Insects usually fly by passively rotating wings,which has been applied to the design of flapping-wing Micro-Air Vehicles(MAVs)to reduce mechanical complexity.In this paper,a robotic passive rotating-wing model is desi...Insects usually fly by passively rotating wings,which has been applied to the design of flapping-wing Micro-Air Vehicles(MAVs)to reduce mechanical complexity.In this paper,a robotic passive rotating-wing model is designed to investigate wing kinematics and lift generation,which are measured by a high-speed camera and a force transducer,respectively.In addition,flow fields are measured using the Particle Image Velocimetry(PIV).Experimental results demonstrate that passive rotating motion has a coordinative relationship with actively stroking motion.As the stroke amplitude or frequency increases,the rotating amplitude is enlarged.To characterize the active stroking motion,a driving Reynolds number Redrivingis defined,which varies from 68 to 366 in this study.Moving the gravity center of the wing towards trailing ed ge induces the increase of additional torque M,which decreases the wing rotating amplitude and promotes the advance of wing rotation.We find that the timing of wing rotation is gradually delayed and the mean lift coefficient C^(-)_(L)monotonously decreases as Redrivingincreases.By increasing the additional torque M,C^(-)_(L)is slightly improved and approaches to the lift coefficient of a real fruit fly at driving Re approximately equal to 230.The instantaneous lifts combined with the vortical structures further demonstrate that the lift generation associated with wing rotation is mainly attributed to the growth of the LeadingEdge Vortex(LEV)and the passive wake capture mechanism.Passive wake capture is influenced by LEV,reversal stroke motion and wing additional torque together,which can only maintain the lift at a high level for a considerable period.The high-lift generation mechanisms of flapping and passive rotating flight could shed light on the simplified design of MAVs and the improvement of their aerodynamic performance.展开更多
The flow dynamics is analyzed through two-dimensional numerical simulations around two circular cylinders arranged side by side, with 4 combinations of alternating motions. All simulations are performed for Re = 1000,...The flow dynamics is analyzed through two-dimensional numerical simulations around two circular cylinders arranged side by side, with 4 combinations of alternating motions. All simulations are performed for Re = 1000, amplitude of oscillation (A) equal to 3, frequency ratio (f<sub>r</sub>) of 0.5, specific rotation (α) equal to 0.5 and different values of spacing ratio (L/D). It is verified that the combination of the type of movement, together with the position of one cylinder in relation to the other, exerts significant influence on the flow dynamics, as well as on the pressure distribution around the cylinder surface and on the average values of the fluid dynamics coefficients. The smallest value of the average pressure coefficient (C<sub>p</sub> = -3.3), is obtained for the oscillating cylinder when placed side by side with the clockwise rotation cylinder, case 3 and L/D = 1.5. On the other hand, the lowest mean drag coefficient (C<sub>d</sub> = 1.0788), is obtained for the cylinder with counterclockwise rotation, located in the lower position in relation to oscillating cylinder in the upper position, with spacing between them of 1.5. Furthermore, it is observed that the rotation movement is more effective in reducing drag than the rotation-oscillation movement, for the studied frequency ratio.展开更多
Wellbore cleaning is a key technology for the Extended Reach Drilling （ERD）. The success of drilling extended reach wells depends directly upon the quality of wellbore cleaning. The rotation of the drillpipe, and hy...Wellbore cleaning is a key technology for the Extended Reach Drilling （ERD）. The success of drilling extended reach wells depends directly upon the quality of wellbore cleaning. The rotation of the drillpipe, and hydraulic and rheological parameters, are the key factors for wellbore cleaning. In this study, Computational Fluid Dynamics （CFD） is applied to simulate solid-liquid two-phase flows in wellbore annulus. The annual flow field with the presence of drillpipe rotation is described through analyzing various rotation conditions. The results indicate that the quasi-spiral flow is the main flow pattern for liquid-solid transport in the horizontal annulus. The influence of rotation on the cuttings transport is also investigated, as the rotation of drillpipe increases the disturbance of liquid to solid in annulus. As a result, the solid flow becomes favorable and the solid volume is reduced. Comparisons with previously published results are also performed to prove the importance of drillpipe rotation in the wellbore clearing for the ERD.展开更多
