Stratified Channel Research Articles

Modal and nonmodal stability analysis of turbulent stratified channel flows

Modal and nonmodal stability analysis of turbulent stratified channel flows

Quantifying and predicting near-wall global intermittency in stably stratified channel flow

Quantifying and predicting near-wall global intermittency in stably stratified channel flow

Comparisons of temperature structures with turbulent structures in thermally stratified channel flows by direct numerical simulation

Direct numerical simulation (DNS) in the thermally stratified turbulent channel flow with the Boussinesq approximation at Reynolds number Reτ≈395, Prandtl number Pr=0.71 and Richardson number Riτ=−10,0 and 10 is performed in this study. Based on the DNS data, the three-dimensional structure of temperature fluctuations and the effect of stratification stability on temperature structure morphology, scale and volume are investigated. Results show that thermal buoyancy has a significant effect on the temperature structure under different stratifications. Specially, the three-dimensional structure of temperature fluctuations has similar morphological characteristics to that of streamwise velocity fluctuations only in the near-wall region under stable and neutral stratifications. The streamwise length of the temperature structure decreases with the height, but the structure volume increases linearly with the height. However, under the unstable stratification (Riτ=−10), the thermal buoyancy makes the turbulence form a quasi-streamwise large-scale convective structure directly enhancing the large-scale temperature structure. So the streamwise length and spanwise width of the temperature structure increase with the height, and the spanwise width exhibits a discontinuous jump with the height. At the same time, the scale size of the temperature structure in the outer regions is almost constant, thus the structure volume increases nonlinearly with the height. In addition, the temperature fluctuations are also affected by thermal buoyancy. The thermal buoyancy enhances the large-scale temperature structure in the near wall region through the modulation of the large-scale turbulent structure in the outer regions on the temperature large-scale fluctuations near the wall. Which results in the similarity between the temperature structure and streamwise velocity structure in the near-wall region being destroyed.

Secondary flows induced by two-dimensional surface temperature heterogeneity in stably stratified channel flow

The structure and impact of thermally induced secondary motions in stably stratified channel flows with two-dimensional surface temperature inhomogeneities is studied using direct numerical simulation (DNS). Starting from a configuration with only spanwise varying surface temperature, where the streamwise direction is homogeneous (Bon & Meyers, J. Fluid Mech., 2022, pp. 1–38), we study cases where the periodic temperature strip length $l_x/h$ (with $h$ the half-channel height) assumes finite values. The patch width ( $l_y/h =\{{\rm \pi} /4, {\rm \pi}/8$ }) and length are varied at fixed stability and two different Reynolds numbers. Results indicate that for the investigated patch widths, the streamwise development of the secondary flows depends on the patch aspect ratio ( $a=l_x/l_y$ ), while they reach a fully developed state after approximately $25l_y$ . The strength of the secondary motions, and their impact on momentum and heat transfer through the dispersive fluxes, is strongly reduced as the length of the temperature strips decreases, and becomes negligible when $a\lesssim 1$ . We demonstrate that upward dispersive and turbulent heat transport in locally unstably stratified regions above the high-temperature patches lead to reduced overall downward heat transfer. Comparison to local Monin–Obukhov similarity theory (MOST) reveals that scaled velocity and temperature gradients in homogeneous stably stratified channel flow at $Re_\tau =550$ agree reasonably well with empirical correlations obtained from meteorological data. For thermally heterogeneous cases with strips of finite length, the similarity functions only collapse higher above the surface, where dispersive fluxes are negligible. Lastly, we show that mean profiles of all simulations collapse when using outer-layer scaling based on displacement thickness.

