Strouhal Number Research Articles

Experimental investigation on fluid-induced vibration of a semi-submerged flexible pipe in oncoming flows

Fluid-induced vibration (FIV) features of the semi-submerged flexible pipe in an oncoming flow are experimentally investigated in this paper. The flexible pipe is towed to simulate the equivalent uniform oncoming flow with a Froude number (Fr) ranging from 0.2 to 2.5. The overtopping states are determined and divided into three regions by the Fr numbers, including non-overtopping, intermitting overtopping, and continuous overtopping regions. Through the displacement reconstruction and wavelet transform methods, the displacement response, frequency, trajectory, and the chaotic characteristics of the semi-submerged pipe are studied. The results show that the FIV displacement responses are evidently affected by the intensity of the overtopping phenomenon. A significant mean displacement in the cross flow (CF) direction can be seen and a maximum value of 0.88D can be reached. The unexpectedly larger FIVs with standard deviation values of around 0.52D can be witnessed in the in-line (IL) direction than those for a fully submerged pipe. Moreover, the FIV frequency response in the IL direction is found to be consistent with that in the CF direction under intermitting overtopping and continuous overtopping state, and the corresponding Strouhal numbers are 0.24 and 0.28, respectively. The FIV response is found to be chaotic in non-overtopping states, while it behaves periodic and quasiperiodic features as overtopping occurs. The “O” shape of the motion trajectory is observed at such overtopping regions. The present work improves the basic understanding of the FIV features of the semi-submerged flexible pipe in the oncoming flow and can provide useful references for designing the relevant marine structures.

Motion of a small bubble in forced vibrating sessile drop

In this letter, the motion of small gas bubbles within sessile water drops on a vibrating substrate is investigated numerically using a two-phase diffuse interface method. Depending on the amplitude of the plate vibration, the motion of the gas bubbles falls into three distinct regimes: oscillating within the drop, sticking to the substrate, or escaping from the drop. In particular, the motion of oscillating bubbles follows a harmonic function, and is found to be closely related to a combined effect of the deformation of the sessile drop and the vibration of the plate. To interpret the underlying mechanism, we analyze the dominant forces acting on the bubbles in the non-inertial framework fixed to the plate, and take account of the periodic deformation of the drop, which effectively induces flow acceleration inside the drop. As a result, we establish a theoretical model to predict the bubble motion, and correlate the amplitude and phase difference of the bubble with the Bond and Strouhal numbers. The theoretical prediction agrees with our numerical results. These findings and theoretical analysis provide new insights into controlling bubble motion in sessile drops.

Numerical simulations of bio-inspired approaches to enhance underwater swimming efficiency

The present study discusses the numerical simulation results of swimming similar to manta rays. The complex three-dimensional kinematics of manta rays were implemented to unravel the intricacies of its propulsion mechanisms by using the discrete vortex method (DVM). The DVM replaces the requirement for a structured grid across the computational domain with a collection of vortex elements. This method simplifies grid generation, especially for intricate geometries, resulting in time and effort savings in meshing complex shapes. By modeling the pectoral fins with discrete panels and utilizing vortex rings to represent circulation and wake, the study accurately computes the pressure distribution, circulation distribution, lift coefficient, and thrust coefficient of the manta ray. This study focuses on the modulation of aerodynamic performance by altering the span length and the length change ratio during the downstroke and upstroke motion (SV). The manta ray's three-dimensional vortex configurations comprise a combination of vortex rings, vortex contrails, and horseshoe vortices. Analysis of the three-dimensional vortex structure indicates the presence of multiple vortex rings and horseshoe vortex rings at higher SV values, while adequate formation of horseshoe vortices is not observed at lower SV values. In terms of propulsive performance, both lift and thrust increase with SV, while the propulsive efficiency demonstrates its peak at SV = 1.75. The analysis reveals that at higher SV values, the net thrust generated primarily originates from the tip of the fins. Moreover, the study illustrates a significant enhancement in propulsive efficiency, particularly in association with optimal Strouhal numbers ranging between 0.3 and 0.4. The key findings of this study may be used in efficient design of agile autonomous underwater vehicles for marine exploration and surveillance applications.