The Rotation and Curvature(RC)correction is an important turbulence model modifi-cation approach,and the Spalart-Allmaras model with the RC correction(SA-RC)has been exten-sively studied and used.As a multiplier of th...The Rotation and Curvature(RC)correction is an important turbulence model modifi-cation approach,and the Spalart-Allmaras model with the RC correction(SA-RC)has been exten-sively studied and used.As a multiplier of the modelling equation’s production term,the rotation function f_(r1)should have a cautiously designed value range,but its limit varies in different models and flow solvers.Therefore,the need of restriction is discussed theoretically,and the common range of f_(r1)is explored in Burgers vortexes.Afterwards,the SA-RC model with different limits is tested numerically.Negative f_(r1)always appears in the SA-RC model,and the difference between simula-tion results brought by the limits is not negligible.A lower limit of 0 enhances turbulence produc-tion,and therefore the vortex structures are dissipated faster and shrink in size,while an upper limit plays an opposite role.Considering that the lower limit of 0 usually promotes the simulation accu-racy and fixes the numerical defect,whereas the upper limit worsens the predictive performance in most cases,it is recommended to limit f_(r1)non-negative while utilizing the SA-RC model.In addi-tion,the RC-corrected model has a better prediction of the attached flow near curved walls,while the SA-Helicity model largely improves the simulation accuracy of three-dimensional large-scale vortices.The model combining both corrections has the potential to become more adaptive and more accurate.展开更多
To study the influence of an elbow inlet on the rotating stall characteristics of a waterjet propulsion pump(WJPP),a three-dimensional internal flow field in a WJPP under a straight-pipe inlet and elbow inlet is numer...To study the influence of an elbow inlet on the rotating stall characteristics of a waterjet propulsion pump(WJPP),a three-dimensional internal flow field in a WJPP under a straight-pipe inlet and elbow inlet is numerically simulated.By comparing the hydraulic performance of WJPP under the two inlet conditions,the internal relationship between the inlet mode and the flow pattern in the pump is clarified.Based on unsteady pressure fluctuation characteristics and wavelet analysis,the influence of the inlet mode on the rotating stall is revealed,and the stall transient propagation characteristics under critical stall conditions are analyzed.The disturbance effects of the inlet channel geometry disappear under low flow rate conditions,the main disturbance is induced by the highspeed countercurrent,and the flow pattern under the elbow inlet is better than that under the straight-pipe inlet.Under the straight-pipe inlet,the single-stall nucleus in the WJPP temporarily experiences a low-frequency and high-amplitude disturbance,which subsequently transforms into a mode of multi-stall nuclei with high-frequency circumferential disturbance.Under the elbow inlet,the rotating stall always maintains a mode of high-amplitude and low-frequency disturbance,which represents the transient characteristics of a single stall core propagating in the circumferential direction inside the channel.The results of this study have a reference value for structural design optimization in a WJPP.展开更多
With the development of aero-engines, the turbine inlet temperature continues to rise. In order to ensure the safety and reliability of the turbine blades, cooling structures must be set inside turbine blades to cool ...With the development of aero-engines, the turbine inlet temperature continues to rise. In order to ensure the safety and reliability of the turbine blades, cooling structures must be set inside turbine blades to cool them. Heat transfer coefficient and flow resistance are the key parameters to measure the cooling characteristics of internal cooling structures. In this paper, the characteristics of flow resistance in a rotating ribbed channel is presented numerical simulation under different rib spacings, rib angles, and thermal boundary conditions. The results show that, separation and reattachment of fluid between ribs is the key effect of rib spacing on flow resistance. The flow resistance is small when the rib spacing is small, because it's difficult for the fluid to form reattachment between the ribs. With the increase of rib spacing, the reattachment phenomenon is more obvious and the flow resistance increases accordingly. In general,p: e=10 channel has the maximum flow resistance. Secondary flow caused by the ribs is the key factor affecting the flow resistance characteristics with different rib angles. The secondary flow interacts with the main flow and causes flow loss through mixing, thus affecting the flow resistance of the channel. Under static condition, the flow resistance of 60°ribbed channel is the largest. The flow resistance of channel was affected by the temperature rise ratio also. And with the increase of the Ro, the temperature rise ratio has a more obvious effect on the flow resistance of the ribbed channel.When Ro=0.45, the flow resistance of the channel with a temperature rise ratio of 0.4 is 2.4 times that of the channel without temperature rise, while when Ro=0.3, it is 1.6 times, and when Ro=0.15, it is 1.2 times.展开更多
