A semi-empirical model that describes a fully developed rough-walled **turbulent** **boundary** layer with sand-grain **roughness** length-scale k s = αx that varies linearly with streamwise distance is first developed, with α a dimensionless constant. For **large** Re x and a free-stream velocity U ∞ ∝ x m , a simple log-wake model of the local **turbulent** mean-velocity profile is used that contains a standard mean-velocity correction for the asymptotic, fully rough regime. A two parameter ( α, m ) family of solutions is obtained for which U ∞ + (or equivalently C f ) and **boundary**-layer measures can be calculated. These correspond to perfectly self-similar **boundary**-layer growth in the streamwise direction with similarity variable z /( α x ) where z is the wall- normal co-ordinate. Results over a range of α are discussed for cases including the zero-pressure gradient ( m = 0) and sink-flow ( m = − 1) **boundary** **layers**. Model trends are supported by high Re wall-modeled LES. Linear streamwise growth of **boundary** layer measures is confirmed, while for each α , mean-velocity profiles and streamwise **turbulent** stresses are shown to collapse against z /( α x ) . Inner scaled velocity defects are shown to collapse against z /∆ , where ∆ is the Rotta-Clauser parameter. The present results suggest that these flows may be interpreted as the fully-rough limit for **boundary** **layers** in the presence of small-scale, linear **roughness**. Next, an LES study of a flat-plate **turbulent** **boundary** layer at high Re under non- equilibrium flow conditions due to the presence of abrupt changes in surface rough- ness is presented. Two specific cases, smooth-rough ( SR ) and rough-smooth ( RS ) transition are examined in detail. Streamwise developing velocity and **turbulent** stress profiles are considered and sharp departures from equilibrium flow properties with subsequent relaxation are shown downstream. Relaxation trends are studied using integral parameters and higher-order mean flow statistics with emphasis on Re τ and k + s dependence. Results are compared with RS experiments at matched

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Although numerical methods based on DNS offer the necessary high fidelity, they impose strict spatial resolution constraints that lead to very high computational cost. Since they have less strict mesh requirements, classical **Large** **Eddy** **Simulation** (LES) methods are more efficient, but necessitate the use of a low-pass filtering operation that produces sub-grid scale terms requiring additional modeling, which in turn introduces further numerical errors. In an effort to find a compromise between accuracy and computational cost, the concept of implicit LES (iLES) emerged from observations reported by Boris et al. [15]. This method has been applied successfully to model several complex flows in engineering and other fields. Fureby and Grinstein [16] justified the use of iLES in free and wall-bounded flows, while Margolin et al. [17] presented a validation of the method through theoretical analysis. More recently, two independent publications applied iLES in two different cases, with both concluding that iLES can achieve near DNS results while utilizing significantly less computational resources. In the first of these studies, Kokkinakis and Drikakis [18] presented results from iLES of a weakly compressible **turbulent** channel flow. In the second, Poggie et al. [19] applied iLES to study TBL flows using a **simulation** setup similar to the one we will present in this paper. This non-

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computational time of iLES9 on the coarsest mesh (G4). The iLES9 simulations on the coarser mesh G3 (~10.5 million mesh points) can achieve similar accuracy to the finest mesh (G1) simulations of iLES5 and iLES2, thus reducing the computational cost by approximately eightfold. Based on the results of FIG. 6a we made an extrapolated estimate of the computational cost that a DNS **simulation** would require using the iLES9 and found that our simulations are ~3.5 times less computationally expensive. The accuracy of our pressure fluctuations predictions, and the associated computational cost, (FIG. 6b) could not be directly compared with other DNS, or experimental studies, as the data in the literature have been obtained at different Mach and Reynolds numbers.

