TY - GEN A1 - Klein, Marten A1 - Seelig, Torsten A1 - Kurgansky, Michael V. A1 - Ghasemi, Abouzar A1 - Borcia, Ion-Dan A1 - Will, Andreas A1 - Schaller, Eberhard A1 - Egbers, Christoph A1 - Harlander, Uwe T1 - Inertial wave excitation and focusing in a liquid bounded by a frustum and a cylinder T2 - Journal of Fluid Mechanics N2 - The mechanism of localized inertial wave excitation and its efficiency is investigated for an annular cavity rotating with Ω0 . Meridional symmetry is broken by replacing the inner cylinder with a truncated cone (frustum). Waves are excited by individual longitudinal libration of the walls. The geometry is non-separable and exhibits wave focusing and wave attractors. We investigated laboratory and numerical results for the Ekman number E ≈ 10−6. inclination α = 5.71◦ and libration amplitudes ε 0.2 within the inertial wave band 0 < ω < 2Ω0 . Under the assumption that the inertial waves do not essentially affect the boundary-layer structure, we use classical boundary-layer analysis to study oscillating Ekman layers over a librating wall that is at an angle α = 0 to the axis of rotation. The Ekman layer erupts at frequency ω = f∗, where f∗ ≡ 2Ω0 sin α is the effective Coriolis parameter in a plane tangential to the wall. For the selected inclination this eruption occurs for the forcing frequency ω/Ω0 = 0.2. For the librating lids eruption occurs at ω/Ω0 = 2. The study reveals that the frequency dependence of the total kinetic energy Kω of the excited wave field is strongly connected to the square of the Ekman pumping velocity wE (ω) that, in the linear limit, becomes singular when the boundary layer erupts. This explains the frequency dependence of non-resonantly excited waves. By the localization of the forcing, the two configurations investigated, (i) frustum libration and (ii) lids together with outer cylinder in libration, can be clearly distinguished by their response spectra. Good agreement was found for the spatial structure of low-order wave attractors and periodic orbits (both characterized by a small number of reflections) in the frequency windows predicted by geometric ray tracing. For ‘resonant’ frequencies a significantly increased total bulk energy was found, while the energy in the boundary layer remained nearly constant. Inertial wave energy enters the bulk flow via corner beams, which are parallel to the characteristics of the underlying Poincaré problem. Numerical simulations revealed a mismatch between the wall-parallel mass fluxes near the corners. This leads to boundary-layer eruption and the generation of inertial waves in the corners. KW - boundary-layer structure KW - geophysical and geological flows KW - waves in rotating fluids Y1 - 2014 U6 - https://doi.org/10.1017/jfm.2014.304 SN - 1750-6859 IS - vol. 751 SP - 255 EP - 297 ER - TY - GEN A1 - Ghasemi, Abouzar A1 - Klein, Marten A1 - Harlander, Uwe A1 - Kurgansky, Michael V. A1 - Schaller, Eberhard A1 - Will, Andreas T1 - Mean flow generation by Görtler vortices in a rotating annulus with librating side walls T2 - Physics of Fluids N2 - Time periodic variation of the rotation rate of an annulus induces in supercritical regime an unstable Stokes boundary layer over the cylinder side walls, generating Görtler vortices in a portion of a libration cycle as a discrete event. Numerical results show that these vortices propagate into the fluid bulk and generate an azimuthal mean flow. Direct numerical simulations of the fluid flow in an annular container with librating outer (inner) cylinder side wall and Reynolds-averaged Navier–Stokes (RANS) equations as diagnostic equations are used to investigate generation mechanism of the retrograde (prograde) azimuthal mean flow in the bulk. First, we explain, phenomenologically, how absolute angular momentum of the bulk flow is mixed and changed due to the propagation of the Görtler vortices, causing a new vortex of basin size. Then we investigate the RANS equations for intermediate time scale of the development of the Görtler vortices and for long time scale of the order of several libration periods. The former exhibits sign selection of the azimuthal mean flow. Investigating the latter, we predict that the azimuthal mean flow is proportional to the libration amplitude squared