Unsteady cylinder wakes from arbitrary bodies with differentiable physics-assisted neural network.

This work describes a hybrid predictive framework configured as a coarse-grained surrogate for reconstructing unsteady fluid flows around multiple cylinders of diverse configurations. The presence of cylinders of arbitrary nature causes abrupt changes in the local flow profile while globally exhibiting a wide spectrum of dynamical wakes fluctuating in either a periodic or chaotic manner. Consequently, the focal point of the present study is to establish predictive frameworks that accurately reconstruct the overall fluid velocity flowfield such that the local boundary layer profile, as well as the wake dynamics, are both preserved for long time horizons. The hybrid framework is realized using a base differentiable flow solver combined with a neural network, yielding a differentiable physics-assisted neural network (DPNN). The framework is trained using bodies with arbitrary shapes, and then it is tested and further assessed on out-of-distribution samples. Our results indicate that the neural network acts as a forcing function to correct the local boundary layer profile while also remarkably improving the dissipative nature of the flowfields. It is found that the DPNN framework clearly outperforms the supervised learning approach while respecting the reduced feature space dynamics. The model predictions for arbitrary bodies indicate that the Strouhal number distribution with respect to spacing ratio exhibits similar patterns with existing literature. In addition, our model predictions also enable us to discover similar wake categories for flow past arbitrary bodies. For the chaotic wakes, the present approach predicts the chaotic switch in gap flows up to the mid-time range.

Parametric analysis on the acoustic characteristics generated by a biomimetic swimmer

Previous studies have shown the excellent hydrodynamic performance of fish swimming. However, the main factors that lead to the low-noise propulsion of fish are still unrevealed. In this study, numerical studies on the characteristics of the far-field sound generated by a bio-inspired swimmer were carried out. The model was simplified as a two-dimension (2D) foil based on the numerous analyses in the past decades. The effects of propulsion methods, model thickness, Strouhal number St, and Reynolds number Re on the flow-induced sound were analysed. Reynolds-Averaged Navier–Stokes (RANS) and Ffowcs Williams–Hawkings (FW–H) equations were employed to simulate the fluid field and the acoustic characteristics, respectively. Simulation results indicated that the sound distribution generated by the biomimetic swimmer exhibits a dipole-like pattern. It was noted that by analysing the effect of motion wavelength on the effective sound pressure, an anguilliform swimmer generates lower sound during propulsion than swimmers with other types of motions. With a small thickness-length ratio, the bio-inspired swimmer could generate large thrust but small sound. Meanwhile, the maximum effective sound pressure is related to the effective lift of the foil.

Spacing Ratio Effects on the Evolution of the Flow Structure of Two Tandem Circular Cylinders in Proximity to a Wall

The flow around two tandem circular cylinders in proximity to a wall is investigated using particle image velocimetry (PIV) for Re = 2 × 103. The spacing ratios L/D are 1, 2, and 5, and the gap ratios G/D are 0.3, 0.6, and 1. The proper orthogonal decomposition (POD) method and λci vortex identification method are used to investigate the evolution of flow structure, and the influences of L/D and G/D on flow physics are shown. At L/D = 2 and G/D = 0.3, a “pairing” process occurs between the wall shear layer and the upstream cylinder’s lower shear layer, resulting in a small separation bubble behind the upstream cylinder. At L/D = 1, the Strouhal number (St) increases with decreasing G/D. At three gap ratios, the St gradually decreases as L/D increases. At G/D = 0.3, there is nearly a 49.98% decrease from St = 0.3295 at L/D = 1 to St = 0.1648 at L/D = 5, which is larger than the reductions in cases of G/D = 0.6 and G/D = 1. The effects of L/D on the evolution of flow structure at G/D = 0.6 are revealed in detail. At L/D = 1, the vortex shedding resembles that of the single cylinder. As L/D increases to 2, a squarish flow structure is formed between two cylinders, and a small secondary vortex is formed due to induction of the lower shear layer of the upstream cylinder. At L/D = 5, there is a vortex merging process between the upper wake vortices of the upstream and downstream cylinders, and the lower wake vortex of the upstream cylinder directly impinges the downstream cylinder. In addition, the shear layers and wake vortices of the upstream cylinder interact with the wake of the downstream cylinder as L/D increases, resulting in reductions in velocity fluctuations, and the production and turbulent diffusion of turbulent kinetic energy are decreased behind the downstream cylinder.