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Recent studies suggest that **large** scale motions within the UMZs strongly influence the trans- port of passive scalars in the **turbulent** **boundary** layer (Finnigan et al., 2009; Michioka & Sato, 2012; Perret & Savory, 2013; Vanderwel & Tavoularis, 2016; Eisma, 2016). Using **large**-**eddy** **simulation** (LES), Finnigan et al. (2009) provided evidence of zones of high concentration gradi- ents above a vegetation canopy (namely, microfronts). These zones were described as resulting from the interaction of two hairpin vortices oriented in opposite directions, one upstream and one downstream, generating strong ejection and sweep events. The convergence of the two hairpin vortices produced an intense and coherent scalar microfront lying between the two vortices. Mi- chioka & Sato (2012) investigated the effects of coherent structures on pollutant removal from an idealized canyon using LES. They found that coherent structures of low momentum fluid con- tribute to pollutant removal, with the removal being directly related to the size of the coherent structures. Vanderwel & Tavoularis (2016) studied the dynamics of coherent structures as a mech- anism for scalar dispersion. They found hairpin vortices to be responsible for the **large** scalar flux and Reynolds stress events in the flow.

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There is a growing need for reliable, accurate LES models suitable for real-world flows. The behavior of the **boundary** layer over aerospace vehicles, for both the inner flow or outer flow, usually exhibits complex behavior of high Reynolds number. In spite of recent advances in computational capabilities, highly accurate simulations, for example, of separated flow on the wings of airplanes or for flow through turbine blades in jet engines has not been achieved. When such simulations become possible at reasonable computational cost, engineers in industry will be able to investigate other critical problems that are at the moment accessible only by costly physical experiments. As a step toward this, we presently consider the LES of the adverse-pressure gradient flat-plate **turbulent** **boundary** layer. The implementation of our wall model and the interior SGS model, which is entirely local in character including its incorporation of local pressure gradients, should be applicable to adverse- pressure-gradient **turbulent** **boundary** **layers** (APGTBL).

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The above schemes have been further combined with the LM correction proposed by Thornber et al. [86]; the theoretical development and justification of the LM correction can be found in [87]. It was demonstrated that the LM correction can significantly reduce the numerical dissipation of Godunov-type methods at low Mach numbers via a progressive central differencing of the velocity components in the post-reconstruction phase. An analysis [87] of the source of the **turbulent** kinetic energy dissipation in upwind schemes revealed that the absolute dissipation of fluctuating kinetic energy is proportional to the temperature multiplied by the change of entropy (assuming an approximately isothermal flow). This neglects the additional dissipation that occurs during isentropic transformation of kinetic energy to internal energy in the form of local compressions and expansions. Using MEA, the evolution of entropy was derived for various compressible numerical schemes and it was demonstrated that the overly dissipative behaviour observed in simulations of homogeneous decaying turbulence is ascribed to numerical dissipation that is proportional to the speed of sound. The LM correction provides a limiting procedure which recovers the accuracy of such schemes with an optimal dissipation in the limit of M → 0 [86]. In this study, the LM correction is further investigated for low Mach **turbulent** **boundary** **layers**.

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In Reynolds Averaged Navier-Stokes turbulence model the **turbulent** fluctuations are expressed through the Reynolds stress tensor which is linked to the mean quantities through some turbulence model (k − ). However for LES the goal is to explicitly resolve the **turbulent** fluctuations and inlet conditions cannot be derived from experi- mental results due to unsteady and pseudo random nature of the flow. This problem is more important for **spatially** developing **turbulent** flows where the **boundary** or shear layer thickness changes rapidly. Even for stationary **turbulent** flows, if realistic initial conditions are not prescribed, the establishment of a fully developed turbulence takes unreasonably long execution time (Smirnov et al. [22]). Hence it is necessory to specify realistic **turbulent** fluctuations at the inlet as the flow downstream is highly dependent on these conditions. The inlet perturbation propagates throughout the domain and helps trigger the turbulence that is to be captured. The fluctuations have been applied as described in Smirnov et al.[22]. The fluctuations are generated by using turbulence intensity I, a pseudo-random number α, and the mean streamwise velocity.