and to the inverse square root of the Ekman number and libration frequency and then confirms this using the numerical data. Additionally, presence of an upscale cascade of energy is shown, using the kinetic energy budget of fluctuating flow. KW - Direct Numerical Simulation KW - Fluid Mechanics KW - Mean Flow KW - Rotation KW - Cylinder KW - Centrifugal KW - Instability KW - Mechanism KW - Vortex Y1 - 2016 U6 - https://doi.org/10.1063/1.4948406 VL - 28 IS - 056603 SP - 1 EP - 23 ER - TY - GEN A1 - Lignell, David O. A1 - Lansinger, Victoria B. A1 - Medina Méndez, Juan Ali A1 - Klein, Marten A1 - Kerstein, Alan R. A1 - Schmidt, Heiko A1 - Fistler, Marco A1 - Oevermann, Michael T1 - One-dimensional turbulence modeling for cylindrical and spherical flows: model formulation and application T2 - Theoretical and Computational Fluid Dynamics N2 - The one-dimensional turbulence (ODT) model resolves a full range of time and length scales and is computationally efficient. ODT has been applied to a wide range of complex multi-scale flows, such as turbulent combustion. Previous ODT comparisons to experimental data have focused mainly on planar flows. Applications to cylindrical flows, such as round jets, have been based on rough analogies, e.g., by exploiting the fortuitous consistency of the similarity scalings of temporally developing planar jets and spatially developing round jets. To obtain a more systematic treatment, a new formulation of the ODT model in cylindrical and spherical coordinates is presented here. The model is written in terms of a geometric factor so that planar, cylindrical, and spherical configurations are represented in the same way. Temporal and spatial versions of the model are presented. A Lagrangian finite-volume implementation is used with a dynamically adaptive mesh. The adaptive mesh facilitates the implementation of cylindrical and spherical versions of the triplet map, which is used to model turbulent advection (eddy events) in the one-dimensional flow coordinate. In cylindrical and spherical coordinates, geometric stretching of the three triplet map images occurs due to the radial dependence of volume, with the stretching being strongest near the centerline. Two triplet map variants, TMA and TMB, are presented. In TMA, the three map images have the same volume, but different radial segment lengths. In TMB, the three map images have the same radial segment lengths, but different segment volumes. Cylindrical results are presented for temporal pipe flow, a spatial nonreacting jet, and a spatial nonreacting jet flame. These results compare very well to direct numerical simulation for the pipe flow, and to experimental data for the jets. The nonreacting jet treatment overpredicts velocity fluctuations near the centerline, due to the geometric stretching of the triplet maps and its effect on the eddy event rate distribution. TMB performs better than TMA. A hybrid planar-TMB (PTMB) approach is also presented, which further improves the results. TMA, TMB, and PTMB are nearly identical in the pipe flow where the key dynamics occur near the wall away from the centerline. The jet flame illustrates effects of variable density and viscosity, including dilatational effects. KW - Cylindrical ODT Y1 - 2018 U6 - https://doi.org/10.1007/s00162-018-0465-1 SN - 0935-4964 SN - 1432-2250 VL - 32 IS - 4 SP - 495 EP - 520 ER - TY - GEN A1 - Klein, Marten A1 - Schmidt, Heiko T1 - Investigating the Reynolds number dependency of the scalar transfer to a wall using a stochastic turbulence model T2 - Proceedings in applied mathematics and mechanics : PAMM Y1 - 2018 U6 - https://doi.org/10.1002/pamm.201800238 SN - 1617-7061 VL - 18 IS - 1 ER - TY - GEN A1 - Klein, Marten A1 - Schmidt, Heiko T1 - Stochastic Modeling of Turbulent Scalar Transport at Very High Schmidt Numbers T2 - Proceedings in applied mathematics and mechanics : PAMM Y1 - 2017 UR - https://onlinelibrary.wiley.com/doi/pdf/10.1002/pamm.201710289 U6 - https://doi.org/10.1002/pamm.201710289 SN - 1617-7061 VL - 17 IS - 1 SP - 639 EP - 640 ER - TY - GEN A1 - Vincze, Miklos A1 - Fenyvesi, Nora A1 - Klein, Marten A1 - Sommeria, Joel A1 - Viboud, Samuel A1 - Ashkenazy, Yossi T1 - Evidence for wind-induced Ekman layer resonance based on rotating tank experiments