Measurement of pressure fluctuation distribution on a flat wall behind supported square cylinder with pressure-sensitive paint

The pressure fluctuation distribution on the floor surface behind a supported square cylinder in a turbulent boundary layer was measured by using pressure-sensitive paint (PSP). Specifically, the accuracy and frequency response of PSP at a Mach number around M = 0.3 were examined. Four square cylinders with different dimensions were investigated in the same turbulent boundary layer, and the detailed relationship between these conditions and Kármán vortex shedding structures was discussed. The values measured with PSP had a similar trend to those measured with a pressure transducer at up to 5 kHz. The peak power spectral density (PSD) of the pressure fluctuations due to Kármán vortex shedding was observed within an error of approximately 30 % at up to frequencies greater than 3 kHz. Moreover, the peak frequency of Kármán vortex shedding was found to decrease with the cylinder height in a manner similar to a previous empirical equation for the Strouhal number. The peak PSD value for the shortest square cylinder (h/w = 3.5, h/δ = 1.1) was twice as high as that for the other cylinders; also, the high-pressure fluctuation area in this case did not spread downstream, which suggests that the flow from the top of the cylinder affected the Kármán vortex shedding generated from the cylinder’s sides. One contour of the two main modes extracted for the highest PSD via the right singular vector vi at the Kármán vortex frequency had an asymmetric distribution behind the supported taller square cylinders (h/w ≥ 7.0, h/δ ≥ 2.3). This result is considered to be derived from the Kármán vortex shedding being mainly generated from the mainstream rather than the boundary-layer flow.

Hydrodynamic Performance Research of Underwater Oscillating Fin With the Compound Locomotion of Two Modes

Abstract The fish-like propulsion robot is becoming a profound intelligent equipment due to its excellent swimming ability and good environmental adaptability. In this paper, we propose the oscillating fin based on the fish swimming mechanism, which is compounded with the locomotion modes of sway and yaw. The kinematic and dynamic models are established to study the locomotion mechanism of the oscillating fin. The hydrodynamic performance of underwater locomotion is investigated to analyze the velocity, the propulsive force, the pressure, the propulsive efficiency, and the vortices property. Finally, the experimental measurements of the robot with oscillating fin propulsion are carried out to analyze the underwater propulsion of the oscillating fin and the unsteady fluid flow with Strouhal number. The results illustrate that the propulsive force is fluctuating, and the velocity is increasing to the maximum value. The underwater propulsion velocity could reach 1.2 m/s in a period of 0.4 s. Besides, the high- and low-pressure regions change alternatively, and the fin deforming process illustrates the vortices property and the locomotion mechanism analyses. The propulsive efficiency of the oscillating fin with compound waves is increased by 11% compared with that of the one without deformation. The experiments of the robot prototype verify the numerical simulation, and the propulsive velocity with a period of 0.4 s is two times larger than that of a period of 0.8 s. The Strouhal number of each motion mode is obtained through theoretical and experimental analyses.

The Aeolian harp sound from the Madelung model of quantum mechanics

According to Madelung, Bohm and Vigier, Wilhelm, Rosen and others, the original Schroedinger equation can be transformed into the hydrodynamical system of equations by using the so called Madelung ansatz. We derive in such quantum hydrodynamics, the non-relativistic and relativistic Strouhal number from the so called von Karman's vortex street. The relativistic derivation of this formula follows from the addition formula for velocities. The Strouhal friction tones are generated also during the motion of cosmic rays in relic photon sea, during the motion of bolids in atmosphere, during the Saturn rings motion in the relic black-body sea, during the motion of bodies in superfluid helium and so on.