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Figure 2 (left) shows the computed profile of mean streamwise velocity compared with the wind tunnel measurements in the whole **boundary** layer; Figure 2 (right) shows the surface layer, which is of principal concern for environmental predictions. The profile of black triangle symbols were obtained when measuring u and v by using the same x-wire system which was intensively used to measure u and w. While it is normalized by u ∗ which was obtained when measuring u and w, which might be one reason why there is some discrepancy between this profile and other measured data in the very near wall region in Figure 2 (right). To show the effects of the new wall model for **roughness**, we also plot a profile obtained using the Schumann (1976) wall model and a profile obtained using the Thomas and Williams wall model. Without the model for the effects of **roughness** on the **boundary** layer, there is poor agreement with experiment. There is very little difference between the results from the new wall model and those from the Thomas and Williams wall model in the surface layer. Near the top of the domain, the results from the Thomas and Williams wall model seem better than those from the new wall model, compared with measurements. However, this is unlikely to be genuine; because the damping factor β is chosen to be 0.25 for comparison (much smaller than it should be in our **simulation**, see Equation 11) much fluctuation has been taken account of in the wall model, making the profile steeper. The effect can also be found in Figure 5, where there is a dramatic sharp peak near the wall in the results using the Thomas and Williams wall model.

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Unsteady **turbulent** flows through a pipe are frequently encountered in engineering appli- cations such as turbo-machinery and heat exchangers, and also in biomedical applications such as airflow in the human lungs and blood flow in **large** arteries. In addition to the practical implications of achieving a better understanding of flows of this type, the study of unsteady **turbulent** flows in pipes provides insight into the underlying physics of tur- bulent **boundary** **layers**. To date, unsteady **turbulent** pipe flows have received relatively little attention compared to steady ones despite their importance.

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Abstract The efficiency and mechanism of an active control device ‘‘SparkJet ” and its application in shock-induced separation control are studied using **large**-**eddy** **simulation** in this paper. The base flow is the interaction of an oblique shock-wave generated by 8 ° wedge and a **spatially**-developing Ma = 2.3 **turbulent** **boundary** layer. The Reynolds number based on the incoming flow property and the **boundary** layer displacement thickness at the impinging point without shock-wave is 20000. The detailed numerical approaches were presented. The inflow turbulence was generated using the digital filter method to avoid artificial temporal or streamwise periodicity. The numerical results including velocity profile, Reynolds stress profile, skin friction, and wall pressure were sys- tematically validated against the available wind tunnel particle image velocimetry (PIV) measure- ments of the same flow condition. Further study on the control of flow separation due to the strong shock-viscous interaction using an active control actuator ‘‘SparkJet ” was conducted. The single-pulsed characteristic of the device was obtained and compared with the experiment. Both instantaneous and time-averaged flow fields have shown that the jet flow issuing from the actuator cavity enhances the flow mixing inside the **boundary** layer, making the **boundary** layer more resis- tant to flow separation. Skin friction coefficient distribution shows that the separation bubble length is reduced by about 35% with control exerted.

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A general approach has been developed for understanding how deep **turbulent** **boundary** **layers** adjust as they ﬂow over and through a canopy of **roughness** elements. Following work on plant canopies, mean momentum equations are obtained by averaging both temporally and **spatially**. These mean ﬂow equations contain two new terms: (i) the drag that arises from averaging **spatially** the form drag due to individual canopy elements; and (ii) a ﬁnite-volume eﬀect whereby momentum is transported by displacement of streamlines around individual canopy elements. The present study has focused on the case when the fraction of volume occupied by the **roughness** elements, β, is small. Over the bulk of the ﬂow, the drag of the canopy elements is the dominant process. In the impact region, just upstream of the canopy, however, the ﬁnite volume eﬀect is **large** when the canopy elements are **large**.

