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## Description

 Title: Turbulence structure and flow resistance in oscillatory boundary layer flows Author(s): Fytanidis, Dimitrios Director of Research: Garcia, Marcelo H. Doctoral Committee Chair(s): Garcia, Marcelo H. Doctoral Committee Member(s): Fischer, Paul; Valocchi, Albert; Parker, Gary; Tinoco, Rafael Department / Program: Civil & Environmental Eng Discipline: Civil Engineering Degree Granting Institution: University of Illinois at Urbana-Champaign Degree: Ph.D. Genre: Dissertation Subject(s): Oscillatory Boundary Layer Turbulence Structure Flow Resistance Phase lag Turbulent Boundary Layer flows Oscillatory Boundary Layer flows Transition Bed shear stress Unsteady flows Unsteady boundary layer flows Stokes' boundary layer Abstract: Wave boundary layer flows play an important role on coastal engineering and coastal ecosystems. However, current state-of-the-art models fail to accurately predict the complex mechanics of the turbulence, sediment and momentum exchange between seabed and free-stream flow under oscillatory flow conditions. This fact highlights the need for the development of better numerical models for non-equilibrium and transitional flows but also may be a sign of an incomplete understanding of the oscillatory boundary layer behavior; especially in the transitional regime as will be shown herein. Recent experimental observations in the Large Oscillatory Water-Sediment Tunnel (LOWST), housed at the Ven Te Chow Hydrosystems laboratory, suggest the presence of phase-lag between the time instance when the maximum bed shear stress occurs with respect to the maximum free-stream velocity. This effect is dominant in the so called transitional/intermittently turbulent flow regime over hydrodynamically smooth beds. This observation, which had never been studied before in the literature, suggests the need for a revision of the "phase lead" diagram that is typically included in coastal engineering handbooks. Although this finding is extremely important for the field of environmental fluid mechanics and coastal sediment transport the exact reason for the existence of the phase lag and how it is associated with turbulent flow structures remain unclear. In addition, inconsistencies of the literature regarding the presence or not of hairpin vortices in OBL flow which in some cases were also supported by the absence of a logarithmic profile or the properties of the logarithmic profile, i.e. slope and intersect in oscillatory boundary layer flows. The aforementioned inconsistencies and knowledge gaps were the main motivations for the current thesis. In the present work, experimental data from the literature and Direct Numerical Simulation modeling, performed using the Spectral Element Based solver NEK5000, are used to elucidate the presence of bed shear stress phase-lag. DNS results confirm the experimental observation which together with data collected from the literature are used to propose a revised phase shift diagram and study the mean flow structures changes across the different regimes. In addition, mean flow characteristics and turbulent statistics are compared with the experimental observations. Flow structure results agree reasonably well with the experimental and numerical data from the literature. The present study enhances the amount of data that are available in the literature for the transitional regime of oscillatory boundary layer flows over smooth walls creating one of the most complete data set which can be used in the future as benchmarks for the development of new simplified models for OBL flows in the intermittently turbulent regime. The analysis of the flow profiles and turbulence characteristics suggest that the profiles agree well with those of unidirectional fully developed zero pressure gradient boundary layers in the parts of the period where the shape factor approaches 1.4. This similarity starts appearing close to a threshold value of $Re_{\delta}=763$ for $\omega t \approx 3\pi/4$. During the deceleration phase, RMS values tend to mimic those of unidirectional flows of similar $Re_{\theta}$ values. For higher $Re_{\delta}$ values this behavior starts towards the end of the acceleration phase. The bed shear stress variation over the period of the oscillation is examined for a wide range of Reynolds numbers $Re_{\delta}$ for pure reciprocating (zero mean flow) Oscillatory Boundary-Layer (OBL) flows over smooth walls. For $Re_{\delta}<552$ the bed shear stress has a single peak associated with the laminar regime. This peak takes place during the middle of the acceleration phase. When $Re_{\delta}= 552$ a second peak appears towards the middle of the deceleration phase. This peak is associated with the transition to turbulence and initially is weaker than the laminar" peak. As the $Re_{\delta}$ is further increased this turbulent" peak becomes larger and also occurs earlier during the deceleration phase. $Re_{\delta}=763$ is a threshold value when the turbulent" peak becomes larger than the laminar" peak. For $Re_{\delta} \ge 1123$ the laminar" peak vanishes due to the enhanced effect of the turbulent" peak. In the same transitional regime the classic logarithmic profile found to be be valid for part of