Stratification and temporal evolution of mixing regimes in diurnally heated river flows

Direct numerical simulations of stratified open channel flows subject to a varying surface heat flux are performed. The influence of the diurnal heating time on the spatial and temporal variation of mixing in the flow and the characteristics of the mean flow state are examined. The control parameters are the bulk stability parameter lambda_{B}, defined through the ratio of the channel height delta and a bulk Obukhov length scale mathscr{L}_{B}, and the diurnal time scale hat{t}, defined as the ratio of the heating time to an eddy turnover time. The Prandtl number Pr and Reynolds number Re_{tau} have values of 1 and 400. Simulations are performed over hat{t} = 1 to 24 and lambda_{B} = 0.6 to 26. Two key flow features are used to classify the flow regimes observed, namely the laminar layer depth (LLD) and stratified layer depth (SLD) where the LLD is defined as the depth from the free surface when the buoyancy Reynolds number Re_{B} approx 7 and the SLD is the depth from the free surface when the turbulent Froude number Fr approx 1. This study attempts to characterise how these length scales vary across the diel cycle. The LLD is a viscous length scale and a regime map of a viscous parameter, the bulk Obhukov Reynolds number Re_mathscr{L}, and hat{t} is presented to classify the LLD behaviour. A regime map of lambda _{B} and hat{t} is presented to classify the behaviour of the SLD. Three classifications for each layer depth behaviour within a diel cycle form the basis of the regime maps for this paper: a neutral flow where the LLD or SLD does not exist (denoted by NL and NS), a stratified flow where the LLD or SLD are diurnally varying (denoted as DL and DS) and a persistent layer of the LLD or SLD (denoted as PL and PS). The transition between the NL to DL is hat{t} propto Re_{mathscr{L}}^{4.5}, DL to PL is hat{t} propto Re_{mathscr{L}}^{- 0.5}, NS to DS is hat{t} propto lambda _{B}^{0} and DS to PS is hat{t} propto lambda _{B}^{1}. The regime maps may be used as a predictive tool to determine when suppressed mixing regimes occur in rivers. At each flow depth, the flow sweeps though a range of mixing states across the diel cycle. The local mixing efficiency are briefly assessed and found to scale well with the instantaneous Fr number according to the regimes proposed by Garanaik and Venayagamoorthy (J. Fluid Mech., vol. 867, 2019, pp. 323-333).

Non-normal energy amplifications in stratified turbulent channels

Non-normal energy amplifications in stratified turbulent channels

Intermittency and critical mixing in internally heated stratified channel flow

Through direct numerical simulations we investigate the effects of spatiotemporal intermittency as a result of stable stratification in surface heated stratified open channel flow. By adapting the density inversion criterion method of Portwood et al. [J. Fluid Mech., vol. 807, 2016, R2] for our flow, we demonstrate that the flow may be robustly separated into regions of active turbulence for which $Re_B \gtrsim {O}(10)$ and surrounding quiescent fluid, where $Re_B$ is the buoyancy Reynolds number. The intermittency in the flow spontaneously manifests as a deformed horizontal interface between the upper quiescent and lower turbulent flow, characterised by vigorous mixing from ‘overturning’ shear instabilities. The resulting vertical intermittency profile is accurately predicted by a local Monin–Obukhov length normalised by viscous wall units $\varLambda ^+$ such that the flow displays intermittency within the parameter range of $2.5 \lesssim \varLambda ^+ \lesssim 260$ . By considering conditional averages of the ‘turbulent’ and ‘quiescent’ flow separately, we find the ‘turbulent’ flow within this region to be described by constant critical gradient Richardson and turbulent Froude numbers of $Ri_{g,c} \approx 0.2$ and $Fr_c \approx 0.3$ . We find that the turbulent flow continues to display a $\varGamma \sim Fr^{-1}$ relationship when $Fr < Fr_c$ , whereas the quiescent flow shows no correlation between $\varGamma$ and $Fr$ , where $\varGamma$ is the flux coefficient. Hence, we demonstrate directly that for our flow, the emergence of an asymptotic ‘saturated’ $\varGamma$ regime in the limit of a low ‘global’ $Fr$ occurs due to intermittency and increasing contributions to measurements of $\varGamma$ from the quiescent flow.

