No abstract

We report measurements of the flow above a planar array of synthetic jets, firing upwards in a spatiotemporally random pattern to create turbulence at an air–water interface. The flow generated by this randomly actuated synthetic jet array (RASJA) is turbulent, with a large Reynolds number and a weak secondary (mean) flow. The turbulence is homogeneous over a large region and has similar isotropy characteristics to those of grid turbulence. These properties make the RASJA an ideal facility for studying the behaviour of turbulence at boundaries, which we do by measuring one-point statistics approaching the air–water interface (via particle image velocimetry). We explore the effects of different spatiotemporally random driving patterns, highlighting design conditions relevant to all randomly forced facilities. We find that the number of jets firing at a given instant, and the distribution of the duration for which each jet fires, greatly affect the resulting flow. We identify and study the driving pattern that is optimal given our tank geometry. In this optimal configuration, the flow is statistically highly repeatable and rapidly reaches steady state. With increasing distance from the jets, there is a jet merging region followed by a planar homogeneous region with a power-law decay of turbulent kinetic energy. In this homogeneous region, we find a Reynolds number of 314 based on the Taylor microscale. We measure all components of mean flow velocity to be less than 10% of the turbulent velocity fluctuation magnitude. The tank width includes roughly 10 integral length scales, and because wall effects persist for one to two integral length scales, there is sizable core region in which turbulent flow is unaffected by the walls. We determine the dissipation rate of turbulent kinetic energy via three methods, the most robust using the velocity structure function. Having a precise value of dissipation and low mean flow allows us to measure the empirical constant in an existing model of the Eulerian velocity power spectrum. This model provides a method for determining the dissipation rate from velocity time series recorded at a single point, even when Taylor's frozen turbulence hypothesis does not hold. Because the jet array offers a high degree of flow control, we can quantify the effects of the mean flow in stirred tanks by intentionally forcing a mean flow and varying its strength. We demonstrate this technique with measurements of gas transfer across the free surface, and find a threshold below which mean flow no longer contributes significantly to the gas transfer velocity.

Liu & Orfila (J. Fluid Mech. vol. 520, 2004, p. 83) derived analytical solutions for viscous boundary layer flows under transient long waves. Their analytical solutions were obtained with the assumption that the nonlinear inertia force was negligible in the momentum equations. In this paper, using Liu & Orfila's solution and the solutions for the nonlinear boundary layer equations, we examine the boundary layer flow characteristics under a solitary wave. It is found that while the horizontal component of the free-stream velocity outside the boundary layer always moves in the direction of wave propagation, the fluid particle velocity near the bottom inside the boundary layer reverses direction as the wave decelerates. Consequently, the bed shear stress also changes sign during the deceleration phase. Laboratory measurements, including the free-surface displacement, particle image velocimetry (PIV) resolved velocity fields of the viscous boundary layer, and the calculated bed shear stress were also collected to check the theoretical results. Excellent agreement is observed.

Flow and transport through aquatic vegetation is characterized by a wide range of length scales: water depth ($H$), plant height ($h$), stem diameter ($d$), the inverse of the plant frontal area per unit volume (${a}^{\ensuremath{-} 1} $) and the scale(s) over which $a$ varies. Turbulence is generated both at the scale(s) of the mean vertical shear, set in part by $a$, and at the scale(s) of the stem wakes, set by $d$. While turbulence from each of these sources is dissipated through the energy cascade, some shear-scale turbulence bypasses the lower wavenumbers as shear-scale eddies do work against the form drag of the plant stems, converting shear-scale turbulence into wake-scale turbulence. We have developed a $k$–$\varepsilon $ model that accounts for all of these energy pathways. The model is calibrated against laboratory data from beds of rigid cylinders under emergent and submerged conditions and validated against an independent data set from submerged rigid cylinders and a laboratory data set from a canopy of live vegetation. The new model outperforms existing $k$–$\varepsilon $ models, none of which include the $d$ scale, both in the emergent rigid cylinder case, where existing $k$–$\varepsilon $ models break down entirely, and in the submerged rigid cylinder and live plant cases, where existing $k$–$\varepsilon $ models fail to predict the strong dependence of turbulent kinetic energy on $d$. The new model is limited to canopies dense enough that dispersive fluxes are negligible.