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Taking into account the fact that the state of turbulence approaches a two-dimensional state close to the wall, a new Reynolds-stress turbulence model is proposed. The rotational properties of the two-dimensional turbulence differ...
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Taking into account the fact that the state of turbulence approaches a two-dimensional state close to the wall, a new Reynolds-stress turbulence model is proposed. The rotational properties of the two-dimensional turbulence differ significantly from the three-dimensional one. Under the system rotating about the axis perpendicular to the plane the turbulence correlations between fluctuating velocities remain invariant, while those combined with fluctuating pressure vary.
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Turbulent flows have been investigated experimentally and analytically in a straight pipe with rough surfaces. Three-dimensional measurements are made using a rotating probe with an inclined hot-wire, to show the effects of a roug...
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Turbulent flows have been investigated experimentally and analytically in a straight pipe with rough surfaces. Three-dimensional measurements are made using a rotating probe with an inclined hot-wire, to show the effects of a rough wall on turbulence properties such as turbulence energy and Reynolds stress and so on. Also, turbulence dissipation is estimated by balancing the turbulence Energy transport equation.
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We report on direct numerical simulations of the decay of initially isotropic, homogeneous turbulence subject to the application of stable density stratification. Flows were simulated for three different initial Reynolds numbers, ...
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We report on direct numerical simulations of the decay of initially isotropic, homogeneous turbulence subject to the application of stable density stratification. Flows were simulated for three different initial Reynolds numbers, but for the same initial Froude number. We find that the flows pass through three different dynamical regimes as they decay, depending on the local values of the Froude number and activity parameter. These regimes are analogous to those seen in the experimental study of Spedding (J. Fluid Mech., vol.?337, 1997, pp.?283–301) for the wake of a sphere. The flows initially decay with little influence of stratification, up to approximately one buoyancy period, when the local Froude number has dropped below 1. At this point the flows have adjusted to the density stratification, and, if the activity parameter is large enough, begin to decay at a slower rate and spread horizontally at a faster rate, consistent with the predictions of Davidson (J. Fluid Mech., vol.?663, 2010, pp.?268–292) and the scaling arguments of Billant & Chomaz (Phys. Fluids, vol.?13, 2001, pp.?1645–1651). We refer to this second regime as the stratified turbulence regime. As the flows continue to decay, ultimately the activity parameter drops below approximately 1 as viscous effects begin to dominate. In this regime, the flows have become quasi-horizontal, and approximately obey the scaling arguments of Godoy-Diana et?al. (J. Fluid Mech., vol.?504, 2004, pp.?229–238).
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The aerodynamic performance of lifting surfaces operating at low Reynolds number conditions is impaired by laminar separation. In most cases, transition to turbulence occurs in the separated shear layer as a result of a series of ...
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The aerodynamic performance of lifting surfaces operating at low Reynolds number conditions is impaired by laminar separation. In most cases, transition to turbulence occurs in the separated shear layer as a result of a series of strong hydrodynamic instability mechanisms. Although the understanding of these mechanisms has been significantly advanced over the past decades, key questions remain unanswered about the influence of external factors such as free-stream turbulence (FST) and others on transition and separation. The present study is driven by the need for more accurate predictions of separation and transition phenomena in 'real world' applications, where elevated levels of FST can play a significant role (e.g. turbomachinery). Numerical investigations have become an integral part in the effort to enhance our understanding of the intricate interactions between separation and transition. Due to the development of advanced numerical methods and the increase in the performance of supercomputers with parallel architecture, it has become feasible for low Reynolds number application (O(10(5))) to carry out direct numerical simulations (DNS) such that all relevant spatial and temporal scales are resolved without the use of turbulence modelling. Because the employed high-order accurate DNS are characterized by very low levels of background noise, they lend themselves to transition research where the amplification of small disturbances, sometimes even growing from numerical round-off, can be examined in great detail. When comparing results from DNS and experiment, however, it is beneficial, if not necessary, to increase the background disturbance levels in the DNS to levels that are typical for the experiment. For the current work, a numerical model that emulates a realistic free-stream turbulent environment was adapted and implemented into an existing Navier-Stokes code based on a vorticity-velocity formulation. The role FST plays in the transition process was then investigated for a laminar separation bubble forming on a flat plate. FST was shown to cause the formation of the well-known Klebanoff mode that is represented by streamwise-elongated streaks inside the boundary layer. Increasing the FST levels led to accelerated transition, a reduction in bubble size and better agreement with the experiments. Moreover, the stage of linear disturbance growth due to the inviscid shear-layer instability was found to not be 'bypassed'.
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Using a large number of numerical simulations we examine the steady state of rotating turbulent flows in triple periodic domains, varying the Rossby number Ro (that measures the inverse rotation rate) and the Reynolds number Re (t...
