Turbulent Coherent Structures Research Articles

Documenting Coherent Turbulent Structures in the Boundary Layer of Intense Hurricanes Through Wavelet Analysis on IWRAP and SAR Data

Documenting Coherent Turbulent Structures in the Boundary Layer of Intense Hurricanes Through Wavelet Analysis on IWRAP and SAR Data

Turbulence Organization and Mean Profile Shapes in the Stably Stratified Boundary Layer: Zones of Uniform Momentum and Air Temperature

A persistent spatial organization of eddies is identified in the lowest portion of the stably stratified planetary boundary layer. The analysis uses flow realizations from published large-eddy simulations (Sullivan et al. in J Atmos Sci 73(4):1815–1840, 2016) ranging in stability from near-neutral to almost z-less stratification. The coherent turbulent structure is well approximated as a series of uniform momentum zones (UMZs) and uniform temperature zones (UTZs) separated by thin layers of intense gradients that are significantly greater than the mean. This pattern yields stairstep-like instantaneous flow profiles whose shape is distinct from the mean profiles that emerge from long-term averaging. However, the scaling of the stairstep organization is closely related to the resulting mean profiles. The differences in velocity and temperature across the thin gradient layers remain proportional to the surface momentum and heat flux conditions regardless of stratification. The vertical thickness of UMZs and UTZs is proportional to height above the surface for near-neutral and weak stratification, but becomes thinner and less dependent on height as the stability increases. Deviations from the logarithmic mean profiles for velocity and temperature observed under neutral conditions are therefore predominately due to the reduction in eddy size with increasing stratification, which is empirically captured by existing Monin–Obukhov similarity relations for momentum and heat. The zone properties are additionally used to explain trends in the turbulent Prandtl number, thus providing a connection between the eddy organization, mean profiles, and turbulent diffusivity in stably stratified conditions.

Large-eddy-simulation of turbulent buoyant flow and conjugate heat transfer in a cubic cavity with fin ribbed radiators

Turbulent convective flow in a cubic cavity is a fundamental model observed in various processes that appeared in environmental and industrial applications. The turbulent fluctuations in the flow field, fluid-solid interaction/coupling, and the transient nature of the problem make it challenging to establish numerical modeling. The turbulent flow and convective heat transfer in a cubic cavity fixed with three fins are studied here. The numerical solutions are obtained through large-eddy simulation with Smagorinsky subgrid-scale model combined with conjugate heat transfer to incorporate temperature distribution in solid fins. The upper and lower walls of the enclosure are differently heated, while the lateral walls are adiabatic, and equally spaced conductive fins are located at the bottom surface. The solutions are initially compared with the numerical and experimental results for validation purposes. Successively, the model is applied to explore the impact of a material (copper) that makes up the horizontal wall on the flow field. We found that the heat transfer essentially alters the turbulent field, and the flow field becomes less homogeneous along the vertical direction. A number of streaky and coherent turbulent structures are found with varying magnitudes. The Q-criterion, second-invariant of the velocity-gradient tensor, predicted that strong vortices occur near the fins and in the surrounding regions of the cavity. Moreover, the energy (entropy) spectral, which plays a crucial role in engineering applications and turbulent theory, is also presented, showing the contribution of each frequency component to the velocity (temperature) variance at a given point. The velocity and temperature fields are found to be anti-symmetric, except close to the front and back walls. The major cause for this is the conducting bottom and fins, which produces thermal stratification in the cavity. The conducting bottom induces the locally unstable thermal stratification in the vicinity of the wall, which intensifies the turbulence as the flow advances toward the temperature-controlled boundaries. Further, the turbulent exchange in the central region is more responsible for the heat transfer than convection that occurs due to the differentially heated walls.

