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This study proposes a self-learning algorithm for closed-loop cylinder wake control targeting lower drag and lower lift fluctuations with the additional challenge of sparse sensor information, taking deep reinforcement learning (DRL) as the starting point. The DRL performance is significantly improved by lifting the sensor signals to dynamic features (DFs), which predict future flow states. The resulting DF-based DRL (DF-DRL) automatically learns a feedback control in the plant without a dynamic model. Results show that the drag coefficient of the DF-DRL model is 25 % less than the vanilla model based on direct sensor feedback. More importantly, using only one surface pressure sensor, DF-DRL can reduce the drag coefficient to a state-of-the-art performance of approximately 8 % at Reynolds number $(Re) = 100$ and significantly mitigates lift coefficient fluctuations. Hence, DF-DRL allows the deployment of sparse sensing of the flow without degrading the control performance. This method also exhibits strong robustness in flow control under more complex flow scenarios, reducing the drag coefficient by 32.2 % and 46.55 % at $Re =500$ and 1000, respectively. Additionally, the drag coefficient decreases by 28.6 % in a three-dimensional turbulent flow at $Re =10\\,000$. Since surface pressure information is more straightforward to measure in realistic scenarios than flow velocity information, this study provides a valuable reference for experimentally designing the active flow control of a circular cylinder based on wall pressure signals, which is an essential step toward further developing intelligent control in a realistic multi-input multi-output system.

Wind is a critical driving force in hydrodynamic and water quality modeling of large shallow lakes, and is characterized by the wind drag coefficient Cd, representing the momentum transfer at the air‐water interface. Contemporary empirical formulae for Cd estimation were derived over oceans and some of which are solely wind velocity U10 dependent. These formulae were previously found to be inadequate in inland lake models often resulting in the water velocity underestimation. To address this problem, a physical scale experiment was designed, in which Cd was measured using a wind profile and eddy covariance methodology. A new wind‐induced wave‐dependent Cd parameterization was also established and validated in two lake studies. The driving force was modified by the wave‐dependent Cd formula in a hydrodynamic model of the shallow Upper Klamath Lake (UKL), OR, USA. The experimental Cd was negatively correlated to the wind velocity up until the critical U10 = 1.6 m s−1 which was 1.0~3.1 times previous empirical extrapolations at light winds. The variation partitioning results showed that wave parameters contributed to more than 30% of Cd variation combined with wind parameters. The modified wind stress field was spatially heterogeneous and the modeled water velocity was closer to the observations at two sites. Significant main circulation and outer bank circulation were modeled accompanied by higher surface vorticity, compared to the original UKL model. Overall, the wave‐dependent Cd formula provided an improvement of the surface flow field in the UKL model and will improve the management of the lake ecosystems. Plain Language Summary As a critical driving force in large shallow lakes, wind parameterization is of great importance for accurate hydrodynamic modeling. Previous wind‐dependent wind drag formulae over oceans usually generate large underestimates of water velocity in lakes. We thus propose a new wave‐dependent Cd parameterization based on an experimental study to improve the Cd parameterization in lakes. The Cd measurements were compared and confirmed by two typical methodologies of wind profile and eddy covariance. The newly derived wave‐dependent Cd parameterization was validated in two lake studies and adapted to a hydrodynamic model of the Upper Klamath Lake, OR, USA. Results showed an improved representation of the wind stress field, surface water velocity, and surface circulation. Our work should therefore be useful when using mechanistic models to manage hydrodynamics and water quality in large shallow lakes. Key Points A wave‐dependent Cd formula was developed based on an experimental study, indicating a negative correlation of Cd with U10 at light winds Spatial heterogeneity of the wind stress field and surface circulation was identified in lake hydrodynamic modeling The adaptation of Cd parameterization in a hydrodynamic model was improved through the wave‐dependent Cd formula

We study experimentally the spatial distribution, settling and interaction of sub-Kolmogorov inertial particles with homogeneous turbulence. Utilizing a zero-mean-flow air turbulence chamber, we drop size-selected solid particles and study their dynamics with particle imaging and tracking velocimetry at multiple resolutions. The carrier flow is simultaneously measured by particle image velocimetry of suspended tracers, allowing the characterization of the interplay between both the dispersed and continuous phases. The turbulence Reynolds number based on the Taylor microscale ranges from $Re_{\\unicode[STIX]{x1D706}}\\approx 200{-}500$ , while the particle Stokes number based on the Kolmogorov scale varies between $St_{\\unicode[STIX]{x1D702}}=O(1)$ and $O(10)$ . Clustering is confirmed to be most intense for $St_{\\unicode[STIX]{x1D702}}\\approx 1$ , but it extends over larger scales for heavier particles. Individual clusters form a hierarchy of self-similar, fractal-like objects, preferentially aligned with gravity and with sizes that can reach the integral scale of the turbulence. Remarkably, the settling velocity of $St_{\\unicode[STIX]{x1D702}}\\approx 1$ particles can be several times larger than the still-air terminal velocity, and the clusters can fall even faster. This is caused by downward fluid fluctuations preferentially sweeping the particles, and we propose that this mechanism is influenced by both large and small scales of the turbulence. The particle–fluid slip velocities show large variance, and both the instantaneous particle Reynolds number and drag coefficient can greatly differ from their nominal values. Finally, for sufficient loadings, the particles generally augment the small-scale fluid velocity fluctuations, which however may account for a limited fraction of the turbulent kinetic energy.