A detailed experimental evaluation of gas –Liquid film attributes in a horizontal rectangular duct by Planar Laser-Induced fluorescence (PLIF) approach

In the current experimental research, we aimed to discover the interfacial behavior of gas–liquid stratified two-phase flow sub-regime by the Planar Laser-Induced Fluorescence (PLIF) method. The introduced research was conducted in a horizontal stratified flow rectangular channel, where respected flow measurements were studied using some quantitative values established visually by obtained PLIF photographs. Moreover, applied indicators in the current study focus on each of the following factors:wave dynamics, liquid film thickness, flow velocities, and frequencies of film disruption waves. Meanwhile, in order to strain the experimental efforts in the study, film thickness measurements were examined in both space and time domains. In addition, integral data supplemented against loaded spatiotemporally recovered information on interface position and two-phase velocity fields collected using planar laser generated fluorescence (PLIF).The presented study ascertains a novel relationship between dimensionless description of wave velocity, film thickness, and frequency for the liquid film. The study was performed under gas shear with inlet water Reynolds values from 88 to 437, and air Reynolds numbers ranging from 6.95 to 34.8 x103. Experimental studies concluded that different modes of wave generation with a decrement in the wave speed, film thickness, and frequency increased at a specific liquid velocity, with increasing the superficial speed. According to the findings, the experimental and theoretical values of the attendance indicators four recognized stratified flow sub-regimes presented in the results, based on both Navier-Stokes, and Kosky models. The observed flow regimes were the Ripple wave, roll wave, Jeffrey wave, and random disturbance wave. Regarding wave frequency studies, the Azzopardi and Bae models used to compare wave frequency, while the Gawas and Sarkhi models were implemented to compare wave velocity.

Exploring the Influence of the Evolution of Discharge Plasma Channel on the Characteristics of Electric Explosion Products

Electrical explosion method as a powerful tool for one-step synthesizing metallic nanoparticles has raised widely interests. In this paper, experiments were performed with three metal wires, namely copper, tungsten and titanium who are the typical representation of non-refractory and refractory metals. High-speed photography along with electrophysical and optical diagnostics were applied to characterize the electrical explosion. Accordingly, SEM and TEM was used to characterize the micro-morphology of explosion products. XRD was used to detect the phase compositions. Experiment results indicated that the products morphology and particle size distribution were influenced by the dynamic behaviors of the exploding wires. Electrothermal instability (ETI) and secondary breakdown were observed in copper wire explosion, the prominent discrepancies of temperature and density among stratified vapor and plasma channel enlarged the inhomogeneity of particle size. The sufficient plasma process maintained the metal vapor at a relatively high temperature and enhance the coalescence process after nucleation in titanium explosion, and the median diameter of particles increased as a result. The core-corona structure happened in tungsten wire explosion led to special heating mechanism (heat transport and/or radiation instead of Joule heating) which may be responsible for the formation of large-size agglomerates. In order to produce high-quality nanoparticles, except suitable experimental conditions, it is necessary to achieve homogeneous explosions. The critical dynamics behaviors including ETI (stratification), breakdown mode (inner or surface), and coexistent multi-states products (melts/vapor/plasma) under low-density current which caused the inhomogeneity should be further considered and eliminated in nanoparticle production.

Wind‐Driven Currents in a “Wide” Narrow Channel, With Application to Douglas Channel, BC

AbstractThis paper applies a structured grid, 3‐Dimensional Regional Ocean Modeling System to examine wind‐driven currents of an idealized stratified channel, representative of Douglas Channel, British Columbia, Canada, where the increased marine activities require an improved understanding of the physical oceanography. The surface along‐channel elevation slope resulting from the wind stress is strongly affected by the surface stratification and can serve as a proxy for gauging surface stratification in operational systems. In the case of strong surface stratification, due to rotational effects an apparently narrow (width ≪ length) channel can be dynamically wide with pronounced cross‐channel variation. The thickness of the surface wind‐driven layer is scaled using the thermal wind relation, which provides a scaling factor to estimate the thickness of the surface layer. This scaling factor is not restricted to the wind‐driven flow and could be expanded to the surface mean estuarine outflow layers.

