Environmental Fluid Mechanics

Measurements of mixing parameters in atmospheric stably stratified parallel shear flow Abstract The mixing coefficient Г = B/ε, defined as the ratio of the magnitude of buoyancy flux B to the rate of turbulent kinetic energy (TKE) dissipation ε, plays a key role in modeling atmospheric and oceanic flows. Г is sometimes estimated using yet another fundamental quantity, the flux Richardson number (or mixing efficiency) Rif = B/P, where P is the rate of production of TKE. In practice, Г and Rif are commonly assumed as constants, but studies show that they depend on multiple parameters determined by the type of flow, for example, the gradient Richardson number Rig for stratified shear flows. During the MATERHORN field program, direct measurements of velocity and temperature profiles as well as B, ε, and P were made over an extended period using a densely instrumented flux tower. A ~ 90 min period of stratified parallel shear flow was identified in the data record, including recurrent intervals of nominally stationary flow. Measurements during this period supported the study of mixing parameters as reported in this paper. Even for this case of nature resembling an ideal flow, Г was found to be dependent on multiple parameters. Nevertheless, for periods robustly identified as shear flow in equilibrium with embedded turbulence, the measurements were in agreement with those of past stratified shear flow experiments in the laboratory. This result points to the challenges of parameterizing turbulent mixing in environmental flow models.

Fine scale structure of convective mixed layer in ice-covered lake Abstract Nonstationary convection forced by distributed buoyancy sources is a fundamental environmental fluid mechanics process, particularly in ice-covered freshwater waterbodies. In this paper, we present novel field-based results that characterise the diurnal evolution of the main energetics of radiatively-driven convection in ice-covered lakes that is the radiatively-induced buoyancy flux, B, and the kinetic energy dissipation rate, \(\varepsilon\). To estimate the spatiotemporal distribution of \(\varepsilon\) , we applied scale similarity of the velocity structure functions to identify the fine turbulence scales from high-frequency velocity measurements. The field study was carried out at Lake Vendyurskoe, Russia, in April 2016. Small-scale velocity fluctuations were measured using acoustic Doppler current profiler in a 2 m layer beneath the ice cover. The method was proven to be valid for low-energy convection without mean shear. The inertial subrange, covering order of magnitude in the spatial domain, was identified by fitting the \(^2/_3\) scaling power law to the structure function method, thus confirming the regime of fully developed turbulence. The calculated rate of dissipation of turbulent kinetic energy \(\varepsilon\) reaches values up to \(3 \times 10^{-9} \hbox { m}^{2}\hbox {s}^{-3}\) . Although a strong correlation between \(\varepsilon\) and B was observed, \(\varepsilon\) picks up about 1 h later after the onset of the heating-phase. This delay roughly corresponds to the turnover time of the energy containing eddies. We finally observed a decay of \(\varepsilon\) at night, during the relaxation-phase, but, interestingly, the level remained above the statistical error.

Efficient and accurate estimation of water surface velocity in STIV Abstract In shallow flow conditions, turbulence effects appear on a water surface as a form of irregularity of surface shape composed of a large number of fluctuating ripples. The intensity of such a fluctuation increases with the Froude number and also with the Reynolds number as can be observed in flooding river flow. In such a flow condition, surface irregularities are viewed as surface features or textures moving with the flow. Although there has been a discussion in terms of the traceability of surface features, the advection speed of surface features agrees well with the surface velocity from a practical point of view. Based on the assumption about the traceability of surface features, image-based techniques have been developed in the past decades. The space–time image velocimetry (STIV) is one of those techniques developed by Fujita et al. (Int J River Basin Man 5(2):105–114, 2007), with success of measuring river surface velocity distributions without seeding the flow. However, there is still some room for improvement in determining accurate surface velocity from a space–time image (STI) used in STIV. For that purpose, a novel technique was developed that utilizes the two dimensional auto-correlation function of the image intensity in an STI together with quality indices of STI. The performance of the new technique was verified using synthetic images as well as its application to the measurement of snowmelt flood.

Characteristic volume fractions of different grains in porous media for anomalous dispersion Abstract Anomalous solute transport in porous media is an important issue in groundwater research. In this paper, we explore the relationship between the anomalous solute transport and the volume fractions of different grains in the porous media. Via simulation, we find that there is a maximum and a minimum in the degree of anomalous transport when changing the volume fractions of different grains. Moreover, the characteristic volume fractions corresponding to the anomalous transport maximum and minimum vary little with the flow field and diffusion coefficient of the solute. We also find that the volume fraction corresponding to the most anomalous dispersion is close to the threshold of the site percolation for simple-cubic networks.