T2 - EPL : a letters journal exploring the frontiers of physics N2 - The temporal variability of wind stress acting on the ocean surface may have a significant impact on the energy transfer between the surface ocean and the abyssal ocean. In particular, the surface ocean layer is expected to deepen when the wind’s frequency matches the inertial (Coriolis) frequency, through “Ekman layer resonance”. Here, we report on laboratory experiments conducted in the large circular rotating tank of the LEGI Coriolis platform (13 m in diameter and 0.5 m in depth) to investigate the effect of oscillating horizontal shear imposed at the water surface. The analysis of the flow structure by means of particle image velocimetry (PIV) reveals a resonant thickening of the top Ekman layer and a marked increase in the kinetic energy of the flow occurs when the forcing frequency coincides with the Coriolis frequency of the rotating tank. The findings are in agreement with the theoretical expectations and constitute evidence for the existence of the Ekman layer resonance (or near inertial resonance) phenomenon in an ocean-like configuration. KW - Fluid Dynamics KW - Rotating Flows KW - Resonance KW - Boundary Layer Y1 - 2019 UR - https://epljournal.edpsciences.org/articles/epl/abs/2019/04/epl19544/epl19544.html U6 - https://doi.org/10.1209/0295-5075/125/44001 SN - 1286-4854 VL - 125 IS - 4 SP - 1 EP - 7 ER - TY - GEN A1 - Klein, Marten A1 - Zenker, Christian A1 - Schmidt, Heiko T1 - Small-scale resolving simulations of the turbulent mixing in confined planar jets using one-dimensional turbulence T2 - Chemical Engineering Science Y1 - 2019 SN - 0009-2509 VL - 204 SP - 186 EP - 202 ER - TY - GEN A1 - Ghasemi, Abouzar A1 - Klein, Marten A1 - Will, Andreas A1 - Harlander, Uwe T1 - Mean flow generation by an intermittently unstable boundary layer over a sloping wall T2 - Journal of Fluid Mechanics Y1 - 2018 U6 - https://doi.org/10.1017/jfm.2018.552 SN - 1750-6859 IS - vol. 853 SP - 111 EP - 149 ER - TY - GEN A1 - Rakhi, Rakhi A1 - Klein, Marten A1 - Medina Méndez, Juan Ali A1 - Schmidt, Heiko T1 - One-dimensional turbulence modelling of incompressible temporally developing turbulent boundary layers with comparison to DNS T2 - Journal of Turbulence N2 - The incompressible temporally developing turbulent boundary layer (TBL) is analysed using the map-based stochastic one-dimensional turbulence (ODT) model. The TBL is a canonical flow problem, which is, in the present study, formed by a planar moving wall and a free stream at rest. An understanding of this idealised flow is of fundamental relevance for the numerical analysis of turbulent boundary-layer-type flows. In the present ODT simulations, the flow variables are resolved on all scales along a wall-normal, one-dimensional domain. These variables are evolved by a deterministic and a stochastic process. The latter models the effect of turbulent advection and pressure fluctuations, whereas the former represents molecular diffusion. The model is appropriate for high Reynolds numbers for which the turbulence field exhibits a broad range of scales and is notionally featureless. We show that ODT is able to capture salient features of the TBL by comparing the various statistics with available reference direct numerical simulation (DNS) results for different bulk Reynolds numbers in the range 250 ≤ Reb ≤ 2000 using fixed model parameters. The influence of the model parameters is analysed for Reb = 1000 and optimal parameter values are provided. The results discussed in this paper suggest that ODT is an economical and reasonably accurate approach for the simulation of transient turbulent boundary-layer-type flows. KW - one-dimensional turbulence KW - stochastic modeling KW - turbulent boundary layers Y1 - 2019 U6 - https://doi.org/10.1080/14685248.2019.1674859 SN - 1468-5248 VL - 20 IS - 8 SP - 506 EP - 543 ER - TY - GEN A1 - Medina Méndez, Juan Ali A1 - Klein, Marten A1 - Schmidt, Heiko T1 - One-Dimensional Turbulence investigation of variable density effects due to heat transfer in a low Mach number internal air flow T2 - International Journal of Heat and Fluid Flow N2 - A novel spatial formulation of the One-Dimensional Turbulence (ODT) model is applied to a vertical pipe-flow with heat