Large Eddy Simulation of Compound Open Channel Flows with Floodplain Vegetation

Floodplain vegetation is of great importance in velocity distribution and turbulent coherent structure within compound open channel flows. As the large eddy simulation (LES) technique can provide detailed instantaneous flow dynamics and coherent turbulent structure predictions, it is of great importance to perform LES simulations of compound open channel flows with floodplain vegetation. In the present study, a wall-modeled large eddy simulation (WMLES) method was employed to simulate the compound open channel flows with floodplain vegetation. The vegetation-induced resistance effect was modeled with the drag force method. The WMLES model, incorporating the drag force method, was verified against flume measurements and an analytical solution of vegetated open channel flows. Numerical simulations were conducted with a depth ratio of 0.5 and four different floodplain vegetation densities (frk = 0, 0.28 m−1, 1.13 m−1 and 2.26 m−1). The main flow velocity, secondary flow, bed shear stress and vortex coherent structure, based on the Q criterion, were obtained and analyzed. Based on the numerical results, the influences of floodplain vegetation density on the flow field and turbulent structure of compound open channel flows were summarized and discussed. Compared to the case without floodplain vegetation, the streamwise velocity in the main channel increased by 10.8%, 19.9% and 24.4% with the frk = 0.28 m−1, 1.13 m−1 and 2.26 m−1, respectively. The results also indicated that, when the floodplain vegetation density increased, the following occurred: the velocity increased in the main channel, while the velocity decreased in the floodplain; the transverse momentum exchange was enhanced; and the strip structures were more concentrated near the junction area of compound open channel flows.

High-enthalpy effects on turbulent coherent structures over a curved compression corner

Direct numerical simulation (DNS) is performed to study high-enthalpy effects on a turbulent boundary layer (TBL) over a curved compression corner. The post-shock flow state behind a wedge flying at Mach 20 and at an altitude of 30 km are chosen for the present simulation. The post-shock temperature is 3400 K, which is high enough to trigger chemical non-equilibrium of the air. A low-enthalpy case is used for comparison. The influences on the instantaneous structures of the streamwise velocity, temperature, and oxygen atoms are examined. The results show that the flow structures are similar on an upstream flat plate in both cases, while on a ramp, streaks of streamwise velocity fluctuations in the high-enthalpy case experience stronger shrink compared with that in the low-enthalpy case. Furthermore, streaks of temperature break into smaller ones when dissociation reactions are introduced. Qualitative and quantitative comparisons are made with the low-enthalpy case; performed using two-point streamwise wall-normal correlation, space–time correlation, and by comparing the propagation velocities of the fluctuations. The results of these analyses validate the observations about the instantaneous fluctuations and show that the differences in the propagation velocity are affected by convection effects and chemical reactions, and that the dissociation reactions accelerate the propagation of temperature fluctuations.

Large-Scale Coherent Turbulence Structures in the Atmospheric Boundary Layer over Flat Terrain

Abstract We investigate characteristics of large-scale coherent motions in the atmospheric boundary layer using field measurements made with two long-range scanning wind lidars. The joint scans provide quasi-instantaneous wind fields over a domain of ∼50 km2, at two heights above flat but partially forested terrain. Along with the two-dimensional wind fields, two-point statistics and spectra are used to identify and characterize the scales, shape, and anisotropy of coherent structures—as well as their influence on wind field homogeneity. For moderate to high wind speeds in near-neutral conditions, most of the observed structures correspond to narrow streaks of low streamwise momentum near the surface, extending several hundred meters in the streamwise direction; these are associated with positive vertical velocity ejections. For unstable conditions and moderate winds, these structures become large-scale rolls, with longitudinal extent exceeding the measuring domain (>∼5 km); they dominate the conventional surface-layer structures in terms of both physical scale and relative size of velocity-component variances, appearing as quasi-two-dimensional structures throughout the entire boundary layer. The observations shown here are consistent with numerical simulations of atmospheric flows, field observations, and laboratory experiments under similar conditions. Significance Statement Coherent structures have attracted the interest of researchers for decades, being viewed as the closest to “order” that we can find within the chaos of turbulence. In the turbulent atmospheric boundary layer, micro- and mesoscale coherent structures come in many shapes and sizes, such as convective cells, rolls, or streaks. In this study we used dual lidars (remote sensing measurements), developing analysis of their tandem usage to characterize in detail some of the large-scale coherent structures generated over flat terrain. This allowed us to better understand the mechanisms that generate such structures and describe their influence on the morphology of the turbulent atmospheric boundary layer across a good deal of its depth.

Coherent near-wall structures and drag reduction by spanwise forcing

We examine interaction mechanisms between the drag-reducing streamwise-traveling waves of spanwise wall velocity applied at the wall of a turbulent channel flow, and near-wall turbulent coherent structures. In particular, we focus our analysis on the drag-reduction-induced modifications of the quasi-streamwise vortices that populate the near-wall region of turbulent flows through a conditional averaging procedure. We observe that, while the streamwise-traveling waves share most of the drag-reducing mechanisms with the spanwise wall oscillations, some important differences related to the finite phase speed of the wave and the different properties of the generalized Stokes layer exist.