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Using a large number of numerical simulations we examine the steady state of rotating turbulent flows in triple periodic domains, varying the Rossby number Ro (that measures the inverse rotation rate) and the Reynolds number Re (that measures the strength of turbulence). The examined flows are sustained by either a helical or a non-helical Roberts force, that is invariant along the axis of rotation. The forcing acts at a wavenumber k(f) such that k(f)L = 4, where 2 pi L is the size of the domain. Different flow behaviours were obtained as the parameters are varied. Above a critical rotation rate the flow becomes quasi-two-dimensional and transfers energy to the largest scales of the system, forming large coherent structures known as condensates. We examine the behaviour of these condensates and their scaling properties close to and away from this critical rotation rate. Close to the critical rotation rate the system transitions supercritically to the condensate state, displaying a bimodal behaviour oscillating randomly between an incoherent-turbulent state and a condensate state. Away from the critical rotation rate, it is shown that two distinct mechanisms can saturate the growth of the large-scale energy. The first mechanism is due to viscous forces and is similar to the saturation mechanism observed for the inverse cascade in two-dimensional flows. The second mechanism is independent of viscosity and relies on the breaking of the two-dimensionalization condition of the rotating flow. The two mechanisms predict different scaling with respect to the control parameters of the system (Rossby and Reynolds), which are tested with the present results of the numerical simulations. A phase space diagram in the Re; Ro parameter plane is sketched.
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We perform numerical simulations of a turbulent channel flow over an hyper-elastic wall. In the fluid region the flow is governed by the incompressible Navier-Stokes (NS) equations, while the solid is a neo-Hookean material satisf...
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We perform numerical simulations of a turbulent channel flow over an hyper-elastic wall. In the fluid region the flow is governed by the incompressible Navier-Stokes (NS) equations, while the solid is a neo-Hookean material satisfying the incompressible Mooney-Rivlin law. The multiphase flow is solved with a one-continuum formulation, using a monolithic velocity field for both the fluid and solid phase, which allows the use of a fully Eulerian formulation. The simulations are carried out at Reynolds bulk Re = 2800 and examine the effect of different elasticity and viscosity of the deformable wall. We show that the skin friction increases monotonically with the material elastic modulus. The turbulent flow in the channel is affected by the moving wall even at low values of elasticity since non-zero fluctuations of vertical velocity at the interface influence the flow dynamics. The near-wall streaks and the associated quasi-streamwise vortices are strongly reduced near a highly elastic wall while the flow becomes more correlated in the spanwise direction, similarly to what happens for flows over rough and porous walls. As a consequence, the mean velocity profile in wall units is shifted downwards when shown in logarithmic scale, and the slope of the inertial range increases in comparison to that for the flow over a rigid wall. We propose a correlation between the downward shift of the inertial range, its slope and the wall-normal velocity fluctuations at the wall, extending results for the flow over rough walls. We finally show that the interface deformation is determined by the fluid fluctuations when the viscosity of the elastic layer is low, while when this is high the deformation is limited by the solid properties.
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The transport equation for the mean turbulent energy dissipation rate (epsilon) over bar along the centreline of a fully developed channel flow is derived by applying the limit at small separations to the two-point budget equation...
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The transport equation for the mean turbulent energy dissipation rate (epsilon) over bar along the centreline of a fully developed channel flow is derived by applying the limit at small separations to the two-point budget equation. Since the ratio of the isotropic energy dissipation rate to the mean turbulent energy dissipation rate (epsilon) over bar (iso)/(epsilon) over bar is sufficiently close to 1 on the centreline, our main focus is on the isotropic form of the transport equation. It is found that the imbalance between the production of (epsilon) over bar due to vortex stretching and the destruction of (epsilon) over bar caused by the action of viscosity is governed by the diffusion of (epsilon) over bar by the wall-normal velocity fluctuation. This imbalance is intrinsically different from the advection-driven imbalance in decaying-type flows, such as grid turbulence, jets and wakes. In effect, the different types of imbalance represent different constraints on the relation between the skewness of the longitudinal velocity derivative S-1,S-1 and the destruction coefficient G of enstrophy in different flows, thus resulting in non-universal approaches of S-1,S-1 towards a constant value as the Taylor microscale Reynolds number, R-lambda, increases. For example, the approach is slower for the measured values of S-1,S-1 along either the channel or pipe centreline than along the axis in the self-preserving region of a round jet. The data for S-1,S-1 collected in different flows strongly suggest that, in each flow, the magnitude of S-1,S-1 is bounded, the value being slightly larger than 0.5.
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We present direct numerical simulations (DNS) of unforced stratified turbulence with the objective of testing the strongly stratified turbulence theory. According to this theory the characteristic vertical scale of the turbulence ...