transfer, analogous to the Direct Numerical Simulation (DNS) performed by Bae et al. [Phys. Fluids 18, (075102) (2006)]. The framework presented here is an extension for radially confined domains of the cylindrical ODT spatial formulation for low Mach number flows with variable density. The variable density simulations for air (Prandtl number Pr = 0.71) are performed at an initial bulk Reynolds number Reb (DNS) = 6000 and Grashof number Gr (DNS) = 6.78*10^6. ODT results are presented for both the spatial formulation introduced in this work and the standard temporal formulation for cylindrical flows introduced by Lignell et al. [Theor. Comput. Fluid Dyn. 32, 4 (2018), pp. 495–520]. Streamwise bulk profiles and radial profiles at specific streamwise positions for the temporal and spatial formulations are in good agreement with the DNS results from Bae et al. For the present application, the spatial formulation yields physically better results in comparison to the temporal formulation. Overall, the findings in the original work of Bae et al. were corroborated with ODT. Although the framework proposed in this work is not a compressible framework and has some clear limitations regarding conservation properties, we suggest its use for future studies in the low Mach number variable density regime. Y1 - 2019 UR - http://www.sciencedirect.com/science/article/pii/S0142727X19301596 U6 - https://doi.org/10.1016/j.ijheatfluidflow.2019.108481 SN - 0142-727X SN - 1879-2278 VL - 80 ER - TY - GEN A1 - Kurgansky, Michael V. A1 - Seelig, Torsten A1 - Klein, Marten A1 - Will, Andreas A1 - Harlander, Uwe T1 - Mean flow generation due to longitudinal librations of sidewalls of a rotating annulus T2 - Geophysical & Astrophysical Fluid Dynamics N2 - Laboratory experiments with a rotating cylindrical annulus arereported that reveal a prograde jet, which is adjacent to a (longitu-dinally) librating inner straight cylindrical wall. Here, wall libration isrealised as a time-harmonic modulation of the inner cylinder’s rota-tion rate. The outer cylindrical wall and bottom and top lids rotatewith constant angular velocity. The main purpose of our study is tocontribute to a qualitative and quantitative understanding of non-linearities that are present in oscillating, but centrifugally stable,vertical boundary layers frequently encountered in rotating wall-bounded flows. We consider a problem that is in a sense comple-mentary to that of previous works that focused on oscillating Ekmanlayers but neglected the vertical Stokes−Stewartson layers. A sim-ple analytical model is proposed that is able to predict the magni-tude and spatial structure of the emerging prograde near-wall jet interms of nonlinearity inherent in the inner cylinder’s boundary layerdynamics. KW - boundary layer structure KW - geophysical and geological flows KW - longitudinal libration Y1 - 2020 U6 - https://doi.org/10.1080/03091929.2019.1692829 SN - 1029-0419 VL - 114 IS - 6 SP - 762 ER - TY - GEN A1 - Klein, Marten A1 - Schmidt, Heiko A1 - Lignell, David O. T1 - Stochastic modeling of surface scalar-flux fluctuations in turbulent channel flow using one-dimensional turbulence T2 - International Journal of Heat and Fluid Flow N2 - Accurate and economical modeling of near-surface transport processes is a standing challenge for various engineering and atmospheric boundary-layer flows. In this paper, we address this challenge by utilizing a stochastic one-dimensional turbulence (ODT) model. ODT aims to resolve all relevant scales of a turbulent flow for a one-dimensional domain. Here ODT is applied to turbulent channel flow as stand-alone tool. The ODT domain is a wall-normal line that is aligned with the mean shear. The free model parameters are calibrated once for the turbulent velocity boundary layer at a fixed Reynolds number. After that, we use ODT to investigate the Schmidt (Sc), Reynolds (Re), and Peclet (Pe) number dependence of the scalar boundary-layer structure, turbulent fluctuations, transient surface fluxes, mixing, and transfer to a wall. We demonstrate that the model is able to resolve relevant wall-normal transport processes across the turbulent boundary layer and that it captures state-space statistics of the surface scalar-flux fluctuations. In addition, we show