Influence of non-uniform thermal boundary on flow and heat transfer characteristics in rectangular channel

In this paper, the flow behavior and heat transfer characteristic in a rectangular channel are numerically investigated. The non-uniform thermal boundary condition is arranged along the streamwise direction at the bottom of the rectangular channel. Furthermore, based on the flow field parameters obtained with numerical simulation, the dynamic modal decomposition (DMD) is carried out for viscous layer, buffer layer, and logarithmic region, respectively. The numerical results show that the hot bands of non-uniform thermal boundary affect the interaction of the velocity streaks along the streamwise direction, which reduces the vorticity of the buffer layer and the fluctuation of the velocity gradient vector. In the terms of entropy analysis, it can be found that the hot bands of non-uniform thermal boundary play a similar role of “riblets” and block the self-sustainment of the turbulent coherent structures. Moreover, the results of DMD manifest that the hot bands of non-uniform thermal boundary can improve the stability of viscous layer and buffer layer. The development of turbulent boundary layer is delayed by affecting the fluid characteristics in buffer layer. Compared to the channel without non-uniform thermal boundary condition, the maximum drag reduction rate of 8.35% can be achieved in considered cases, while a reduction in heat transfer performance of 2.74% occurs. In addition, the comprehensive performance coefficient increases slightly to 1.0013.

Aspect-ratio dependence of heat and angular momentum transport in turbulent Taylor-Couette flows with axial thermal forcing

• Scaling law of transports determined in finite systems can be extrapolated to large-scale flows. • Coherent turbulent structures in form of Taylor vortices promote heat and angular transports. • Magnitudes of both heat and angular momentum transport depend on domain aspect-ratio. We report numerical studies of the effects of geometry factors, i.e. the aspect ratio Γ and radius ratio η , on the axial heat transport N u and the radial angular momentum transport N ω by turbulent Taylor-Couette flows that are subjected to a vertically destabilizing temperature gradient. For a given Reynolds number R e the magnitudes of both N u and N ω exhibit a pronounced aspect-ratio dependence. The angular momentum transport is reduced in long cylinders, since endwall effects are weakened as Γ increases. For the heat transfer in large- Γ cylinders, a significant N u -reduction appears for low- R e regime, whereas N u can be greatly enhanced in the regime of turbulent Taylor vortex (TV). The former N u -reduction is associated with the process that the thermal plumes are swept away by the Ekman vortices near the boundaries, and the fluid exchange is severely restricted between adjacent vortices in the bulk region. The latter N u -enhancement is attributed to the strengthened shears arising in large- Γ cylinders, resulting in a more turbulent boundary layer. Moreover, the pronounced inter-mixing of turbulent TVs continuously pumps the hot (cold) fluids into the bulk, intensifying the transport processes. It is found that although the constraints from the endwalls impact the global heat and angular momentum transport in the low- R e regime, they hardly affect their scaling properties in the high- R e regime with large Γ . We thus expect that the scaling relationship of N u ( R e ) and N ω ( R e ) determined with finite Γ can be extrapolated to large-scale, and even vertically unbounded industrial and geophysical flows.

Mode vortex and turbulence in ventilated cavitation over hydrofoils

In this paper, the complex interaction of gas-vortex-turbulence in ventilated cavitation over a NACA0015 hydrofoil is investigated by using large eddy simulation. The proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) are used for analyzing the three-dimensional fluctuation modes of gas-liquid interfaces induced by turbulent coherent structures in ventilated cavitation. The results show that among the first four dominant POD modes possessing 99.5% modal kinetic energy in the ventilated cavitating flow, and the turbulent POD mode 2 contains the multi-scale coherent structures and acts as a bridge for the energy scale transition from mode 1 to mode 3 through the gas-liquid interface oscillations. The DMD modal structures are reconstructed from the roller-shaped energetic structure captured by POD mode 2, which further reveal the process of breaking down near the hydrofoil leading edge, changing into the hairpin shape and finally stretching into the horseshoe shape above the hydrofoil trailing edge for the turbulent coherent structures on the cavity interfaces. Such low-frequency wake structures are energetic but sustained by means of the high-frequency turbulent fluctuations, with the interfacial oscillation amplitude changed through the formation and transition of the multi-scale coherent structures. Further, the modal turbulent kinetic energy transport theory is introduced to describe the ventilated coherent structures. It is worth noting that the large-scale energetic structures in POD mode 2 are mainly drawing energy from mean flows through the Reynolds stress, and the modal turbulent energy stored by shedding vortex and air cavities in the ventilated wake flow is redistributed and balanced due to the turbulent and pressure diffusion effects. Besides, the uneven spatial distribution of turbulent energy caused by the vortex structures of different modal scales is proved to promote the spatial oscillation level of the ventilated cavity interfaces. This study is helpful to understand the interaction mechanism between turbulence and gas-liquid interfacial fluctuations for the ventilated wake flow.

