase and in-quadrature components from streamwise pressure profiles and compare them to hydrodynamic predictions calibrated on shear stress data.

Hydrodynamic roughness induced by a multiscale topography

“…Consistently with a similar anomaly for the stress and pressure response (Claudin et al. 2017, 2021), it can be associated, in the model, with the lag between the thickness of the viscous sub-layer (parametrised by ) and the pressure gradient (2.5). This anomaly plays a key role in the formation of sedimentary, dissolution or sublimation bedforms, especially in low-pressure planetary conditions (Durán Vinent et al.…”

“…It is most pronounced when the flow is hydrodynamically smooth and it becomes less and less significant as R d increases (figure 4b). This striking behaviour is similar to what is also observed in the flow linear response for the behaviour of the stress coefficients A and B (Charru et al 2013;Claudin et al 2017), and the pressure coefficients C and D (Claudin, Louge & Andreotti 2021), when 10 −4 kz 0 10 −2 . This 'anomaly' takes place at the transition between a laminar and a turbulent response of the flow to the elevation profile, discussed above.…”

“…2013; Claudin et al. 2017), and the pressure coefficients and (Claudin, Louge & Andreotti 2021), when . This ‘anomaly’ takes place at the transition between a laminar and a turbulent response of the flow to the elevation profile, discussed above.…”

Water Vapor Transport Across an Arid Sand Surface—Non‐Linear Thermal Coupling, Wind‐Driven Pore Advection, Subsurface Waves, and Exchange With the Atmospheric Boundary Layer

“…Fourrière (2009) and Fourrière et al. (2010) calculated the coefficients $$\mathcal{C}$$ and $$\mathcal{D}$$ in terms of the parameter ln(2 πz 0 / λ 0 ), where z 0 is the hydrodynamic roughness (Claudin et al., 2016). Through Darcy's Equation 17, the gradient of the pressure field in Equation 34 then induces the seepage velocity at x = 0, $$${u}_{s}={U}^{2}\left[\frac{K\rho {\left({v}_{\tau }/U\right)}^{2}}{\mu (1-\nu )}\right]{\omega }_{{X}_{0}}\delta {p}^{\ast }\equiv {U}^{2}\,{\tau }_{K}\,{\omega }_{{X}_{0}}\,\delta {p}^{\ast },$$$ which, like surface pressure, features a peak lagging behind the harmonic ripple profile by a distance λ 0 ϕ 0 /(2 π ) along the wind.…”

“…is the dimensionless excursion from the ambient pressure p a at the surface, with phase lag 𝐴𝐴 𝐴𝐴0 = arctan(∕) > 0 . Fourrière ( 2009) and Fourrière et al (2010) calculated the coefficients 𝐴𝐴  and 𝐴𝐴  in terms of the parameter ln(2πz 0 / λ 0 ), where z 0 is the hydrodynamic roughness (Claudin et al, 2016). Through Darcy's Equation 17, the gradient of the pressure field in Equation 34 then induces the seepage velocity at x = 0,…”