During starts and turns, between and within laps, the swimmer’s velocity is not constant; thus, besides the drag force, the swimmer experiences an additional (inertial) force. Some of the water around the swimmer is set in motion and this can be thought of as an added mass (MA,a) the swimmer has to accelerate (in addition to body mass, M0): the higher MA,a, the higher the resistive and inertial forces that oppose the swimmer’s motion during acceleration phases. This study introduces a novel method to determine MA,a, consisting of a standing start maximal test. Sixteen male swimmers (526.1 ± 65.8 FINA Points) performed maximal sprints during which their instantaneous speed was assessed using an IMU positioned on their sacrum. The estimation of MA,a was based on the swimmer’s maximum velocity (vmax) and acceleration time (τ), as determined using a standing start test, and the active drag coefficient (ka) and mean propulsive force (FP), as determined using the residual thrust method. On average vmax = 1.73 ± 0.11 m.s−1, τ = 1.14 ± 0.11 s, FP = 146.8 ± 20 N and ka = 47.9 ± 5.7 kg.m−1. MA,a in surface swimming (28.7 ± 15.2 % M0) is similar to the added mass that can be determined in passive conditions underwater (MA,p = 25 ± 3 % M0) but presents a larger variability. This variability could not be attributed to the swimmer’s technical level, e.g the active to passive drag ratio: ka/kp, where kp = 26.6 ± 3.3 kg.m−1 (determined using passive towing experiments).

This study investigates the exchange of momentum between the atmosphere and ocean using data collected from four oceanic field experiments. Direct covariance estimates of momentum fluxes were collected in all four experiments and wind profiles were collected during three of them. The objective of the investigation is to improve parameterizations of the surface roughness and drag coefficient used to estimate the surface stress from bulk formulas. Specifically, the Coupled Ocean–Atmosphere Response Experiment (COARE) 3.0 bulk flux algorithm is refined to create COARE 3.5. Oversea measurements of dimensionless shear are used to investigate the stability function under stable and convective conditions. The behavior of surface roughness is then investigated over a wider range of wind speeds (up to 25 m s −1 ) and wave conditions than have been available from previous oversea field studies. The wind speed dependence of the Charnock coefficient α in the COARE algorithm is modified to , where m = 0.017 m −1 s and b = −0.005. When combined with a parameterization for smooth flow, this formulation gives better agreement with the stress estimates from all of the field programs at all winds speeds with significant improvement for wind speeds over 13 m s −1 . Wave age– and wave slope–dependent parameterizations of the surface roughness are also investigated, but the COARE 3.5 wind speed–dependent formulation matches the observations well without any wave information. The available data provide a simple reason for why wind speed–, wave age–, and wave slope–dependent formulations give similar results—the inverse wave age varies nearly linearly with wind speed in long-fetch conditions for wind speeds up to 25 m s −1 .

A suite of six idealized supercell simulations is performed in which the surface drag coefficient C d is varied over a range of values from 0 to 0.05 to represent a variety of water and land surfaces. The experiments employ a new technique for enforcing a three-force balance among the pressure gradient, Coriolis, and frictional forces so that the environmental wind profile can remain unchanged throughout the simulation. The initial low-level mesocyclone lowers toward the ground, intensifies, and produces a tornado in all experiments with C d ≥ 0.002, with the intensification occurring earlier for larger C d . In the experiment with C d = 0, the low-level mesocyclone remains comparatively weak throughout the simulation and does not produce a tornado. Vertical cross sections through the simulated tornadoes reveal an axial downdraft that reaches the ground only in experiments with smaller C d , as well as stronger corner flow in experiments with larger C d . Material circuits are initialized enclosing the low-level mesocyclone in each experiment and traced backward in time. Circulation budgets for these circuits implicate surface drag acting in the inflow sector of the supercell as having generated important positive circulation, and its relative contribution increases with C d . However, the circulation generation is similar in magnitude for the experiments with C d = 0.02 and 0.05, and the tornado in the latter experiment is weaker. This suggests the possible existence of an optimal range of C d values for promoting intense tornadoes within our experimental configuration.