Prediction of Horizontal Gas–Liquid Segregated Flow Regimes with an All Flow Regime Multifluid Model

The generalized multifluid modelling approach (GEMMA) has been developed to handle the multiplicity of flow regimes and the coexistence of interfaces of largely different scales in multiphase flows. The solver, based on the OpenFOAM reactingEulerFoam family of solvers, adds interface resolving-like capabilities to the multifluid solver in the cells occupied by large interfaces. In this paper, GEMMA is further developed to predict stratified and slug flow regimes in horizontal ducts. The suppression of the turbulence and the wall-like behaviour of large interfaces is modelled with an additional dissipation source. This enables an accurate prediction of the velocity and of the turbulence kinetic energy in a stratified channel flow and the capturing of the formation and the travel of liquid slugs in an annulus. Large interfaces are identified and tracked, not only in the smooth and wavy stratified regimes but also in the much more perturbed interfaces of liquid slugs. The present work confirms GEMMA to be a reliable approach to provide all flow regime modelling capabilities. Further development will be focused on large interface momentum-transfer modelling, responsible for the overestimation of the interfacial shear and the limited liquid excursion during slugs, and the extension to interface break-up and the entrainment of bubbles and droplets, to handle the entire range of regimes encountered in horizontal flows.

Amplification of turbulence by sharp meanders on thermally stratified open channel flow

In order to unravel the effects of meander bends on the mechanism by which the turbulence kinetic energy (TKE) is produced, redistributed and dissipated in a thermally stratified curved open-channel flow, Direct Numerical Simulation (DNS) was carried out through an idealized sharp meander with and without an internal heat source. The heat source models radiative heating from above and varies with height due to progressive absorption. In both cases, we find a pronounced local increase in TKE starting in the region approximately 25% of the distance through the bend. Here a local extremum of TKE is found near the channel bed at the inner bank and close to the free surface at the outer bank. This grows to a more generalised increase in turbulence that starts at a location approximately 35% of the distance through the bend and peaks at the meander apex before gradually weakening in the downstream part of the bend. However, while only showing a marked increase in the mid-depth region near the inner bank in the neutral case, turbulence is amplified more strongly in the stratified case with the high TKE values spread out across the whole channel width. This is due to the two observed separated shear layers converging in the bend apex in this case. There is only one SSL observed in the neutral case. An investigation of the TKE budget terms for the stratified case at the turbulence amplification location was undertaken to elucidate the mechanisms leading to the production, dissipation and transport of TKE in these regions.

Parameterization of mixing in stratified open channel flow

The dynamics and parameterization of mixing in temporally evolving turbulent open-channel flow is investigated through direct numerical simulations as the flow transitions from an initially neutral state to stable stratification. We observe three distinctly different mixing regimes separated by transitional values of turbulent Froude number $Fr$ : a weakly stratified regime for $Fr >1$ ; an intermediate regime for $0.3< Fr<1$ ; and a saturated regime for $Fr<0.3$ . The mixing coefficient $\varGamma =B/\epsilon _K$ , (where $B$ is the buoyancy flux and $\epsilon _K$ is the dissipation rate of kinetic energy), is well predicted by the parameterization schemes of Maffioli et al. (J. Fluid Mech., vol. 794, 2016) and Garanaik & Venayagamoorthy (J. Fluid Mech., vol. 867, 2019, pp. 323–333) across all three regimes through instantaneous measurements of $Fr$ and the ratio $L_E/L_O$ , where $L_E$ and $L_O$ are the Ellison and Ozmidov length scales, respectively. The flux Richardson number $R_f = B/(B+\epsilon _K)$ shows linear dependence on the gradient Richardson number $Ri_g$ up to a transitional value of $Ri_g =0.25$ , past which it saturates again to a constant value independent of $Fr$ or $Ri_g$ . By examining the flow as a balance of inertial, shear and buoyancy forces, we derive physically based scaling relationships to demonstrate that $Ri_g \sim Fr^{-2}$ and $Ri_g \sim Fr^{-1}$ in the weakly and moderately stratified regimes and that $Ri_g$ becomes independent of $Fr$ in the saturated regime. Our results suggest that the $L_E/L_O \sim Fr^{-1}$ scaling of Garanaik & Venayagamoorthy (J. Fluid Mech., vol. 867, 2019, pp. 323–333) in the intermediate regime manifests due to the influence of mean shear. The differences in the relationships between $Fr$ and $L_E/L_O$ for non-sheared flows within this regime are discussed.