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into question because of the increasing density and pressure fluctuations at high Mach numbers. **Turbulent** fluctuations can even become locally supersonic relative to the sur- rounding flow, creating the so-called **eddy** shocklets that could significantly modify the dynamics of the flow. However, the Mach number at which Morkovin’s hypothesis would lose significant accuracy remains largely undetermined. There are still limited measure- ments at hypersonic speeds that are detailed and accurate enough for testing the validity of Morkovin’s hypothesis. Experimental investigations of hypersonic **turbulent** **boundary** **layers** have been conducted historically with hot-wire anemometry (see, for example, the review by Roy and Blottner (Roy and Blottner, 2006)). A recent investigation by Williams et al. (Williams et al., 2018) showed that much of the historical hot-wire measurements of turbulence statistics su ff ered from poor frequency response and / or spatial resolution. Hot- wire anemometry may also su ff er from uncertainties associated with the mixed-mode sen- sitivity of the hot wires, given that the hot wire measures a combination of the fluctuating mass flux and the fluctuating total temperature (Kovasznay, 1953). In addition to hot-wire anemometry, direct measurements of **spatially** **varying** velocity fields of high-speed turbu- lent **boundary** **layers** have been attempted using Particle Image Velocimetry (PIV) (Ekoto et al., 2008; Peltier et al., 2016; Tichenor et al., 2013; Williams et al., 2018). Among the

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From numerical perspective, it is evident that most of the **eddy** resolving simulations in literature have addressed transition induced by isolated rough- ness in supersonic flows. The objective of the present study is to investigate the effect of distributed **roughness** on subsonic **boundary** **layers** typically observed in turbomachines. However, unlike the recent work [32, 33, 42, 43, 47] where a flat plate has been subjected to turbine blade loading which triggered flow separation, current simulations are much more fundamental and consider a flat pate in the absence of pressure gradients. In contrast to the simulations of Muppidi and Mahesh [29], the rough surface is specified over the entire length of the flat plate. The motivation for such an arrangement is to cover the tran- sition behaviour over a wide range of Reynolds numbers based on **roughness** height. Hence, once the flow undergoes transition, the current distribution also helps to explore the effects of surface **roughness** on the **spatially** developing TBLs and further validate the numerical framework.

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The LES-ODT approach is based on LES solutions for momentum and pressure on a coarse grid and solutions for momentum and reactive scalars on a fine, one-dimensional, but three-dimensionally coupled ODT subgrid, which is embedded into the LES computa- tional domain. Although one-dimensional, all three velocity components are transported along the ODT domain. The low-dimensional spatial and temporal resolution of the sub- grid scales describe a new modeling paradigm, referred to as autonomous microstructure evolution (AME) models, which resolve the multiscale nature of turbulence down to the Kolmogorv scales. While this new concept aims to mimic the **turbulent** cascade and to re- duce the number of input parameters, AME enables also regime-independent combustion modeling, capable to simulate multiphysics problems simultaneously. The LES as well as the one-dimensional transport equations are solved using an incompressible, low Mach number approximation, however the effects of heat release are accounted for through variable density computed by the ideal gas equation of state, based on temperature vari- ations. The computations are carried out on a three-dimensional structured mesh, which is stretched in the transverse direction. While the LES momentum equation is integrated with a third-order Runge-Kutta time-integration, the time integration at the ODT level is accomplished with an explicit Forward-Euler method. Spatial finite-difference schemes of third (LES) and first (ODT) order are utilized and a fully consistent fractional-step method at the LES level is used. Turbulence closure at the LES level is achieved by utiliz- ing the Smagorinsky model. The chemical reaction is simulated with a global single-step, second-order equilibrium reaction with an Arrhenius reaction rate.

