Session P14: Turbulence: Boundary Layers (3:10pm - 3:55pm CST)

Effects of heterogeneous peri-urban landscape and thermal stability on wind profiles at Cedar Rapids, Iowa

The atmospheric boundary-layer wind over heterogeneous urban and peri-urban areas is challenging to characterize using standard models due to variability in the urban canopy structure, underlying terrain, and thermal stability. Often wind measurements are made by meteorological towers at fixed elevations, and data are extrapolated up to the height of interest. However, wind constantly adapts to the changing surface and thermal conditions, hardly reaching an equilibrium state assumed in theoretical models. Therefore, tower measurements are highly site specific and require careful evaluation in the urban or peri-urban areas. This study investigates the variability of wind profiles with a year of wind data from a 106-m met tower on the south edge of Cedar Rapids, Iowa. The mean wind profiles can be well described by the power law model, where the shear exponent generally increases from unstable to strongly stable cases. The complex terrain reveals pronounced effects on horizontal turbulence intensity, showing a peak value at 32 $m$ aloft from the ground level, attributable to the wake induced by the upwind tree canopy above the rolling hill terrain. This study sheds light on the effects of peri-urban landscape and thermal stability on wind profiles at a realistic field site.   

Compliant wall excitation in turbulent channel flow: A data-driven analysis of the fluid-solid coupling and wall-pressure sources using SPOD

We numerically simulate the response of a compliant-wall in a turbulent channel flow using direct numerical simulation (DNS) at $Re_{\tau}=180$ and $400$. To understand the fluid-solid coupling as a function of frequency, we combine the modal decomposition of the solid and the Poisson equation for the fluid wall-pressure fluctuation to derive an expression for the plate averaged displacement spectrum of the form $\phi^a_{dd}(\omega)=\int_{-\delta}^{+\delta}\int_{-\delta}^{+\delta}\Gamma_{dd}(r,s,\omega)\,\mathrm{dr}\mathrm{ds}$. Here, $\delta$ is the half-channel height and $\Gamma^a(r,s,\omega)$ is called the net - displacement source cross-spectral density (CSD). Using the same framework, we derive a similar expression for the net - wall-pressure source CSD ($\Gamma_{pp}(r,s,\omega)$) that integrates to give the wall-pressure spectrum. We compute the CSDs using the DNS data. Spectral Proper Orthogonal Decomposition (SPOD) of the CSD supports the case that for both the structural response and the wall pressure, we can decompose the sources into an active part that contributes to the entire PSD and an inactive part that undergoes destructive interference. Analysis of the SPOD modes reveals the dominance of the buffer layer sources at these Reynolds numbers.   

The coherent structure of the kinetic energy transfer in shear turbulence

The cascade of energy in turbulent flows, i.e. the transfer of kinetic energy from large to small flow scales or vice versa (backward cascade), has been the cornerstone of most theories and models of turbulence since the 1940s. Yet, understanding the spatial organisation of kinetic energy transfer remains an outstanding challenge in fluid mechanics. Here, we unveil the three-dimensional structure of the energy cascade across the shear-dominated scales using numerical data of homogeneous shear turbulence. We show that the characteristic flow structure associated with the energy transfer is a vortex shaped as an inverted hairpin followed by an upright hairpin. The asymmetry between the forward and backward cascade arises from the opposite flow circulation within the hairpins, which triggers reversed patterns in the flow.   

How history effects influence favourable pressure gradient turbulent boundary layers

A new direct numerical simulation database of a non-equilibrium turbulent boundary layer (TBL) that evolves under an adverse pressure gradient (APG) followed by a favourable pressure gradient (FPG) is presented. The TBL in the FPG region reaches up to Re$_\theta$ = 12650, and the shape factor H varies from 2.95 to 1.4. The non-dimensional pressure gradient is maintained constant in both the APG and FPG zones with the same absolute value. The database provides information about how history effects influence TBLs. The mean velocity profile in the inner layer of the FPG TBL, which is exposed to a FPG after having been exposed to an APG, returns to match the law of wall but only in the viscous wall region of TBL up to y$^+$ $\approx$ 60 at H = 1.6. On the other hand, the mean velocity profile in the outer layer of the TBL preserves the history effect of the APG and departs from the expected FPG behaviour. The accumulated outer peaks of Reynolds stresses still preserve their strength while inner peaks emerge. The database proves that the inner and outer layers of the boundary layer respond differently to the pressure gradient. Further results on history effects will be presented at the meeting.   

