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This study derives and compares vortex identification methods for detecting vortices in planar velocity fields. Two-dimensional (2D) forms of the commonly used ∆, Q, λ ci , and λ 2 criteria are derived in detail based on the 2D counterpart of the full velocity gradient tensor. These four criteria are compared mathematically and experimentally in the case of using zero thresholds. The results show that while all methods are capable of extracting strong vortices, their efficiencies in identifying weaker vortices are not necessarily the same. The ∆ and λ ci criteria impose the least requirements on the identified structures and extract the most number of vortices, and the λ 2 criterion is the most restrictive one and tends to discard the weakest vortices. However, non-zero thresholds are generally necessary for applying vortex identification criteria in real turbulent flows, and normalizing the vortex indicators with their root mean squares is needed to enable the selection of universal threshold for vortices residing at different wall-normal positions in wall turbulence. The introduction of threshold makes the four vortex identification criteria equally efficacious, and equivalent thresholds are proposed to facilitate quantitative comparison of results based on different criteria in wall turbulence. C 2015 AIP Publishing LLC.

Collision between two identical counterflowing gravity currents was studied in the laboratory with the goal of understanding the fundamental turbulent mixing physics of flow collisions in nature, for example katabatic flows and thunderstorm outflows. The ensuing turbulent mixing is a subgrid process in mesoscale forecasting models, and needs to be parameterized using eddy diffusivity. Laboratory gravity currents were generated by simultaneously removing two identical locks, located at both ends of a long rectangular tank, which separated dense and lighter water columns with free surfaces of the same depth $H$. The frontal velocity $u_{f}$ and the velocity and density fields of the gravity currents were monitored using time-resolved particle image velocimetry and planar laser-induced fluorescence imaging. Ensemble averaging of identical experimental realizations was used to compute turbulence statistics, after removing inherent jitter via phase alignment of successive data realizations by iteratively maximizing the cross-correlation of each realization with the ensemble average. Four stages of flow evolution were identified: initial (independent) propagation of gravity currents, their approach while influencing one another, collision and resulting updraughts, and postcollision slumping of collided fluid. The collision stage, in turn, involved three phases, and produced the strongest turbulent mixing as quantified by the rate of change of density. Phase I spanned $-0.2\leqslant tu_{f}/H<0.5$, where collision produced a rising density front (interface) with strong shear and intense turbulent kinetic energy production ($t$ is a suitably defined time coordinate such that gravity currents make the initial contact at $tu_{f}/H=-0.2$). In Phase II ($0.5\leqslant tu_{f}/H<1.2$), the interface was flat and calm with negligible vertical velocity. Phase III ($1.2\leqslant tu_{f}/H<2.8$) was characterized by slumping which led to hydraulic bores propagating away from the collision area. The measurements included root mean square turbulent velocities and their decay rates, interfacial velocity, rate of change of fluid-parcel density, and eddy diffusivity. These measures depended on the Reynolds number $Re$, but appeared to achieve Reynolds number similarity for $Re>3000$. The eddy diffusivity $K_{T}$, space–time averaged over the spatial extent ($H\times H$) and the lifetime ($t\approx 3H/u_{f}$) of collision, was $K_{T}/u_{f}H=0.0036$ for $Re>3000$, with the area $A$ of active mixing being $A/H^{2}=0.037$.

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Long streamwise-elongated high-and low-speed streaks are repeatedly observed near the free surface in open channel flows in natural rivers and lab experiments. Super-streamwise vortex model has been proposed to explain this widespread phenomenon for quite some time. However, statistical evidence of the existence of the super-streamwise vortices as one type of coherent structures is still insufficient. Correlation and proper orthogonal decomposition (POD) analysis based on PIV experimental data in the streamwise-spanwise plane near the free surface in a smooth open channel flow are employed to investigate this topic. Correlation analysis revealed that the streaky structures appear frequently near the free surface and their occurrence probability at any spanwise position is equal. The spanwise velocity fluctuation usually flows from low-speed streaks toward high-speed streaks. The average spanwise width and spacing between neighboring low (or high) speed streaks are approximately h and 2h respectively. POD analysis reveals that there are streaks with different spanwise width in the instantaneous flow fields. Typical streamwise rotational movement can be sketched out directly based on the results from statistical analyses. Pointby-point analysis indicates that this pattern is consistent everywhere in the measurement window and is without any inhomogeneity in the spanwise direction, which reveals the essential difference between coherent structures and secondary flow cells. The pattern found by statistical analysis is consistent with the notion that the super-streamwise vortices exist universally as one type of coherent structure in open channel flows. Key Points:Statistical results directly sketch out streamwise rotational movement without any hypothesis Super-streamwise vortices are one type of coherent structure rather than secondary flow cells Transportation of super-streamwise vortices results in the streaky structures (2016), Statistical analysis of turbulent super-streamwise vortices based on observations of streaky structures near the free surface in the smooth open channel flow, Water Resour.

The dynamic importance of spanwise vorticity and vortex filaments has been assessed in steady, uniform open-channel flows by means of particle image velocimetry (PIV). By expressing the net force due to Reynolds' turbulent shear stress, ( )

A turbulent horseshoe vortex (HV) system is generated around a wall-normal cylinder when the approaching boundary layer separates from the wall. This study investigates the dynamics of the turbulent HV system around a circular cylinder in open channel flows with cylinder Reynolds numbers ranging from 8600 to 13900. The velocity fields in the upstream symmetry plane of the cylinder are measured using time-resolved particle image velocimetry. The joint probability density function of the streamwise and vertical velocities in the HV system region is found to exhibit three peaks, indicating that three major types of flow events are induced by the turbulent HV system. The conditional averaged velocity fields based on the characteristic velocity vectors of these events are obtained by using the method of linear stochastic estimation. The estimated flow fields reveal that the turbulent HV system interplays mainly among the back-flow, intermediate, and zero-flow modes. These modes are present for the smallest, moderate, and largest percentage of time, respectively, within the present Reynolds-number range. The major mechanism for triggering the zero-flow mode is the occurrence of an inrush of high-momentum fluid from the inner region of the approaching flow. The intermediate mode appears when the inrush of fluid is weaker than the reverse flow below the primary HV or a tertiary vortex approaches the primary HV.