Aerodynamic characteristics and wake formation behind a pair of side-by-side rectangular cylinders using the lattice Boltzmann method

In this work, the lattice Boltzmann method is used to numerically analyze the interactions of flowing fluid with two side-by-side rectangular cylinders at a fixed Reynolds number of 150. The gap ratios between the cylinders are varied from 0.5 to 5 while the aspect ratios of both cylinders are varied from 0.25 to 4. The deflected, bistable, flip-flopping, chaotic, single bluff body, two pairs’ street of anti-phase vortex shedding, anti-phase synchronized, and in-phase non-synchronized wake patterns are observed upon varying the aspect ratios as well as the gap ratios. The observed results show that the mean drag coefficients of both side-by-side rectangular cylinders, as well as that of the single cylinder, exhibit decreasing trends till the aspect ratio = 2 and become almost constant afterward. The Strouhal number varies abruptly at the gap ratio of 0.5 and becomes steady for gap ratios = 2 and 5. The root-mean-square values of lift coefficients of two side-by-side rectangular cylinders exhibit variations till the aspect ratio equal to 1.5 and then becomes constant afterward. This study also reveals that an increment in aspect ratios results in the minimization of the drag force and controls the wake, while the increment in gap ratio results in stabilizing the chaos produced in the flow structure due to jet flow influence. The wake patterns in this study are found to be consistent with the numerical and experimental work of other researchers.

Enhanced recovery caused by nonlinear dynamics in the wake of a floating offshore wind turbine

An experimental study in a wind tunnel is presented to explore the wake of a floating wind turbine subjected to harmonic side-to-side and fore–aft motions under laminar inflow conditions. The wake recovery is analysed as a function of the frequency of motion $f_p$ , expressed by the rotor-based Strouhal number, $St = f_p D / U_{\infty }$ ( $D$ is the rotor diameter, $U_{\infty }$ the inflow wind speed). Our findings indicate that both directions of motion accelerate the transition to the far-wake compared with the fixed turbine. The experimental outcomes confirm the computational fluid dynamics results of Li et al. (J. Fluid Mech., vol. 934, 2022, p. A29) showing that sideways motions lead to faster wake recovery, especially for $St \in [0.2, 0.6]$ . Additionally, we find that fore–aft motions also lead to better recovery for $St \in [0.3, 0.9]$ . The recovery is closely linked to nonlinear spatiotemporal dynamics found in the shear layer region of the wake. For both directions of motion and $St \in [0.2, 0.55]$ , the noisy wake dynamics lock in to the frequency of the motion. In this synchronised-like state, sideways motions result in large coherent structures of meandering, and fore–aft movements induce coherent pulsing of the wake. For fore–aft motion and $St \in [0.55, 0.9]$ , the wake shows a more complex quasiperiodic dynamic, namely, a self-generated meandering mode emerges, which interacts nonlinearly with the excitation frequency $St$ , as evidenced by the occurrence of mixing components. The coherent structures grow nonlinearly, enhance wake mixing and accelerate the transition to the far-wake, which, once reached, exhibits universal behaviour.

Tertiary wake mode in flows past elliptic cylinders

Linear stability analysis of the steady flow past elliptic cylinders of different aspect ratio (Ar) has been conducted for the flow Reynolds number (Re) in the range 30–200. A new unstable mode, which we refer as tertiary wake mode, has been discovered. Two other unstable modes (the primary wake mode and the secondary wake mode), already reported in the literature, are also found. The critical Re for the onset of instability of these modes and the corresponding Strouhal number (St) have been reported. Modes that have large growth rates tend to come close to the cylinder surface, and the extent to which they spread downstream in the wake is less compared to the weaker modes. The size of the vortical structures in a mode is inversely related to its St. The change in the characteristics of these modes with respect to change in Ar and Re, as well as their evolution leading to the fully developed flow, has been studied. Selective suppression of the unstable modes is effected using a slip-plate placed on the wake centerline. For Re = 150, it is shown that selective suppression of the unstable modes leads to different fully developed unsteady flows.