This work is devoted to the experimental study of inertial wave regimes in a non-uniform rotating cylinder with antiparallel inclined ends.In this setting,the cross-section of the cylinder is divided into two regions ...This work is devoted to the experimental study of inertial wave regimes in a non-uniform rotating cylinder with antiparallel inclined ends.In this setting,the cross-section of the cylinder is divided into two regions where the fluid depth increases or decreases with radius.Three different regimes are found:inertial wave attractor,global oscillations(the cavity’s resonant modes)and regime of symmetric reflection of wave beams.In linear wave regimes,a steady single vortex elongated along the rotation axis is generated.The location of the wave’s interaction with the sloping ends determines the vortex position and the vorticity sign.In non-linear regimes several pairs of the triadic resonance subharmonics are detected simultaneously.The instability of triadic resonance is accompanied by the periodic generation of mean vortices drifting in the azimuthal direction.Moreover,the appearance frequency of the vortices is consistent with the low-frequency subharmonic of the triadic resonance.The experimental results shed light on the mechanisms of the inertial wave interaction with zonal flow and may be useful for the development of new methods of mixing.展开更多
In gas injection refining processes,wide dispersion of small bubbles in the bath is indispensable for high refining efficiency.Eccentric mechanical stirring with unidirectional impeller rotation was tested using a wat...In gas injection refining processes,wide dispersion of small bubbles in the bath is indispensable for high refining efficiency.Eccentric mechanical stirring with unidirectional impeller rotation was tested using a water model for pursuing better bubble disintegration and dispersion.Effects of various factors on bubble disintegration and dispersion were investigated.These factors were stirring mode,eccentricity and rotation speed,nozzle structure,nozzle immersion depth,and gas flow rate.Gas injection from a nozzle at the end of the impeller shaft and from an immersed lance was studied.Under eccentric stirring,a vortex was formed away from the shaft.Small bubbles were produced in the strong turbulence or high shear stress field near the rotating impeller and moved in the direction to the vortex keeping up with the macroscopic flow induced by the mechanical stirring.Thus small bubbles could disperse widely in the bath under eccentric stirring with unidirectional rotation.展开更多
Non-spherical particles exist widely in natural and industrial fluid systems and the motions of nonspherical particles are significantly different from that of spherical particles.In this paper,a simplified model of n...Non-spherical particles exist widely in natural and industrial fluid systems and the motions of nonspherical particles are significantly different from that of spherical particles.In this paper,a simplified model of non-spherical particles considering particle drag correction,lift,and rotation was established.Based on the Eulerian-Lagrangian simulation,the dispersion characteristics of spherical and nonspherical particles with different Stokes numbers in a high-speed turbulent jet were analyzed and compared considering the effect of particle rotation.The results show that,the differences in particle dispersion and radial velocity fluctuation between non-spherical particles and spherical particles in the jet are significant,especially when Stokes number is large.Moreover,the effects of different type of forces on the dispersion of non-spherical particles and spherical particles were compared in detail,which revealed that the change of the Magnus force caused by the increase in the angular velocity of non-spherical particles plays a dominant role in the differences of particle dispersion.展开更多
The instability of forced flow in a rotating cylindrical pool with a differentially rotating disk on the free surface is investigated through a series of unsteady three-dimensional numerical simulations.The results sh...The instability of forced flow in a rotating cylindrical pool with a differentially rotating disk on the free surface is investigated through a series of unsteady three-dimensional numerical simulations.The results show that the basic flow state of this system is axisymmetric and steady,but has rich structures at the meridian plane.However,when the rotation Reynolds number exceeds a critical value,the flow will undergo a transition to three-dimensional oscillatory flow,characterized by the velocity fluctuation waves traveling in the azimuthal direction.The main characteristics of the flow patterns are presented,including the propagating direction,velocity,amplitude and wave number,which depend on the rotation rates and directions of the disk and the cylindrical pool,and the critical conditions for the onset of oscillatory flow are also determined.For the case of disk-only rotation,the centrifugal instability is responsible for the flow transition,and when the disk isoand counter-rotates with the cylindrical pool,the mechanisms for the transition are elliptic and of circular shear instabilities,respectively.展开更多