Unstable turbulent channel flow response to spanwise-heterogeneous heat fluxes: Prandtl's secondary flow of the third kind

Turbulent secondary flows are defined as Prandtl's secondary flow of the first or second kind, the former produced by stretching and/or tilting of vorticity, the latter produced via spatial heterogeneity of Reynolds stresses. Both mechanisms are instantaneously active within inertia-dominated wall turbulence; Reynolds stress spatial heterogeneity is required for Reynolds-averaged secondary flows. Spanwise-variable surface roughness can induce turbulent stress spatial heterogeneity in the spanwise–wall-normal plane and provide sustenance for streamwise-aligned mean secondary flows. Herein, we demonstrate that turbulent secondary flows can also be sustained by spanwise variability in the surface heat flux in unstably stratified turbulent channels, defined hereafter as Prandtl's secondary flow of the third kind. Support for this mechanism is established with scaling arguments, while large-eddy simulation is used to model inertia-dominated channel turbulence responding to a lower boundary with uniform aerodynamic/hydrodynamic roughness but spanwise-variable surface heat flux. Transport equations for streamwise vorticity and turbulent kinetic energy, $k$ , outline the conditions needed for third-kind production: shear and buoyancy production over the elevated heat flux regions necessitates lateral entrainment of low- $k$ fluid, inducing mean counter-rotating secondary cells aligned such that upwelling and downwelling occur over the high and low heat flux regions, respectively. Buoyancy-driven production of $k$ alters aggregate flow response and thus is a distinctly different mechanism responsible for sustenance of secondary flows.

The chemical continuous time random walk framework for upscaling transport limitations in fluid–solid reactions

Fluid-solid reactions play a key role in a large range of biogeochemical processes. Transport limitations at the pore scale limit the amount of solute available for reaction, so that reaction rates measured under well-mixed conditions tend to strongly overestimate rates occurring in natural and engineered systems. Although different models have been proposed to capture this phenomenon, linking pore-scale structure, flow heterogeneity, and local reaction kinetics to upscaled effective kinetics remains a challenging problem. We present a new theoretical framework to quantify these dynamics based on the chemical continuous time random walk framework. We study a fluid–solid reaction with the fluid phase undergoing advective–diffusive transport. We consider a catalytic degradation reaction, AF+BS→BS, where AF is in fluid phase and BS is in solid phase and homogeneous over the fluid–solid interface, allowing us to focus on the role of transport limitations and medium structure. Our approach is based on the concept of inter-reaction times, which result from the times between contacts of transported reactants with the solid phase. We use this formulation to quantify the global kinetics of fluid-reactant mass and test our predictions against numerical simulations of advective–diffusive transport in stratified channel flow and Stokes flow through a beadpack. The theory captures the decrease of effective reaction rates compared to the well-mixed prediction with increasing Damköhler number due to transport limitations. Although we consider simple kinetics and media, these findings will contribute to the understanding and modeling of the effect of transport limitations in more complex reactive transport problems.

Nonlinear instability of interfacial waves in stratified laminar channel flow

The evolution of interfacial waves is investigated for a stratified laminar-laminar flow in a plane channel using numerical simulations based on the Volume of Fluid (VOF) method. Different nonlinear instability mechanisms that can promote saturation or rapid amplification of interfacial waves are investigated. Controlled disturbances are introduced at the interface between the two fluids, to assess five different scenarios of nonlinear interactions including harmonic excitation, subharmonic resonance, interaction between a short and a long wave, and two kinds of modulated wavepackets. Present simulations suggest that the same non-resonant type of wave interaction dominates the nonlinear stages of evolution in all the scenarios, for the fluid properties and parameters covered in this work. This mechanism involves the amplification of harmonics by quadratic nonlinearities and leads to the finite-amplitude saturation of interfacial waves, which results in a wavy flow. Reduced order models based on interaction of few wavelengths and described by the Stuart–Landau equation are proposed for the prediction of the nonlinear flow dynamics of laminar liquid-liquid two-phase flows.