The Role of Turbulent Coherent Structures on Microalgal Mixing for Nutrient Removal in Jet and Paddlewheel Raceway Ponds

Outdoor studies were conducted on microalgae cultures in two raceway ponds (kept in constant motion with either jet or paddlewheel) with a flatbed to treat anaerobic digestion piggery effluent and to observe the characteristics of turbulence on microalgal mixing and growth. Acoustic Doppler Velocimeters (ADV) were deployed to record the instantaneous velocity components and acoustic backscatter as a substitution of microalgae concentration. The present research on microalgal mixing considers the effect of event-based turbulent features such as the widely known ‘turbulent bursting’ phenomenon. This is an important aspect, as turbulent coherent structures can result in microalgal mixing, which can lead to significant changes in microalgal growth. The experimental results presented in this paper of two contrasting environments of jet- and paddlewheel-driven ponds suggested that: (1) turbulent bursting events significantly contributed to microalgal mixing when paddlewheels and jets were used; (2) among four type of turbulent bursting events, ejections and sweeps contributed more to the total microalgal mixing; and, (3) a correlation was revealed using wavelet transform between the momentum and microalgal mixing flux when either jet or paddlewheel were used. Such similarities in jet and paddlewheel raceway ponds highlight the need to introduce turbulent coherent structures as an essential parameter for microalgal mixing studies.

The evolution of coherent vortical structures in increasingly turbulent stratified shear layers

We study the morphology of Eulerian vortical structures and their interaction with density interfaces in increasingly turbulent stably stratified shear layers. We analyse the three-dimensional, simultaneous velocity and density fields obtained in the stratified inclined duct laboratory experiment (SID). We track, across 15 datasets, the evolution of coherent structures from pre-turbulent Holmboe waves, through intermittent turbulence, to full turbulence and mixing. We use the rortex–shear decomposition of the local vorticity vectors into a rortex vector capturing rigid-body rotation and a shear vector. We describe the morphology of ubiquitous hairpin-like vortical structures (revealed by the rortex), similar to those commonly observed in boundary-layer turbulence. These are born as relatively weak vortices around the strong three-dimensional shearing structures of confined Holmboe waves, and gradually strengthen and deform under increasing turbulence, transforming into pairs of upward- and downward-pointing hairpins propagating in opposite directions on the top and bottom edge of the shear layer. The pair of legs for each hairpin are counter-rotating and entrain fluid laterally and vertically, whereas their arched-up ‘heads’, which are transverse vortices, entrain fluid vertically. We then elucidate how this large-scale vortex morphology stirs and mixes the density field. Essentially, vortices located at the sharp density interface on either edge of the mixing layer (mostly hairpin heads) engulf blobs of unmixed fluid into the mixing layer, whereas vortices inside the mixing layer (mostly hairpin legs) further stir it, generating strong, small-scale shear, enhancing mixing. These findings provide new insights into the role of turbulent coherent structures in shear-driven stratified mixing.

Objective phase-space identification of coherent turbulent structures in 1D time series data

Turbulent flow has been known to contain coherent flow structures. The size, shape, timescale and dynamics of these coherent structures are important in understanding turbulent flow processes such as pollutant mixing and particle transport. A range of methods exist for the detection of coherent structures in 2D or 3D data, but there are limited objective methods available for 1D data. Existing 1D techniques are subjective, require calibration with manual visualizations, or are based only on detecting velocity extremes and thus only detect structures according to a limited definition. A technique is presented here for objectively detecting structures using a phase-space method modified from a previously described despiking method. This method requires no calibration or subjective input, and identifies structures based on extremes in velocity, acceleration and jerk. This method gives turbulence statistics comparable with previous methods while recognizing a broader and more realistic definition of the physical properties of coherent structures by considering also the first and second derivative of velocity.