Energy Transfer Mechanisms in Adverse Pressure Gradient Turbulent Boundary Layers

The spectral distributions of the transport equation budgets of all Reynolds stresses in adverse gradient pressure (APG) turbulent boundary layers (TBLs) are examined to understand the energy transfer mechanisms in the inner and outer layers of APG TBLs. The spectra of the budget terms are obtained for two streamwise positions, which correspond to small and large velocity defect situations, of a non-equilibrium APG TBL using temporally collected data. The turbulence production is predominantly in the inner layer and due to small-scale structures for the small defect case, although there are energy-carrying large-scale structures in the outer layer. In the large defect situation, there is significant production in both inner and outer layers at small and large scales, respectively. Furthermore, the behavior of the pressure-strain rate and production spectra illustrates that the inter-component energy transfer from the streamwise component to the other components and production happen at similar wavelengths and wall-normal positions. More detailed results about energy transport between the inner and outer layers will be presented at the meeting.   

Design and setup of a wing model in the Minimum-Turbulence-Level wind tunnel

A reinforced fiber-glass model of a NACA 4412 wing profile is designed and set-up in the Minimum-Turbulence-Level (MTL) wind-tunnel facility at KTH (Sweden), aiming to complement and extend the high-fidelity numerical work performed by our research group on the same airfoil, including DNS and LES. The experiments includepressure scans, wake characterizations and boundary layer measurements by means of hot-wire anemometry at selected angles of attack (AoA, from 0 up to stall) and chord Reynolds numbers in the range 200k-2000k. In the present work the data is compared both to the aforementioned reference high-fidelity data and $k-\omega$ SST RANS simulations in which the wing is placed in a virtual wind-tunnel. The preliminary results show an excellent agreement with the reference numerical data, however, the effective angle of attack of the wing is affected by the interference of the test section, specially at high AoA, affecting the flow-separation position. Apart from creating an extensive statistical database for both the boundary-layer and wake flow, the spanwise coherence of the airfoil at different conditions (both attached and separated flow is investigated. This is crucial in order to determine the minimum requirements that high-fidelity simulations should have.   

Statistical State Dynamics based Study of the Roll-Streak Instability in Rotating, Stratified, and Shearing Flow.

Rolls and Streaks are coherent structures frequently observed in nature(e.x. Hurricane Boundary Layer Rolls and Elongated Streamwise Rolls in Channel Flows). Some Flows can support laminar mean flow instability. And, many of previous studies attempted to ascribe Roll-Streak formation to instability of laminar mean flow. While a normal dynamical system can only support instability through an eigenmode of the mean state, shear flows are highly non-normal and can support strong transient growth. Pseudospectra Theory tells us transient optimals coming from non-normality can be very easily destabilized via Reynolds Stress Torque. This instability arising from destabilization of transient optimal, through interaction of mean flow and perturbation about it, is analytical only within the framework of S3T(Stochastic Structural Stability Theory) and presents to be different from instability of laminar mean flow . We report studies on interaction between these two instabilities when various physics(e.x. Rotation, Stratification, and Shear) are present. In various scenarios, we try to answer which one of these instabilities is dominant and whether they compete or synergize each other. And, interaction of these two instabilities can be studied analytically only within the framework of S3T. Some of the examples include Reynolds-Tiederman Profile which does not support any unstable eigenmode to Orr-Sommerfield equation and Squire equation. Others include Slowly Rotating Couette, Ekman Layer, and Density Front which already supports or can support, via some choice of parameters, mean flow instability.