基金supported by the National Nature Science Foundation of China(Nos.12102259,12202273)the China Postdoctoral Science Foundation(No.2018M642007)。
文摘Insects usually fly by passively rotating wings,which has been applied to the design of flapping-wing Micro-Air Vehicles(MAVs)to reduce mechanical complexity.In this paper,a robotic passive rotating-wing model is designed to investigate wing kinematics and lift generation,which are measured by a high-speed camera and a force transducer,respectively.In addition,flow fields are measured using the Particle Image Velocimetry(PIV).Experimental results demonstrate that passive rotating motion has a coordinative relationship with actively stroking motion.As the stroke amplitude or frequency increases,the rotating amplitude is enlarged.To characterize the active stroking motion,a driving Reynolds number Redrivingis defined,which varies from 68 to 366 in this study.Moving the gravity center of the wing towards trailing ed ge induces the increase of additional torque M,which decreases the wing rotating amplitude and promotes the advance of wing rotation.We find that the timing of wing rotation is gradually delayed and the mean lift coefficient C^(-)_(L)monotonously decreases as Redrivingincreases.By increasing the additional torque M,C^(-)_(L)is slightly improved and approaches to the lift coefficient of a real fruit fly at driving Re approximately equal to 230.The instantaneous lifts combined with the vortical structures further demonstrate that the lift generation associated with wing rotation is mainly attributed to the growth of the LeadingEdge Vortex(LEV)and the passive wake capture mechanism.Passive wake capture is influenced by LEV,reversal stroke motion and wing additional torque together,which can only maintain the lift at a high level for a considerable period.The high-lift generation mechanisms of flapping and passive rotating flight could shed light on the simplified design of MAVs and the improvement of their aerodynamic performance.
文摘The flow dynamics is analyzed through two-dimensional numerical simulations around two circular cylinders arranged side by side, with 4 combinations of alternating motions. All simulations are performed for Re = 1000, amplitude of oscillation (A) equal to 3, frequency ratio (f<sub>r</sub>) of 0.5, specific rotation (α) equal to 0.5 and different values of spacing ratio (L/D). It is verified that the combination of the type of movement, together with the position of one cylinder in relation to the other, exerts significant influence on the flow dynamics, as well as on the pressure distribution around the cylinder surface and on the average values of the fluid dynamics coefficients. The smallest value of the average pressure coefficient (C<sub>p</sub> = -3.3), is obtained for the oscillating cylinder when placed side by side with the clockwise rotation cylinder, case 3 and L/D = 1.5. On the other hand, the lowest mean drag coefficient (C<sub>d</sub> = 1.0788), is obtained for the cylinder with counterclockwise rotation, located in the lower position in relation to oscillating cylinder in the upper position, with spacing between them of 1.5. Furthermore, it is observed that the rotation movement is more effective in reducing drag than the rotation-oscillation movement, for the studied frequency ratio.
基金supported by the Program for Innovative Research Team in University, Ministry of Education (Grant No. IRT0411)the project of CNOOC Research (Grant No. 2008ZX0 5056-02-03-06)
文摘Wellbore cleaning is a key technology for the Extended Reach Drilling （ERD）. The success of drilling extended reach wells depends directly upon the quality of wellbore cleaning. The rotation of the drillpipe, and hydraulic and rheological parameters, are the key factors for wellbore cleaning. In this study, Computational Fluid Dynamics （CFD） is applied to simulate solid-liquid two-phase flows in wellbore annulus. The annual flow field with the presence of drillpipe rotation is described through analyzing various rotation conditions. The results indicate that the quasi-spiral flow is the main flow pattern for liquid-solid transport in the horizontal annulus. The influence of rotation on the cuttings transport is also investigated, as the rotation of drillpipe increases the disturbance of liquid to solid in annulus. As a result, the solid flow becomes favorable and the solid volume is reduced. Comparisons with previously published results are also performed to prove the importance of drillpipe rotation in the wellbore clearing for the ERD.
基金supported by the National Natural Science Foundation of China(Nos.51976006,51790513)the Aeronautical Science Foundation of China(No.2018ZB51013)+1 种基金the National Science and Technology Major Project,China(2017-II-003-0015)the Open Fund from State Key Laboratory of Aerodynamics,China(No.SKLA2019A0101).