Dynamics of particle-laden turbulent Couette flow: Turbulence modulation by inertial particles

In particle-laden turbulent flows, it is established that the turbulence in the carrier fluid phase gets affected by the dispersed particle phase for volume fractions above 10−4. Hence, reverse coupling or two-way coupling becomes relevant in that volume fraction regime. Due to their greater inertia, larger particles change either the mean flow or the intensity of fluid-phase fluctuations. In a recent study [Muramulla et al., “Disruption of turbulence due to particle loading in a dilute gas–particle suspension,” J. Fluid Mech. 889, A28 (2020)], a discontinuous decrease of turbulence intensity is observed in a vertical particle-laden turbulent channel flow for a critical volume fraction O(10−3) for particles with varying Stokes numbers (St) in the range of 1−420 based on the fluid-integral time scales. The collapse of turbulent intensity is found out to be the result of a “catastrophic reduction of turbulent energy production rate.” Mechanistically, a turbulent Couette flow differs from a pressure-driven channel flow in many ways, such as fluid-phase mean-velocity profile and turbulent coherent structures. In the particle-laden Couette flow, particles are treated as neutrally buoyant. Therefore, it is worth investigating the mechanism of turbulence modulation by inertial particles in the particle-laden turbulent Couette flow. In this article, the turbulence modulation in the fluid phase in the presence of inertial particles is investigated using two-way coupled direct numerical simulations of a particle-laden sheared turbulent suspension. The particle volume fraction (ϕ) is varied from 1.75×10−4 to 1.05×10−3 and the Reynolds number based on the half-channel width (δ) and the wall velocity (U) (Reδ) is 750. The particles are of high inertia with St∼367 based on a fluid integral timescale represented by δ/U. A discontinuous decrease in turbulence intensity and Reynolds stress is observed beyond a critical volume fraction ϕcr∼7.875×10−4. The drastic reduction of shear production of turbulence leads to the collapse of fluid-phase turbulence. The stepwise particle injection and stepwise removal study confirm the role of critical volume loading in the discontinuous transition. Additionally, the effect of the nature of particle–particle and particle–wall collisions has been investigated. It is observed that the inelastic collisions increase the ϕcr marginally although the nature of turbulence modulation remains similar. The explicit role of the inter-particle collisions has also been investigated by switching off the particle–particle collisions. In this case, ϕcr increases more than in the case of an inelastic collision. The turbulence modulation carries the signatures of transition from sheared turbulence to particle-driven fluid fluctuation at higher volume loading.

Application of Hausdorff fractal derivative to the determination of the vertical sediment concentration distribution

The Rouse formula and its variants have been widely used to calculate the steady-state vertical concentration distribution for suspended sediment in steady sediment-laden flows, where the diffusive flux is assumed to be Fickian. Turbulent flow, however, exhibits fractal properties, leading to non-Fickian diffusive flux for sediment particles. To characterize non-Fickian dynamics of suspended sediment, the current study proposes a Hausdorff fractal derivative based advection-dispersion equation (HADE) model, where the Fickian diffusive flux in the Rouse model is replaced by a fractal derivative re-scaled using a constant diffusivity. The order of the Hausdorff fractal derivative is designed to characterize the influence of the multi-fractal turbulence structure on sediment diffusion. Applications show that the HADE model, with the analytical solution expressed using a stretched exponential function, can accurately describe the observed vertical concentration profiles for suspended sediment with different sizes. This improvement well captures the non-exponential decay of the vertical sediment concentration in turbulent flow. Further analyses of measured sediment concentration profiles reveal that the Hausdorff fractal order decreases with the Rouse parameter, which describes the stronger impact of turbulent flow and a more uniform sediment concentration profile for smaller particles. Model comparisons also show that the HADE model provides better performance in describing the sediment concentration profiles than the improved Rouse formula and the standard fractional derivative advection-dispersion equation (FADE), which either under- or over-estimates vertical displacement of sediment particles, likely due to coherent turbulent structures.

Performance study of spiral finned tubes on heat transfer and wake flow structure

Heat exchangers have been widely utilised in many industrial and residential sectors. In this paper, the turbulent flow of a heat exchanger with spiral finned tubes (SFT) is numerically simulated using a large eddy simulation (LES), which outperforms existing two-equation solvers in finding the details of flow structure around bluff bodies. This work aims to find the coherent structures around spiral fins using the Q-criteria and to obtain flow topologies playing an important role to improve the heat transfer of spiral finned tubes. The SFT shows three primary flow regions representing various vortex structures. The study also observes how turbulent flow changes with different Reynolds numbers and how turbulent coherent structure changes with varying Nu numbers on the fin surface. The result shows that the correlation coefficient reaches 0.81 by examining the correlation of the Nu number and the Q values over the time series at each sampling point. In addition, the modal information of temperature variation is estimated using dynamic mode decomposition analysis. The dynamic mode of temperature shows highly consistent with the Q criterion distribution.