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We present direct numerical simulations (DNS) of unforced stratified turbulence with the objective of testing the strongly stratified turbulence theory. According to this theory the characteristic vertical scale of the turbulence is given by l(v) similar to u(h)/N, where u(h) is the horizontal velocity scale and N the Brunt-Vaisala frequency. Combined with the hypothesis of the energy dissipation rate scaling as epsilon similar to u(h)(3)/l(h), this theory predicts inertial range scalings for the horizontal spectrum of horizontal kinetic energy and of potential energy, according to E(k(h)) proportional to k(h)(-5/3). We begin by presenting a scaling analysis of the horizontal vorticity equation from which we recover the result regarding the vertical scale, l(v) similar to u(h)/N, highlighting in the process the important dynamical role of large-scale vertical shear of horizontal velocity. We then present the results from decaying DNS, which show a good agreement with aspects of the theory. In particular, the vertical Froude number is found to reach a constant plateau in time, of the form Fr-v = u(h)/(Nl(v))= C with C = O(1) in all the runs. The derivation of the dissipation scaling epsilon similar to u(h)(3)/l(h) at low Reynolds number in the context of decaying stratified turbulence highlights that the same scaling holds at high R = ReFrh2 >> 1 as well as at low R << 1, which is known (see Brethouwer et al., J. Fluid Mech., vol. 585, 2007, pp. 343-368) but not sufficiently emphasized in recent literature. We find evidence in our DNS of the dissipation scaling holding at R = O(1), which we interpret as being in the viscous regime. We also find epsilon(k) similar to u(h)(3)/l(h) and epsilon(p) similar to u(h)(3)/l(h) (with epsilon = epsilon(k) + epsilon(p)), in our high-resolution run at earlier times corresponding to R = O(10), which is in the transition between the strongly stratified and the viscous regimes. The horizontal spectrum of horizontal kinetic energy collapses in time using the scaling E-h(k(h)) = C-1 epsilon(2/3)/k(h)(-5/3) and the horizontal potential energy spectrum is well described by E-p(k(h)) = C-2 epsilon(p)epsilon(-1/3)(k)k(h)(-5/3). The presence of an inertial range in the horizontal direction is confirmed by the constancy of the energy flux spectrum over narrow ranges of k(h). However, the vertical energy spectrum is found to differ significantly from the expected E-h(k(v)) similar to N(2)k(v)(-3) scaling, showing that Fr-v is not of order unity on a scale-by-scale basis, thus providing motivation for further investigation of the vertical structure of stratified turbulence.
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We investigate a model of thin layer turbulence that follows the evolution of the two-dimensional motions u(2D)(x, y) along the horizontal directions (x,y) coupled to a single Fourier mode along the vertical direction (z) of the f...
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We investigate a model of thin layer turbulence that follows the evolution of the two-dimensional motions u(2D)(x, y) along the horizontal directions (x,y) coupled to a single Fourier mode along the vertical direction (z) of the form u(q) (x,y,z) /= [v(x) (x,y) sin (qz) , v(y) (x,y) sin (qz), v(z)(x,y) cos(qz)], reducing thus the system to two coupled, two-dimensional equations. The model, despite its simplicity and ad hoc construction, displays a rich behaviour. Its reduced dimensionality allows a thorough investigation of the transition from a forward to an inverse cascade of energy as the thickness of the layer H = pi/q is varied. Starting from a thick layer and reducing its thickness it is shown that two critical heights are met: (i) one for which the forward unidirectional cascade (similar to three-dimensional turbulence) transitions to a bidirectional cascade transferring energy to both small and large scales and (ii) one for which the bidirectional cascade transitions to a unidirectional inverse cascade when the layer becomes very thin (similar to two-dimensional turbulence). The two critical heights are shown to have different properties close to criticality that we are able to analyse with numerical simulations for a wide range of Reynolds numbers and aspect ratios.
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Recent studies have demonstrated that large- and very-large-scale motions in the logarithmic region of turbulent boundary layers 'amplitude modulate' dynamics of the near-wall region (Marusic et al. Science, vol. 329, 2010, pp. 19...
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Recent studies have demonstrated that large- and very-large-scale motions in the logarithmic region of turbulent boundary layers 'amplitude modulate' dynamics of the near-wall region (Marusic et al. Science, vol. 329, 2010, pp. 193-196; Mathis et al., J Fluid Mech., vol. 628, 2009a, pp. 311-337). These contributions prompted development of a predictive model for near-wall dynamics (Mathis et al., I Fluid Merit., vol. 681, 2011, pp. 537-566) that has promising implications for large-eddy simulations of wall turbulence at high Reynolds numbers (owing to the presence of smaller scales as the wall is approached). Existing studies on the existence of amplitude modulation in wall-bounded turbulence have addressed smooth-wall flows, though high Reynolds number rough-wall flows are ubiquitous. Under such conditions, the production of element-scale vortices ablates the viscous wall region and a new near-wall layer emerges: the roughness sublayer. The roughness sublayer depth scales with aggregate roughness element height, h, and is typically 2h similar to 3h. Above the roughness sublayer. Townsend's hypothesis dictates that turbulence in the logarithmic layer is unaffected by the roughness sublayer (beyond its role in setting the friction velocity and thus inducing a deficit in the mean streamwise velocity known as the roughness function). Here, we present large-eddy simulation results of turbulent channel flow over rough walls. We follow the decoupling procedure outlined in Mathis et al. (J. Fluid Mech., vol. 628. 2009a, 311-337) and present evidence that outer-layer dynamics amplitude modulate the roughness sublayer. Below the roughness element height, we report enormous sensitivity to the streamwise-spanwise position at which flow statistics are measured, owing to spatial heterogeneities in the roughness sublayer imparted by roughness elements. For y/h greater than or similar to 1.5 (i.e. above the cubes, but within the roughness sublayer), topography dependence rapidly declines.
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