Aerodynamic interaction between galloping instability and vortices in corner-cut rectangular cylinders

Studies on bluff-body aerodynamics have emphasized that galloping instability is strongly associated with the Kármán vortex. This study discusses the aerodynamic interactions between the galloping instability and Kármán and motion-induced vortices, analyzes the effects of these vortices on vortex-induced vibration and galloping, and investigates the stabilizing effects of various corner cuts on a rectangular cylinder. Wind tunnel tests were performed on a rectangular cylinder with a side ratio of 1.5 under a smooth flow for seven different corner shapes. The rectangular cylinder with cut corners significantly reduced both the aerodynamic force coefficients and the Kármán vortex shedding intensity. Furthermore, spring-supported free vibration tests indicated that the onset reduced wind velocities were high in the response amplitudes of all corner-cut sections that were analyzed despite the significantly low onset reduced wind velocities of the Kármán vortex-induced vibration, which were denoted as the reciprocal of the Strouhal number and closely associated with the onset of galloping. This was attributed to the motion-induced vortex dominating the vibration when the Kármán vortex shedding intensity was reduced. Therefore, this study clarified one of the factors that affected the onset-reduced wind velocity of galloping.

Impact of Flow Unsteadiness on Turbine Airfoil Heat Transfer via Streaming

Abstract Thermal management of turbine airfoils is a critical design consideration, but the impact of unsteadiness on heat transfer of attached flow regions has received less attention in the literature. When turbine surfaces are subjected to unsteady zero-mean flow fluctuations, either naturally or artificially, the mean velocity around them is modified due to a nonlinear interaction of fluctuations, known as streaming. In this numerical study, we examine the effect of streaming on heat transfer and skin friction in a simplified model of the flow over a turbine blade. Both heat transfer and skin friction modifications were found to strongly depend on the amplitude and wave speed of the unsteady flow perturbations. Over a wide range of disturbance parameters, skin friction modification was negligible, but a significant effect on heat transfer due to streaming was identified. Moreover, the impact of favorable pressure gradients, which are typical for turbine airfoils, on the streaming phenomena was also considered, and it was found that flow regions of zero-pressure gradient produced the strongest amplification of heat transfer, although the effect of the pressure gradient varied with Strouhal number. Due to its significant effect on wall heat transfer, the streaming phenomenon should be taken into account during the design and measurement of the thermal properties of unsteady systems.

Fluid structure interaction problem for flow past three unequal sized square cylinders at different Reynolds numbers

The flow past three square cylinders of unequal size placed in an inline arrangement is studied using the lattice Boltzmann method at different Reynolds numbers [Re = (u∞ d)/ν] within the range of Re = 120, 150, 160, 175, and 200 for various gap spacings (g = s/d), ranging from 1 to 6. This study focused on the symmetric examination of flow behavior for various gap spacing within the three unequal-sized square cylinders. The main objective of this study was to investigate the effects of Reynolds numbers and gap spacing for flow structure mechanism and vortex shedding suppression in between the gap and down-stream position of all three cylinders. Results are obtained in terms of vorticity contours visualization, drag and lift coefficients, Strouhal number, and physical parameters. In vorticity contour visualization, different flow behaviors are observed, known as flow regimes, and are named according to their characteristics, and they are (i) steady flow regime, (ii) shear layer reattachment flow regime (SLR), (iii) fully developed vortex shedding flow regime, (iv) two-row fully developed vortex shedding flow regime, and (v) fully developed irregular vortex shedding flow regime. The present study also includes a discussion on aerodynamic forces, namely the mean drag coefficient (Cdmean), root mean square of the lift coefficient (Clrms), and Strouhal numbers (St) for three cylinders with sizes d = 20, d1 = 15, and d2 = 10, respectively. The maximum value of Cdmean for the first cylinder (C1) is obtained at (Re, g) = (200, 3) that is, 1.5156, where the existing flow regime is the SLR flow regime, while for C2 and C3, the maximum Cdmean values are examined at critical flow behaviors, where the existing flow regime is a fully developed irregular vortex shedding flow regime. Negative values of Cdmean are also examined for cylinders C2 and C3 at some combinations of (Re, g), attributed to the effect of thrust. Furthermore, it is noticed that the values of Strouhal number are increased with an increment in values of gap spacing. The highest value of the Strouhal number for all three cylinders is observed for C1 at (Re, g) = (120, 5), reaching 0.1556 along with a two-row fully developed flow regime. Furthermore, it is investigated from the present problem that the position of unequal sized square cylinders strongly influenced the flow structure mechanism. The information found and discussed in this study could be effective for structure designing arrangement in the case of three square cylinders of unequal size placed in a horizontal arrangement.