In this paper, we revisit the problem of wind–wave interaction with emphasis on strong winds. For these events, it is assumed that nonlinearity is so large that the slope of the wind waves has reached a limiting steepness. Recent observations suggest that the drag decreases with wind in the strong wind speed regime. In this paper, we try to explain this. In the first step, we introduce a model for surface gravity waves and calculate explicitly the background roughness length from the original approach of Janssen. It is found that for young, steep wind sea, the background roughness length almost vanishes, giving a reduced drag. In addition, it is shown that for steep waves, the slowing down of the wind by waves is a nonlinear process; hence, the growth rate of the waves by wind depends in a nonlinear fashion on the wave spectrum. For strong winds, it is found that, as waves are typically steep, this nonlinear effect gives a further reduction of the wind input. As a consequence, in these extreme circumstances, the drag coefficient decreases with wind.

The mean skin-friction drag in a wall-bounded turbulent flow can be decomposed into different physics-informed contributions based on the mean and statistical turbulence quantities across the wall layer. Following Renard & Deck’s study (J. Fluid Mech., vol. 790, 2016, pp. 339–367) on the skin-friction drag decomposition of incompressible wall-bounded turbulence, we extend their method to a compressible form and use it to investigate the effect of density and viscosity variations on skin-friction drag generation, using direct numerical simulation data of compressible turbulent channel flows. We use this novel decomposition to study the skin-friction contributions associated with the molecular viscous dissipation and the turbulent kinetic energy production and we investigate their dependence on Reynolds and Mach number. We show that, upon application of the compressibility transformation of Trettel & Larsson (Phys. Fluids, vol. 28, 2016, 026102), the skin-friction drag contributions can be only partially transformed into the equivalent incompressible ones, as additional terms appear representing deviations from the incompressible counterpart. Nevertheless, these additional contributions are found to be negligible at sufficiently large equivalent Reynolds number and low Mach number. Moreover, we derive an exact relationship between the wall heat flux coefficient and the skin-friction drag coefficient, which allows us to relate the wall heat flux to the skin-friction generation process.

Large-eddy microscale simulations of eleven local climate zone-based (LCZ) urban morphologies with various building plane and frontal area density are used to investigate the flow characteristics and provide vertical profiles of velocity, sectional drag coefficient, and turbulence mixing length. The urban morphologies are procedurally generated to mimick real urban districts. The simulations are performed with the MesoNH-IBM meteorological research model, which allows to represent explicitly the obstacles and to account for the impact of the large scale turbulence structures on the urban canopy layer (UCL). The results show that, in heterogeneous building height UCLs, the streamwise velocity profile is not exponential, the mixing length is not constant and the equivalent sectional drag coefficient formula based on bulk morphology parameters is not valid. Comparatively to an non-urban mixing length increasing linearly with the distance from the ground, the UCL mixing length is higher for z/hmean∈[0-≈0.75], because of the turbulent structures generated by the buildings and lower above, because of the shear generated at the building roofs. These differences extend up to several times the mean building height. The vertical profile of the dispersive momentum flux (DMF) in the UCL is in agreement with the literature; positive DMF is found upstream of the buildings whereas negative DMF is localized downstream. Although the DMF is lower than the turbulent momentum flux for most of the LCZs, it is not negligible for midrise and highrise LCZs. The large-scale atmospheric boundary-layer turbulence has a negligible influence on most of the investigated horizontally-averaged quantities. This suggests that considering a neutral stratification and a wind flow aligned with the buildings, most of the turbulence within the UCL is generated by the buildings themselves.

Developing urban land surface models for modeling cities at high resolutions needs to better account for the city‐specific multi‐scale land surface heterogeneities at a reasonable computational cost. We propose using an encoder‐decoder convolutional neural network to develop a computationally efficient model for predicting the mean velocity field directly from urban geometries. The network is trained using the geometry‐resolving large eddy simulation results. Systematic testing on urban structures with increasing deviations from the training geometries shows the prediction error plateaus at 15%, compared to errors sharply increasing up to 35% in the null models. This is explained by the trained model successfully capturing the effects of pressure drag, especially for tall buildings. The prediction error of the aerodynamic drag coefficient is reduced by 32% compared with the default parameterization implemented in mesoscale modeling. This study highlights the potential of combining computational fluid dynamics modeling and machine learning to develop city‐specific parameterizations. Plain Language Summary Predicting the velocity field in the urban area with fine resolution at the meter scale is computationally expensive. Yet a detailed velocity field is necessary for improving the accuracy of urban land surface representation in weather and climate models. We propose using a convolutional neural network to predict the velocity field from the three‐dimensional (3D) building distribution. The similarity between the predicted velocity fields and LES simulations in the testing geometries illustrates the prediction capability of the trained model. We also investigate the aerodynamic drag coefficient, a key parameter for quantifying the land‐atmosphere momentum exchange. The results indicate that the trained model prediction is much closer to values derived from large‐eddy simulation models than those from the default parameterization scheme, showing the promise of using machine learning to improve urban land surface modeling. Key Points Machine learning (ML) can help develop city‐specific parameterization that fully utilizes urban form data It is a first attempt to develop an ML model for high‐Reynolds number urban canopy flow with multiple bluff‐body obstacles Limitation of the geometry to flow field approach is quantified by accessing the extrapolative capability of the trained model