文摘The Rotation and Curvature(RC)correction is an important turbulence model modifi-cation approach,and the Spalart-Allmaras model with the RC correction(SA-RC)has been exten-sively studied and used.As a multiplier of the modelling equation’s production term,the rotation function f_(r1)should have a cautiously designed value range,but its limit varies in different models and flow solvers.Therefore,the need of restriction is discussed theoretically,and the common range of f_(r1)is explored in Burgers vortexes.Afterwards,the SA-RC model with different limits is tested numerically.Negative f_(r1)always appears in the SA-RC model,and the difference between simula-tion results brought by the limits is not negligible.A lower limit of 0 enhances turbulence produc-tion,and therefore the vortex structures are dissipated faster and shrink in size,while an upper limit plays an opposite role.Considering that the lower limit of 0 usually promotes the simulation accu-racy and fixes the numerical defect,whereas the upper limit worsens the predictive performance in most cases,it is recommended to limit f_(r1)non-negative while utilizing the SA-RC model.In addi-tion,the RC-corrected model has a better prediction of the attached flow near curved walls,while the SA-Helicity model largely improves the simulation accuracy of three-dimensional large-scale vortices.The model combining both corrections has the potential to become more adaptive and more accurate.
基金the Key International Cooperative research of National Natural Science Foundation of China(52120105010)National Natural Science Foundation of China(52179085)+1 种基金the National Key R&D Program Project(2020YFC1512405)the Fifth“333 High-Level Talented Person Cultivating Project"of Jiangsu Province,and Funded projects of“Blue Project”in Jiangsu Colleges and Universities.
文摘To study the influence of an elbow inlet on the rotating stall characteristics of a waterjet propulsion pump(WJPP),a three-dimensional internal flow field in a WJPP under a straight-pipe inlet and elbow inlet is numerically simulated.By comparing the hydraulic performance of WJPP under the two inlet conditions,the internal relationship between the inlet mode and the flow pattern in the pump is clarified.Based on unsteady pressure fluctuation characteristics and wavelet analysis,the influence of the inlet mode on the rotating stall is revealed,and the stall transient propagation characteristics under critical stall conditions are analyzed.The disturbance effects of the inlet channel geometry disappear under low flow rate conditions,the main disturbance is induced by the highspeed countercurrent,and the flow pattern under the elbow inlet is better than that under the straight-pipe inlet.Under the straight-pipe inlet,the single-stall nucleus in the WJPP temporarily experiences a low-frequency and high-amplitude disturbance,which subsequently transforms into a mode of multi-stall nuclei with high-frequency circumferential disturbance.Under the elbow inlet,the rotating stall always maintains a mode of high-amplitude and low-frequency disturbance,which represents the transient characteristics of a single stall core propagating in the circumferential direction inside the channel.The results of this study have a reference value for structural design optimization in a WJPP.
基金Beijing Nova Program (No. 20220484129)National Natural Science Foundation of China (No.52376042)+1 种基金Advanced Aerodynamic Innovation Workstation (Grant No. HKCX2022-01-07)National Science and Technology Major Project (Grant No. J2019-II-0022-0043)。
文摘With the development of aero-engines, the turbine inlet temperature continues to rise. In order to ensure the safety and reliability of the turbine blades, cooling structures must be set inside turbine blades to cool them. Heat transfer coefficient and flow resistance are the key parameters to measure the cooling characteristics of internal cooling structures. In this paper, the characteristics of flow resistance in a rotating ribbed channel is presented numerical simulation under different rib spacings, rib angles, and thermal boundary conditions. The results show that, separation and reattachment of fluid between ribs is the key effect of rib spacing on flow resistance. The flow resistance is small when the rib spacing is small, because it's difficult for the fluid to form reattachment between the ribs. With the increase of rib spacing, the reattachment phenomenon is more obvious and the flow resistance increases accordingly. In general,p: e=10 channel has the maximum flow resistance. Secondary flow caused by the ribs is the key factor affecting the flow resistance characteristics with different rib angles. The secondary flow interacts with the main flow and causes flow loss through mixing, thus affecting the flow resistance of the channel. Under static condition, the flow resistance of 60°ribbed channel is the largest. The flow resistance of channel was affected by the temperature rise ratio also. And with the increase of the Ro, the temperature rise ratio has a more obvious effect on the flow resistance of the ribbed channel.When Ro=0.45, the flow resistance of the channel with a temperature rise ratio of 0.4 is 2.4 times that of the channel without temperature rise, while when Ro=0.3, it is 1.6 times, and when Ro=0.15, it is 1.2 times.