Study on the aerodynamic characteristics and flow mechanism of square cylinders with rounded corners

In order to elucidate the variation patterns of the aerodynamic characteristics of square cylinders with rounded corners with respect to corner radius ratio and angles of incidence, and to reveal their underlying mechanisms, a wind tunnel test was performed to examine the surface wind pressure of square cylinders with a corner radius ratio R/D (where R represents the corner radius and D signifies the characteristic dimension of the object) of 0, 0.1, 0.2, 0.3, and 0.4. The experiment was conducted at a Reynolds number of 120,000 while varying the angles of incidence between 0° and 45°. In this study, aerodynamic forces, Strouhal numbers, and wind pressure were analyzed. Additionally, the flow field was visualized using a large eddy simulation (LES). The results indicate that the critical angle of incidence αcr of square cylinders with rounded corners decreases as the corner radius ratio increases. αcr represents the angle at which the mean drag and fluctuating lift are minimum and the mean lift and Strouhal number are maximum. Significant negative pressure is observed near the windward rounded corner of the square cylinders with rounded corners in the vicinity of αcr, with the highest value occurring at an R/D of 0.2. Fluctuating wind pressures could attain larger values in the vicinity of the leeward rounded corners where α = 12.5°∼20° and α = 45°. Increasing R/D to a certain value significantly alters the flow structure compared to a square cylinder with R/D= 0. This is due to the shear layer flowing close to the wall, as it does not separate at the windward rounded corner.

Flow and noise control of a cylinder using grooves filled with porous material

In the present numerical study, we propose a new passive flow control mechanism at the Reynolds number of 3900. The novel method benefits from making grooves in the cylinder wall while the grooves are filled with porous materials of a specific permeability. According to the literature survey, while the porous medium is potentially an effective noise control method, it has serious drawbacks, mainly significant pressure drop. In the present study, instead of a porous coating, porous fillers are introduced offering substantial reduction of the noise level, in addition to managing the hydrodynamic parameters. To find a suitable design for the grooves and porous fillers, a systematic parametric study is performed on the number, sequence and size of the grooves, as well as the porous fillers' permeabilities. Based on the results, the newly proposed method dominated the traditional full porous coating by limiting the turbulent kinetic energy (TKE). The results of the parametric study indicated that grooves at an angle of 90° relative to the front stagnation point reduced the overall sound pressure level (OASPL) by 1.25 dB; meanwhile, the high-intensity TKE region shrunk. Further reductions were achieved by deeper grooves and porous fillers, as the drag coefficient, the lift coefficient, the Strouhal number, and the OASPL reduced up to 40.2%, 27.4%, 10.6%, and 3 dB, respectively. The proposed passive control method will be helpful for various industrial applications of cylinders through rigorous control of aerodynamic parameters and the noise level.