Verification of a 3D CFD model for vertical slot fish-passes Abstract In the present work, we verified a 3D computational fluid dynamics model for vertical slot fish-passes (VSFs) that employs the renormalization-group k-epsilon turbulence model (RNG KE) and the volume of fluid (VOF) method. We compared model calculations with experiments in two pool designs T1 and T2 of an experimental VSF and with 2D calculations using the shallow water equations (SWE) and the standard k-epsilon (2D SKE) model. Calculations of the 3D model showed (1) good agreement with experiments and 2D calculations in predicting mean flow velocities, (2) better performance in the determination of the water surface in the VSF, which is attributed to the accurate VOF method, (3) superior prediction of turbulence characteristics than the 2D model, which is due to the 3D RNG KE model that overcomes the problem of turbulence overestimation of the 2D SKE model, and to the fact that the 3D model takes into account the 3D features of the flow in the fish pass. Moreover, the present 3D calculations showed that the common assumptions in VSFs that (1) the flow is 2D, and (2) the simulation of 4 pools of a VSF is sufficient to obtain satisfactory results, are not always valid. Flow can be considered as 2D only in pool design T2 and for certain geometries and flow characteristics in pool design T1; while, eventually, all the pools of a fish pass need to be modeled to ensure accurate results. Finally, the present work illustrates the need to perform fish experiments simultaneously with flow experiments.

A non-negative and high-resolution finite volume method for the depth-integrated solute transport equation using an unstructured triangular mesh Abstract This paper proposes a new high-resolution finite volume method for solving the two-dimensional (2D) solute transport equation using an unstructured mesh. A new simple r-factor algorithm is introduced into the Total Variation Diminishing flux limiter to achieve a more efficient yet accurate high-resolution scheme for solving the advection term. To avoid the physically-meaningless negative solutions resulted from using the Green–Gauss theorem, a nonlinear two-point flux approximation scheme is adopted to deal with the anisotropic diffusion term. The developed method can be readily coupled with a two-dimensional finite-volume-based flow models under unstructured triangular mesh. By integrating with the ELCIRC flow model, the proposed method was verified using three idealized benchmark cases (i.e., advection of a circle-shaped solute field, advection in a cyclogenesis flow field and transport of a initially square-shaped solute plume), and further applied to simulate the non-reactive solute transport process driven by irregular tides in the Deep Bay, eastern Pearl River Estuary of China. These cases are also simulated by models using other existing methods, including different r-factor for advection term and the Green–Gauss theorem for diffusion term. The comparison between the results from the new method and those from other existing methods demonstrated the new method could describe advection induced concentration shock and discontinuities, and anisotropic diffusion at high resolution without providing spurious oscillations and negative values.

Turbulence investigation in the roughness sub-layer of a near wall flow Abstract The turbulence behaviour along a wall roughened by pyramidal elements was analysed in the region extending from the apex of the roughness elements up to the external limit of the roughness sub-layer. The data used for the analysis were obtained by particle image velocimetry technique. The rough wall turbulent boundary layer flow is characterized by a relatively low Reynolds number. All the results on the rough wall were compared with data referring to the canonical flow on a smooth wall turbulent boundary layer. Mean values and turbulence quantities for the two flows collapse when approaching the external limit of the roughness sublayer. The quadrant analysis of the Reynolds shear stress, in the region near the surface, shows that the contribution of the sweep motions is about equivalent for the two flows (except for wall distances lower than 40 viscous units). The contribution of the ejection motions appears to be more important over the smooth wall than over the rough wall with increasing differences approaching the wall. The probability density functions of the streamwise fluctuating velocity field for the rough wall case appear to be positively skewed in the zone very close to the pyramid apex, in contrast with the behavior observed for the smooth wall case at corresponding distances from the wall. The integral and Taylor scales for the rough wall case appear to be strongly reduced by the presence of the roughness, while the Kolmogorov microscale shows higher values.

