Oblique instability of a stratified oscillatory boundary layer

The instability and dynamics of a vertical oscillatory boundary layer in a container filled with a stratified fluid are addressed. Past experiments have shown that when the boundary oscillation frequency is of the same order as the buoyancy frequency, the system is unstable to a herringbone pattern of oblique waves. Prior studies assuming the basic state to be a unidirectional oscillatory shear flow were unable to account for the oblique waves. By accounting for confinement effects present in the experiments, and the ensuing three-dimensional structure of the basic state, we are able to numerically reproduce the experimental observations, opening the door to fully analysing the impacts of stratification on such boundary layers.

Mean flow structure and velocity–bed shear stress maxima phase difference in smooth wall, transitionally turbulent oscillatory boundary layers: direct numerical simulations

Direct numerical simulations of oscillatory boundary-layer flows in the transitional regime were performed to explain discrepancies in the literature regarding the phase difference ${\rm \Delta} \phi$ between the bed-shear stress and free-stream velocity maxima. Recent experimental observations in smooth bed oscillatory boundary-layer (OBL) flows, showed a significant change in the widely used ${\rm \Delta} \phi$ diagram (Mier et al., J. Fluid Mech., vol. 922, 2021, A29). However, the limitations of the point-wise measurement technique did not allow us to associate this finding with the turbulent kinetic energy budget and to detect the approach to a ‘near-equilibrium’ condition, defined in a narrow sense herein. Direct numerical simulation results suggest that a phase lag occurs as the result of a delayed and incomplete transition of OBL flows to a stage that mimics the fully turbulent regime. Data from the literature were also used to support the presence of the phase lag and propose a new ${\rm \Delta} \phi$ diagram. Simulations performed for ${\textit {Re}}_{\delta }=671$ confirmed the sensitivity in the development of self-sustained turbulence on the background disturbances ( $\textit{Re}_{\delta}=U_{o}\delta/\nu$ , where $\delta=[2\nu/\omega]^{1/2}$ is the Stokes' length, $U_{o}$ is the maximum free stream velocity of the oscillation, $\nu$ is the kinematic viscosity and $\omega=2{\rm \pi}/T$ is the angular velocity based on the period of the oscillation T). Variations of the mean velocity slope and intersect values for oscillatory flows are also explained in terms of the proximity to near-equilibrium conditions. Relaminarization and transition effects can significantly delay the development of OBL flows, resulting in an incomplete transition. The shape and defect factors are examined as diagnostic parameters for conditions that allow the formation of a logarithmic profile with the universal von Kármán constant and intersect. These findings are of relevance for environmental fluid mechanics and coastal morphodynamics/engineering applications.

Turbulence statistics in smooth wall oscillatory boundary layer flow

Turbulence characteristics of an asymmetric oscillatory boundary layer flow are analysed through two-component laser-Doppler measurements carried out in a large oscillatory flow tunnel and direct numerical simulation (DNS). Five different Reynolds numbers, $R_{\unicode[STIX]{x1D6FF}}$, in the range 846–2057 have been investigated experimentally, where $R_{\unicode[STIX]{x1D6FF}}=\tilde{u} _{0max}\unicode[STIX]{x1D6FF}/\unicode[STIX]{x1D708}$ with $\tilde{u} _{0max}$ the maximum oscillatory velocity in the irrotational region, $\unicode[STIX]{x1D6FF}$ the Stokes length and $\unicode[STIX]{x1D708}$ the fluid kinematic viscosity. DNS has been carried out for the lowest three $R_{\unicode[STIX]{x1D6FF}}$ equal to 846, 1155 and 1475. Both experimental and numerical results show that the flow statistics increase during accelerating phases of the flow and especially at times of transition to turbulent flow. Once turbulence is fully developed, the near-wall statistics remain almost constant until the late half-cycle, with values close to those reported for steady wall-bounded flows. The higher-order statistics reach large values within a normalized wall distance of approximately $y/\unicode[STIX]{x1D6FF}=0.2$ at phases corresponding to the onset of low-speed streak breaking, because of the intermittency of the velocity fluctuations at these times. In particular, the flatness of the streamwise velocity fluctuations reaches values of the order of ten, while the flatness of the wall-normal velocity fluctuations reaches values of several hundreds. Far from the wall, at locations where the vertical gradient of the streamwise velocity is zero, the skewness is approximately zero and the flatness is approximately equal to 3, representative of a normal distribution. At lower elevations the distribution of the fluctuations deviate substantially from a normal distribution, but are found to be well described by other standard theoretical probability distributions.

On the formation of sediment chains in an oscillatory boundary layer

The dynamics of spherical particles resting on a horizontal wall and set into motion by an oscillatory flow is investigated by means of a fully coupled model. Both a smooth wall and a rough wall, the latter being composed of resting particles with a random arrangement and with the same diameter as the moving particles, are considered. The fluid and particle motions are determined by means of direct numerical simulations of Navier–Stokes equations and Newton’s laws, respectively. The immersed boundary approach is used to force the no-slip condition on the surface of the particles. In particular, the process of formation of transverse sediment chains, within the boundary layer but orthogonal to the direction of fluid oscillations, is simulated in parameter ranges matching those of laboratory experiments investigating rolling-grain ripple formation. The numerical results agree with the experimental observations and show that the transverse sediment chains are generated by steady recirculating cells, generated by the interaction of the fluid and particle oscillations.