the period for $Re_{\delta} \ge 763$. Von Karman's constant" $\kappa$ and $A_{s}$ values differ from the equilibrium values at the transitional regime. However, depending on the $Re_{\delta}$ the logarithmic profile with $\kappa \sim 0.41$ and $A_{s} \sim 5.1$ still become valid for part of the period. The $y^{+}$ region where the log-profiles are valid depends on $Re_{\delta}$. Starting from $Re_{\delta} \sim 763$ the profiles match a log-law at the deceleration phase. As the $Re_{\delta}$ increases the logarithmic profile becomes valid in a more extended region and for a more extended part of the period. In addition, variation of $\kappa$ values is observed due to the effects of pressure gradient. Log-law is valid for high $u_{*}^{2}/\omega \nu$ values (which is the dimensionless parameter proposed in the literature to define the regime for which log-law should be valid). However, the effect of the positive or negative pressure gradients are not included in this non-dimensional number. Regarding the phase difference, the typical phase lead" of 0.79 radians (45 degrees) is observed until $Re_{\delta}\sim 550$. After that the phase lead is reduced until a value of $\sim0.61$ rads ($\sim35$ degrees) until $Re_{\delta}<750$. For $Re_{\delta}\sim750$, a phase lag ($\Delta \phi <0$) of 0.46 rads (26.5 degrees) occurs. For higher $Re_{\delta}$ the phase lag becomes smaller until it turns zero for approximately $Re_{\delta}$ of 1000. $\Delta \phi$ gets positive values up to approximately $\sim \pi/18$ ($\sim10$ degrees) for $Re_{\delta}=1450$. Finally, as $Re_{\delta}$ increases further , $\Delta \phi$ decreases again following the prediction of theoretical solutions. Turbulent statistics from the detailed DNS simulations concludes that the presence of phase lag between the bed-shear stress and free stream velocity maxima is the result of a late transition to a stage that mimics the characteristics of quasi-equilibrium during the deceleration phase. However, this transition remains incomplete as neither the ensemble average velocity profile (slope and intersect) nor the diagnostics for the quasi-equilibrium, namely the shape factor $H$ and the defect shape factor $G$ get equilibrium values. Nevertheless, in these parts of the period TKE production to dissipation ratio $Pr/\epsilon$ becomes $\sim1$ and the Corrsin shear parameter ($2k/|\epsilon|S$) approaches a value of $~7$ which seem to be necessary conditions for a logarithmic profile to exist. In addition, probability density functions of the streamwise component of the bed-shear stress in OBL flows seem to be well described by a log-normal distribution while the spanwise component of the bed-shear stress follows a normal distribution. This prediction is good for the parts of the flow that exhibit a near-equilibrium behavior and for $Re_{\delta} \ge 1000$. The $\tau_{x_{rms}}$ and $\tau_{z_{rms}}$ values can be predicted using empirical equations from the literature. These predictions are valid for the turbulent part of the period and until Clauser's parameter $\beta$ gets a value of $\beta\sim1$. After that, the flow becomes quickly separated ($\beta \rightarrow \infty$) and the shear stress approaches zero ($\tau_{b} \rightarrow 0$). This finding is important for the development of predictive models for sediment transport and entrainment in coastal environments. Vortical structures are presented highlighting that the existence of hairpin vortices packets, the well accepted building block of turbulent boundary layer, exist also in OBL flows. Quantitative information is given regarding the spacing of the quasi-streamwise vortices which confirm the spacing of $\sim 100$ viscous units. The results reveal that for the examined transitionally turbulent flows, turbulent spots, which consist of hairpin packets, start appearing towards the end of the accelerations phase and then grow and merge with neighboring turbulent spots during the deceleration phase. The turbulent spots then dissipate under the effect of adverse pressure gradient near flow reversal and then experience re-laminarization at the beginning of the new acceleration phase. Additionally, quadrant analysis results are shown highlighting the dominance of Q2-Q4 event (ejections and sweeps) near the wall at the part of the period that are near equilibrium". This is also consistent with the proposed hairpin packets-based model for turbulent boundary layers. Finally, data of turbulence anisotropy are presented, and the Reynolds stress and dissipation rate anisotropy tensors results are compared against a simple anisotropy model, typically used by second-moment closures for the estimation of average dissipation rates of the Reynolds Stresses. The applied model agrees well with the observations of DNS results. Dissipation rate anisotropy scales with the anisotropy of the Reynolds stresses near the wall. Good collapse of turbulence dissipation rate anisotropy against the anisotropy is achieved for the parts of the flow which are in near-equilibrium. Issue Date: 2020-12-03 Type: Thesis URI: http://hdl.handle.net/2142/109615 Rights Information: Copyright 2020. Dimitrios Fytanidis Date Available in IDEALS: 2021-03-05 Date Deposited: 2020-12
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