基金supported by the Ministry of Education of the Russian Federation(Project KPZU-2023-0002).
文摘This work is devoted to the experimental study of inertial wave regimes in a non-uniform rotating cylinder with antiparallel inclined ends.In this setting,the cross-section of the cylinder is divided into two regions where the fluid depth increases or decreases with radius.Three different regimes are found:inertial wave attractor,global oscillations(the cavity’s resonant modes)and regime of symmetric reflection of wave beams.In linear wave regimes,a steady single vortex elongated along the rotation axis is generated.The location of the wave’s interaction with the sloping ends determines the vortex position and the vorticity sign.In non-linear regimes several pairs of the triadic resonance subharmonics are detected simultaneously.The instability of triadic resonance is accompanied by the periodic generation of mean vortices drifting in the azimuthal direction.Moreover,the appearance frequency of the vortices is consistent with the low-frequency subharmonic of the triadic resonance.The experimental results shed light on the mechanisms of the inertial wave interaction with zonal flow and may be useful for the development of new methods of mixing.
基金Projects (50974035,51074047) supported by the National Natural Science Foundation of ChinaProject (20090407) supported by the Doctoral Fund of Ministry of Education,ChinaProject (200921007) supported by Liaoning Key Science and Technology,China
文摘In gas injection refining processes,wide dispersion of small bubbles in the bath is indispensable for high refining efficiency.Eccentric mechanical stirring with unidirectional impeller rotation was tested using a water model for pursuing better bubble disintegration and dispersion.Effects of various factors on bubble disintegration and dispersion were investigated.These factors were stirring mode,eccentricity and rotation speed,nozzle structure,nozzle immersion depth,and gas flow rate.Gas injection from a nozzle at the end of the impeller shaft and from an immersed lance was studied.Under eccentric stirring,a vortex was formed away from the shaft.Small bubbles were produced in the strong turbulence or high shear stress field near the rotating impeller and moved in the direction to the vortex keeping up with the macroscopic flow induced by the mechanical stirring.Thus small bubbles could disperse widely in the bath under eccentric stirring with unidirectional rotation.
基金supported by National Science and Technology Major Project of China(2019-I-0022-0021)Seed fund of Shanxi Research Institute for Clean Energy,Tsinghua Universitythe National Natural Science Foundation of China(51761125011)。
文摘Non-spherical particles exist widely in natural and industrial fluid systems and the motions of nonspherical particles are significantly different from that of spherical particles.In this paper,a simplified model of non-spherical particles considering particle drag correction,lift,and rotation was established.Based on the Eulerian-Lagrangian simulation,the dispersion characteristics of spherical and nonspherical particles with different Stokes numbers in a high-speed turbulent jet were analyzed and compared considering the effect of particle rotation.The results show that,the differences in particle dispersion and radial velocity fluctuation between non-spherical particles and spherical particles in the jet are significant,especially when Stokes number is large.Moreover,the effects of different type of forces on the dispersion of non-spherical particles and spherical particles were compared in detail,which revealed that the change of the Magnus force caused by the increase in the angular velocity of non-spherical particles plays a dominant role in the differences of particle dispersion.
基金supported by the National Natural Science Foundation of China (Grant No. 50776102)
文摘The instability of forced flow in a rotating cylindrical pool with a differentially rotating disk on the free surface is investigated through a series of unsteady three-dimensional numerical simulations.The results show that the basic flow state of this system is axisymmetric and steady,but has rich structures at the meridian plane.However,when the rotation Reynolds number exceeds a critical value,the flow will undergo a transition to three-dimensional oscillatory flow,characterized by the velocity fluctuation waves traveling in the azimuthal direction.The main characteristics of the flow patterns are presented,including the propagating direction,velocity,amplitude and wave number,which depend on the rotation rates and directions of the disk and the cylindrical pool,and the critical conditions for the onset of oscillatory flow are also determined.For the case of disk-only rotation,the centrifugal instability is responsible for the flow transition,and when the disk isoand counter-rotates with the cylindrical pool,the mechanisms for the transition are elliptic and of circular shear instabilities,respectively.