Effects of surface roughness on the drag coefficient of spheres freely rolling on an inclined plane

An experimental investigation identifying the effects of surface roughness on the drag coefficient ( $C_{D}$ ) of freely rolling spheres is reported. Although lubrication theory predicts an infinite drag force for an ideally smooth sphere in contact with a smooth wall, finite drag coefficients are obtained in experiments. It is proposed that surface roughness provides a finite effective gap ( $G$ ) between the sphere and panel, resulting in a finite drag force while also allowing physical contact between the sphere and plane. The measured surface roughnesses of both the sphere and panel are combined to give a total relative roughness ( $\xi$ ). The measured $C_{D}$ increases with decreasing $\xi$ , in agreement with analytical predictions. Furthermore, the measured $C_{D}$ is also in good agreement with the combined analytical and numerical predictions for a smooth sphere and wall, with a gap approximately equal to the root-mean-square roughness ( $R_q$ ). The accuracy of these predictions decreases for low mean Reynolds numbers ( $\overline {Re}$ ), due to the existence of multiple scales of surface roughness that are not effectively captured by $R_{q}$ . Experimental flow visualisations have been used to identify critical flow transitions that have been previously predicted numerically. Path tracking of spheres rolling on two panels with different surface roughnesses indicates that surface roughness does not significantly affect the sphere path or oscillations. Analysis of sphere Strouhal number ( $St$ ) highlights that wake shedding and sphere oscillations are coupled at low $\overline {Re}$ but with increasing $\overline {Re}$ , the influence of wake shedding on the sphere path diminishes.

Fluid dynamics of a flapping wing interacting with the boundary layer at a flat wall

In this paper, we consider the fluid dynamics of a flapping wing interacting with a boundary layer developed at a no-slip flat wall. Direct numerical simulations are carried out via implementing the non-iterative immersed boundary-lattice Boltzmann method, over a Reynolds number range of 10≤Re≤1000, for a fixed Strouhal number of St = 0.3 and for a given symmetric plunging and pitching flapping motion. The interactions between the wing and the boundary layer are modulated by varying the mean distance of the wing to the wall H0. The results indicate that the presence of the boundary layer at the wall amplifies the fluctuations in both lift and drag due to the boundary layer separation, in contrast to the pure ground effect. This separation also leads to the decrease in both average lift and average drag over one flapping cycle when H0 is low. When it comes to the flow patterns in the wake, it generally gets more complex for a low H0 and/or a high Re. Secondary vortices can be observed for Re≥500 in the present configuration, which either evolve by themselves or interact with the vortices in the wake while being convected downstream and dissipated via viscosity. In the end, a dynamic mode decomposition analysis is performed to explore further the flow structures in the wake. One observes the sheltering effect of the boundary layer that the vortices in the wake are prevented from penetrating the boundary layer, while this effect will not hold if the vortex intensity is sufficiently high, such as the low order mode of the case for Re≥1000 in this study.

Tracking the Nearfield Evolution of an Initially Shallow, Neutrally Buoyant Plane Jet Over a Sloping Bottom Boundary

AbstractUnderstanding coastal plane jets which occur when a body of water discharges into an ocean or a lake through a channel or outlet is important, since they play a significant role in sediment, nutrient, and pollutant exchange. This study investigates the nearfield of initially shallow, neutrally buoyant plane jets, bounded by a free surface and a sloping bottom (Sloping Bottom Jet; SBJ) that issue into a laterally unconfined quiescent ambient both experimentally and numerically, and compares them with a plane jet flowing over a horizontal bottom (Horizontal Bottom Jet; HBJ). Results revealed that, different from the HBJ, the width and centerline velocity of SBJ decrease near the mouth. The SBJ width gradually increases after that as the transverse longitudinal velocity profile progressively transforms from a “top‐hat” into a Gaussian distribution. Once the Gaussian distribution is established, both jets diverge and centerline velocity decreases. Shear layers are generated on the sides of both jets with Kelvin Helmholtz‐type Coherent Structures (KHCS) developing inside. KHCS produce periodic velocity fluctuations with a Strouhal number of ∼0.079 and contribute significantly to momentum exchange and turbulent kinetic energy production. Since the thickness of the SBJ increases longitudinally, the vertical extent of KHCS also increases. When the two shear layers meet and merge at the centerline, they cause a flapping motion of the jet. This location is closer to the jet mouth for SBJs than for the HBJ. These findings demonstrate that a sloping bottom modifies the flow field from quasi‐2D for the HBJ to strongly 3D for SBJs.