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Abstract. **Large**-**eddy** **simulation** (LES) and Lagrangian stochastic modeling of passive particle dispersion were ap- plied to the scalar flux footprint determination in the stable atmospheric **boundary** layer. The sensitivity of the LES re- sults to the spatial resolution and to the parameterizations of small-scale turbulence was investigated. It was shown that the resolved and partially resolved (“subfilter-scale”) eddies are mainly responsible for particle dispersion in LES, im- plying that substantial improvement may be achieved by us- ing recovering of small-scale velocity fluctuations. In LES with the explicit filtering, this recovering consists of the ap- plication of the known inverse filter operator. The footprint functions obtained in LES were compared with the func- tions calculated with the use of first-order single-particle Lagrangian stochastic models (LSMs) and zeroth-order La- grangian stochastic models – the random displacement mod- els (RDMs). According to the presented LES, the source area and footprints in the stable **boundary** layer can be sub- stantially more extended than those predicted by the modern LSMs.

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The system of carrier phase (liquid) and dispersed phase (particles) is described in this work using Euler-Lagrange approach. This means that the liquid is considered to be continuum and its motion is described by the Euler equation of motion. The particles are considered as mass points and for their **simulation** is used Lagrangian approach. For each particle is assembled equations of motions based on the second Newton’s law.

DNS and LES of **turbulent** **boundary**-layer flows suffer from the need to prescribe accurate three-dimensional and time-dependent inflow-**boundary** conditions. This is a rather important issue due to the sensitivity of the governing equations to the choice of **boundary** conditions. Perhaps the most common approach is the rescaling/recycling technique proposed by Lund et al. [33]. This is one of the most accurate approaches since it only requires one empirical relation, introducing almost no inflow transient. However, we argue that this technique suffers from two important drawbacks for the present SBLI study. First, the extension of the method (originally designed for incompressible flows) to compressible flows raises the issue of the rescaling of the thermodynamic variables and the so-called pres- sure drift (see Sagaut et al. [41] and references therein). Secondly, the recycling nature of the method will, by construction, introduce a distinct low-frequency tone that can interfere with the study of the low-frequency content in SBLI [1] 2 . All the LES [19, 32, 47] and most of the DNS [54, 1] results available so far on SBLI have used the recycling technique. However, for their DNS, Pirozzoli and Grasso [37] have chosen to use a long domain to simulate the transition to turbulence (note that to achieve this, they forced the flow at the wall over a short streamwise distance). Similarly, for his compression-ramp DNS, Adams [2] used a precursor flat plate DNS where a bypass- transition technique was used. Although very appealing, the overall computational cost of those approaches is prohibitive if we want to

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Over the last twenty years, LES of wall-bounded flows have received considerable attention (Piomelli & Balaras 2002, for a review), with the **turbulent** plane-channel flow (Kim, Moin & Moser 1987) being the prototypical case. This flow allows for the investigation of shear effects in a simple geometry and has therefore provided a useful test bed of our **eddy**-viscosity model. Furthermore, we have been able to confront our results on mean velocity, turbulence intensities and Reynolds stress profiles with the well-established literature present on that case, e.g. the comprehensive DNS database obtained by Moser, Kim & Mansour (1999) or Hoyas & Jimenez (2006).

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Dynamic Mode Decomposition (DMD) refers to the frequency based decomposition of a flowfield and was first proposed by Schmid & Sesterhenn[56]. It is analogous to a Fourier transform of the full spatial flowfield. It can be used to extract the flow features oscillating at a particular frequency to better understand the flowfield, instead of placing individual probes at various different locations in the flow to extract the time history of flow variables. Its application has been demonstrated by Schmid[55] for a plane channel flow, flow past a two-dimensional cavity, wake flow behind a flexible membrane and a jet passing between two cylinders. Rowleyet al.[50] showed that DMD is an approximation of the Koopman operator for a given system and applied it to a three-dimensional jet in crossflow problem, where they observe two dominant frequencies in the flow which correspond to the jet shear layer roll up and a **boundary** layer mode respectively. The current work applies the DMD algorithm to **large** unstructured datasets (upto 80 million grid points). This chapter briefly summarizes the algorithm and is validated for the flow past a cylinder at low Reynolds numbers. The algorithm is then tested on three complex problems: low speed jet in crossflow, sonic jet in a supersonic crossflow and a supersonic jet in subsonic crossflow.

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