that the predicted mean scalar transfer, which is quantified by the Sherwood (Sh) number, self-consistently reproduces established scaling regimes and asymptotic relations. For high asymptotic Sc and Re, ODT results fall between the Dittus-Boelter, Sh ∼ Re^(4/5) Sc^(2/5), and Colburn, Sh ∼ Re^(4/5) Sc^(1/3), scalings but they are closer to the former. For finite Sc and Re, the model prediction reproduces the relation proposed by Schwertfirm and Manhart (Int. J. Heat Fluid Flow, vol. 28, pp. 1204-1214, 2007) that yields locally steeper effective scalings than any of the established asymptotic relations. The model extrapolates the scalar transfer to small asymptotic Sc ≪ Re_τ^(-1) (diffusive limit) with a functional form that has not been previously described. KW - one-dimensional turbulence KW - stochastic modeling KW - fluctuation modeling KW - passive scalar KW - scalar transfer KW - Schmidt number dependence KW - surface flux Y1 - 2021 UR - https://arxiv.org/abs/2111.15359 U6 - https://doi.org/10.1016/j.ijheatfluidflow.2021.108889 SN - 0142-727X VL - 93 (2022) SP - 1 EP - 19 ER - TY - GEN A1 - Sharma, Sparsh A1 - Klein, Marten A1 - Schmidt, Heiko T1 - Features of far-downstream asymptotic velocity fluctuations in a round jet: A one-dimensional turbulence study T2 - Physics of Fluids KW - stochastic modeling KW - turbulent round jet KW - one-dimensional turbulence KW - jet similarity KW - multi-scale fluctuation modeling Y1 - 2022 UR - https://aip.scitation.org/doi/10.1063/5.0101270 U6 - https://doi.org/10.1063/5.0101270 SN - 1089-7666 VL - 34 IS - 8 ER - TY - GEN A1 - Klein, Marten A1 - Schmidt, Heiko T1 - Exploring stratification effects in stable Ekman boundary layers using a stochastic one-dimensional turbulence model T2 - Advances in Science and Research N2 - Small-scale processes in atmospheric boundary layers are typically not resolved due to cost constraints but modeled based on physical relations with the resolved scales, neglecting expensive backscatter. This lack in modeling is addressed in the present study with the aid of the one-dimensional turbulence (ODT) model. ODT is applied as stand-alone column model to numerically investigate stratification effects in long-lived transient Ekman flows as canonical example of polar boundary layers by resolving turbulent winds and fluctuating temperature profiles on all relevant scales of the flow. We first calibrate the adjustable model parameters for neutral cases based on the surface drag law which yields slightly different optimal model set-ups for finite low and moderate Reynolds numbers. For the stably stratified cases, previously calibrated parameters are kept fixed and the model predictions are compared with various reference numerical simulations and also observations by an exploitation of boundary layer similarity. ODT reasonably captures the temporally developing flow for various prescribed stratification profiles, but fails to fully capture the near-surface laminarization by remaining longer in a fully developed turbulent state, which suggests preferential applicability to high-Reynolds-number flow regimes. Nevertheless, the model suggests that large near-surface turbulence scales are primarily affected by the developing stratification due to scale-selective buoyancy damping which agrees with the literature. The variability of the wind-turning angle represented by the ensemble of stratified cases simulated covers a wider range than reference reanalysis data. The present study suggests that the vertical-column ODT formulation that is highly resolved in space and time can help to accurately represent multi-physics boundary-layer and subgrid-scale processes, offering new opportunities for analysis of very stable polar boundary layer and atmospheric chemistry applications. KW - stochastic turbulence modeling KW - one-dimensional turbulence KW - stable stratification KW - atmospheric boundary layer KW - wind veering angle KW - Richardson number Y1 - 2022 UR - https://asr.copernicus.org/articles/19/117/2022/ U6 - https://doi.org/10.5194/asr-19-117-2022 SN - 1992-0636 N1 - This article is part of the special issue “21st EMS Annual Meeting – virtual: European Conference for Applied Meteorology and Climatology 2021”. VL - 19/2022 SP - 117 EP - 136 ER -