On the dissipation rate of temperature fluctuations in stably stratified flows

In this study, we explore several integral and outer length scales of turbulence which can be formulated by using the dissipation of temperature fluctuations (chi) and other relevant variables. Our analyses directly lead to simple yet non-trivial parameterizations for both spatially-averaged overline{chi } and the structure parameter of temperature (C_T^2). For our purposes, we make use of high-fidelity data from direct numerical simulations of stratified channel flows.

Revisiting inclination of large-scale motions in unstably stratified channel flow

Observational and computational studies of inertia-dominated wall turbulence with unstable thermal stratification have demonstrated that the inclination angle of large-scale motions (LSMs) increases with increasing buoyancy (as characterized by the Monin–Obukhov stability variable ). The physical implications of this structural steepening have received relatively less attention. Some authors have proposed that LSMs thicken – yet remain attached to the wall – with increasing buoyancy (Salesky & Anderson, J. Fluid Mech., vol. 856, 2018, pp. 135–168), while others have presented evidence that the upstream edge of an LSM remains anchored to the wall while its downstream edge lifts away from the wall (Hommema & Adrian, Boundary-Layer Meteorol., vol. 106, 2003, pp. 147–170). Using a suite of large-eddy simulations (LES) of unstably stratified turbulent channel flow, we demonstrate that buoyancy acts to lift LSMs away from the wall, leaving a wedge of fluid beneath with differing momentum. We develop a prognostic model for LSM inclination angle that accounts for this observed structure, where the LSM inclination angle is the sum of the inclination angle observed in a neutrally stratified wall-bounded turbulent flow, , and the stability-dependent inclination angle of the wedge . Reported values of from the literature, LES results and atmospheric surface layer observations are found to be in good agreement with the new model for .

All-terminal reliability of multi-AUV cooperative systems in horizontally stratified SOFAR channel

ABSTRACT This work develops a calculation method of all-terminal reliability for multi-AUV cooperative systems in horizontally stratified sound fixing and raging channel (SOFAR channel), considering the sound speed profile in SOFAR channel. The working environment of multi-AUV (autonomous underwater vehicle) cooperative systems is complex and the reliability under different environmental conditions is different. This work adopts the Kraken normal mode method to get the transmission loss, and calculates the reliability of the communication link based on the relationship between the transmission loss and signal-to-noise ratio. All-terminal reliability of multi-AUV cooperative systems can be obtained.

Evolution of thermally stratified turbulent open channel flow after removal of the heat source

Evolution of thermally stratified open channel flow after removal of a volumetric heat source is investigated using direct numerical simulation. The heat source models radiative heating from above and varies with height due to progressive absorption. After removal of the heat source the initial stable stratification breaks down and the channel approaches a fully mixed isothermal state. The initial state consists of three distinct regions: a near-wall region where stratification plays only a minor role, a central region where stratification has a significant effect on flow dynamics and a near-surface region where buoyancy effects dominate. We find that a state of local energetic equilibrium observed in the central region of the channel in the initial state persists until the late stages of the destratification process. In this region local turbulence parameters such as eddy diffusivity $k_{h}$ and flux Richardson number $R_{f}$ are found to be functions only of the Prandtl number $Pr$ and a mixed parameter ${\mathcal{Q}}$, which is equal to the ratio of the local buoyancy Reynolds number $Re_{b}$ and the friction Reynolds number $Re_{\unicode[STIX]{x1D70F}}$. Close to the top and bottom boundaries turbulence is also affected by $Re_{\unicode[STIX]{x1D70F}}$ and vertical position $z$. In the initial heated equilibrium state the laminar surface layer is stabilised by the heat source, which acts as a potential energy sink. Removal of the heat source allows Kelvin–Helmholtz-like shear instabilities to form that lead to a rapid transition to turbulence and significantly enhance the mixing process. The destratifying flow is found to be governed by bulk parameters $Re_{\unicode[STIX]{x1D70F}}$, $Pr$ and the friction Richardson number $Ri_{\unicode[STIX]{x1D70F}}$. The overall destratification rate ${\mathcal{D}}$ is found to be a function of $Ri_{\unicode[STIX]{x1D70F}}$ and $Pr$.