First coherent structure in elasto-inertial turbulence

Two dimensional channel flow simulations of FENE-P fluid in the elasto-inertial turbulence regime reveal distinct regimes ranging from chaos to a steady travelling wave which takes the form of an arrowhead structure. This coherent structure provides new insights in the polymer/flow interactions driving EIT, which are observed in a set of controlled numerical experiments and the study of transfer between elastic and turbulent kinetic energy.

Flow Field around a Vertical Cylinder in Presence of Long Waves: An Experimental Study

Long waves caused by storm surges or river floods can significantly impact marine and fluvial structures such as bridge piers. Apart from the forces that they generate on the structure, they also contribute to the formation of turbulent eddies downstream of the obstacle. This is relevant, as in this way they can affect both an erodible bottom and the ecosystem. The present study describes a medium-scale experiment, in which the propagation of two different long waves released on a steady current is investigated in the presence of a bottom-mounted rigid emergent cylinder. Velocity measurements were acquired by a Particle Image Velocimetry (PIV) system, providing instantaneous flow velocity vectors on selected 2D planes. For each experimental condition, the time-varying velocity field near the cylinder was examined in selected vertical and horizontal planes. First, we tested which analytical theory or approximated method can best represent the experimental waves. After this, we estimated the horizontal maps of velocity and vorticity downstream of the obstacle and finally processed the velocity signals by means of a wavelet-based technique, to derive the length scales of turbulent eddies. In such a way, we specifically derived how the spreading of coherent turbulent structures downstream of the cylinder depends on the features of the flume, cylinder, and wave.

Large-eddy simulation of supercritical free-surface flow in an open-channel contraction

Large-eddy simulations (LES) of supercritical flow in a straight-wall, open-channel contraction of 6° and contraction ratio of 2:1 are performed. The LES code solves the filtered Navier-Stokes equations for two-phase flows (water-air) and employs the level-set method. The simulation was validated by replicating a previously reported experiment. Contours of the time-averaged velocities indicate that the flow loses energy and momentum in the contracting channel. Further, secondary currents in the contraction are redistributing momentum and are responsible for local up-and down-flows. The turbulent kinetic energy reaches very high values at the entrance of the contraction, mainly contributed by the streamwise normal stress. The flow contains coherent turbulence structures which are responsible for carrying low-momentum from the bed and the water surface towards the channel centre. Flow deceleration results in significant turbulence anisotropy in the contracted section. It is shown that mainly pressure drag contributes to the energy loss in the contraction.

Study on the Characteristics of Boundary Layer Flow under the Influence of Surface Microstructure

The energy consumption of a vehicle is closely related to the resistance it receives, and it is of great significance to study the drag reduction of a vehicle to promote energy conservation and emissions reductions. Boundary layer control drag reduction is mainly achieved by controlling the coherent structure in turbulence and reducing its burst intensity and frequency. It can be divided into an active control drag reduction and passive control drag reduction. In passive drag reduction, the advantages of the surface groove drag reduction are relatively obvious. In this paper, the large eddy simulation method is used to study the boundary layer flow with triangular groove and rectangular groove plates along the flow direction under subsonic flow, and to explore the influence of a surface micro-groove structure on the boundary layer flow. The simulation results show that the fluid inside the groove can be blocked by the triangular groove which can keep the low-velocity fluid at the bottom of the groove, and that it can increase the thickness of the viscous bottom layer as well as reduce the velocity gradient at the wall. The spanwise stress component of the Reynolds stress in the triangular groove boundary layer and the burst of turbulence on the wall are inhibited, and the spanwise flow in the boundary layer is blocked. In the subsonic range, about 10% shear force can be reduced because there are secondary vortices induced by the upper flow vortices at the top of the groove wall, and these secondary vortices can restrain the rising of the low-speed strip in the groove and reduce the burst of turbulence. The rectangular groove creates a weak blocking effect on the fluid inside the groove, which can only inhibit spanwise pulsation under subsonic speed. The wall shear stress cannot be reduced when the flow velocity is low, and it even increases.