Evolution and decay of gravity wavefields in weak-rotating environments: a laboratory study Abstract Gravity waves are prominent physical features that play a fundamental role in transport processes of stratified aquatic ecosystems. In a two-layer stratified basin, the equations of motion for the first vertical mode are equivalent to the linearised shallow water equations for a homogeneous fluid. We adopted this framework to examine the spatiotemporal structure of gravity wavefields weakly affected by the background rotation of a single-layer system of equivalent thickness \(h_{\ell }\) , via laboratory experiments performed in a cylindrical basin mounted on a turntable. The wavefield was generated by the release of a diametral linear tilt of the air–water interface, \(\eta _{\ell }\) , inducing a basin-scale perturbation that evolved in response to the horizontal pressure gradient and the rotation-induced acceleration. The basin-scale wave response was controlled by an initial perturbation parameter, \({\mathcal{A}}_{*} = \eta _{0}/h_{\ell }\) , where \(\eta _{0}\) was the initial displacement of the air–water interface, and by the strength of the background rotation controlled by the Burger number, \({\mathcal{S}}\) . We set the experiments to explore a transitional regime from moderate- to weak-rotational environments, \(0.65\le {\mathcal{S}} \le 2\) , for a wide range of initial perturbations, \(0.05\le {\mathcal{A}}_{*}\le 1.0\) . The evolution of \(\eta _{\ell }\) was registered over a diametral plane by recording a laser-induced optical fluorescence sheet and using a capacitive sensor located near the lateral boundary. The evolution of the gravity wavefields showed substantial variability as a function of the rotational regimes and the radial position. The results demonstrate that the strength of rotation and nonlinearities control the bulk decay rate of the basin-scale gravity waves. The ratio between the experimentally estimated damping timescale, \(T_{d}\) , and the seiche period of the basin, \(T_{g}\) , has a median value of \(T_{d}/T_{g}\approx 11\) , a maximum value of \(T_{d}/T_{g}\approx 10^{3}\) and a minimum value of \(T_{d}/T_{g}\approx 5\) . The results of this study are significant for the understanding the dynamics of gravity waves in waterbodies weakly affected by Coriolis acceleration, such as mid- to small-size lakes.

Turbulent secondary flows in wall turbulence: vortex forcing, scaling arguments, and similarity solution Abstract Spanwise surface heterogeneity beneath high-Reynolds number, fully-rough wall turbulence is known to induce a mean secondary flow in the form of counter-rotating streamwise vortices—this arrangement is prevalent, for example, in open-channel flows relevant to hydraulic engineering. These counter-rotating vortices flank regions of predominant excess(deficit) in mean streamwise velocity and downwelling(upwelling) in mean vertical velocity. The secondary flows have been definitively attributed to the lower surface conditions, and are now known to be a manifestation of Prandtl’s secondary flow of the second kind—driven and sustained by spatial heterogeneity of components of the turbulent (Reynolds averaged) stress tensor (Anderson et al. J Fluid Mech 768:316–347, 2015). The spacing between adjacent surface heterogeneities serves as a control on the spatial extent of the counter-rotating cells, while their intensity is controlled by the spanwise gradient in imposed drag (where larger gradients associated with more dramatic transitions in roughness induce stronger cells). In this work, we have performed an order of magnitude analysis of the mean (Reynolds averaged) transport equation for streamwise vorticity, which has revealed the scaling dependence of streamwise circulation intensity upon characteristics of the problem. The scaling arguments are supported by a recent numerical parametric study on the effect of spacing. Then, we demonstrate that mean streamwise velocity can be predicted a priori via a similarity solution to the mean streamwise vorticity transport equation. A vortex forcing term has been used to represent the effects of spanwise topographic heterogeneity within the flow. Efficacy of the vortex forcing term was established with a series of large-eddy simulation cases wherein vortex forcing model parameters were altered to capture different values of spanwise spacing, all of which demonstrate that the model can impose the effects of spanwise topographic heterogeneity (absent the need to actually model roughness elements); these results also justify use of the vortex forcing model in the similarity solution.

Modelling of turbulent dispersion for numerical simulation of wind-driven rain on bridges Abstract Wind-driven rain (WDR) is responsible for many potential negative effects on bridges, such as structural cracking, aggregate erosion, steel corrosion and storm water management problems and so on. Hence, accurate evaluations of the WDR effects on bridges are essential to provide solutions for preventing material degradation and improving durability capability of bridges. However, in most previous WDR numerical studies, the turbulent dispersion of raindrops was neglected. In this paper, the turbulent dispersion is integrated into Eulerian multiphase model to investigate the WDR effects on a bridge with rectangular cross-section. Especially, the influences of the turbulent dispersion are discussed in detail by comparing the WDR simulation results for the cases with and without consideration of the turbulent dispersion in terms of WDR flow fields, volume fraction, specific catch ratio, catch ratio, rain loads and aerostatic force coefficients. The results indicate that the turbulent dispersion for a certain range of raindrop size is needed to be taken into account for obtaining accurate WDR simulation results for bridges.