Vortex Circulation Research Articles

A New Closure Assumption and Formulation Based on the Helmholtz Decomposition for Improving Retrievals for Vortex Circulations from Single-Doppler Radar Observations

Abstract Doppler weather radars are powerful tools for investigating the inner-core structure and intensity of tropical cyclones (TCs). The Doppler velocity can provide quantitative information on the vortex structure in the TCs. The generalized velocity track display (GVTD) technique has been used to retrieve the axisymmetric circulations and asymmetric tangential flows in the TCs from ground-based single-Doppler radar observations. GVTD can have limited applicability to asymmetric vortices due to the closure assumption of no asymmetric radial flows. The present study proposes a new closure formulation that includes asymmetric radial flows, based on the Helmholtz decomposition. Here it is assumed that the horizontal flow is predominantly rotational and expressed with a streamfunction, but limited inclusion of wavenumber-1 divergence is available. Unlike the original GVTD, the decomposition introduces consistency along the radius by solving all equations simultaneously. The new approach, named GVTD-X, is applied to analytical vortices and a real TC with asymmetric structures. This approach makes the retrieval of axisymmetric flow relatively insensitive to the contamination from asymmetric flows and to small errors in storm center location. For an analytical vortex with a wavenumber-2 asymmetry, the maximum relative error of the axisymmetric tangential wind retrieved by GVTD-X is less than 2% at the radius of the maximum wind speed. In practical applications, errors can be evaluated by comparing results for different maximum wavenumbers. When applied to a real TC, GVTD-X largely suppressed an artificial periodic fluctuation that occurs in GVTD from the aliasing of the neglected asymmetric radial flows. Significance Statement In tropical cyclone (TC) wind retrievals from single-Doppler weather radar observations, closure assumptions are required for the retrieval equations. The present study proposes a new closure allowing asymmetric radial winds and improving retrievals for TC winds in the previously developed technique. The relative error of the axisymmetric tangential wind in idealized vortices from the new approach is less than 2% at the radius of the maximum wind speed. In applying to a real TC with an elliptical eyewall, we found that the new approach can largely suppress an artificial evolution of the tangential winds in the previous retrieval technique.

Modulation of tropical cyclone rapid intensification by mesoscale asymmetries

AbstractComputer model simulations are one of the most important tools in current use for understanding tropical cyclone (TC) formation and rapid intensification (RI). These include “idealized” simulations in which a TC‐like vortex is placed in a hypothetical environment with predefined sea surface temperature and vertical profiles of temperature, humidity, and wind that are either constant or slowly varying across a large domain. The vast majority of such simulations begin with a perfectly circular vortex as the precursor to a TC. However, most real TCs form or intensify while interacting with asymmetric wind fields either within or external to the vortex circulation. This study introduces a method to initialize idealized TC simulations with asymmetries, and investigates the extent to which such asymmetries might delay RI in favorable environments. It is shown that mesoscale asymmetries can delay RI and reduce the fastest rates of intensification, and that these effects are statistically significantly increased when relatively low values of vertical shear of the horizontal wind are present. In some cases the asymmetries tilt the vortex directly through advection. In other cases, the wind asymmetries increase the disorganization of the convection or increase the size of the inner‐core wind field, and thus make the weaker TC more susceptible to environmental wind shear. The results suggest that mesoscale asymmetries of the wind field could be useful predictors for delay of RI in otherwise favorable environments.

Analysis of Rotor Tip Vortex Circulation in the Near Field

Analysis of Rotor Tip Vortex Circulation in the Near Field

Prediction method of tip vortex circulation based on hydrofoil load

In this paper, a theoretical derivation from the perspective of the force on the slender bodies arranged along the hydrofoil span is performed to explain why the vortex circulation Γvortex should theoretically be equal to the maximum bound circulation Γ0 around the hydrofoil. Then, a more accurate and operable prediction formulation based on hydrofoil load, Γvortex=kΓ0‾, is proposed, where k = 0.9–1. Γ0‾ is the averaged hydrofoil circulation along spanwise direction and its value can be obtained easily from hydrofoil load. To validate our new formulation, two typical vortex flows, i.e., tip leakage vortex (TLV) flow and tip vortex (TV) flow, are simulated with large eddy method. Our numerical results confirm that the variations of hydrofoil load along span would lead to streamwise vorticity, and then the rolling-up of latter leads to the vortex formation (Green, 1995). However, since the influential region of vortex is limited that not all streamwise vorticity could be entrained into the vortex and there are viscous and dissipation effects, the actual Γvortex cannot reach Γ0 but it is quite close to Γ0‾. The prediction formulation agrees well with the numerical results and available measured data.

Streamwise vortex breakdown due to the interaction with crossed shock waves

This paper presents a vortex breakdown study due to the interaction between a Batchelor vortex and the crossing of oblique shock waves with Mach numbers of 3.5 and 5.0, favourable for supersonic mixing and combustion, respectively. Numerical simulations were conducted to investigate the effects of the circulation intensity and shock angle on vortex breakdown. The results indicate that a breakdown occurs at the shock angle $\beta \geqslant 45^\circ$ or the vortex circulation $q = 0.32$ , and the configuration is a bubble structure with a recirculation region; most of the breakdowns possess a stagnation point. Furthermore, the structure differs from that of a normal shock wave and vortex interaction because the bubble region is subsonic and does not comprise a normal shock wave on the inside. Additionally, this vortex breakdown shows that the momentum flux on the centreline decreases once at the tip of the bubble owing to a sudden drop in velocity in the subsonic region. In addition, the enstrophy production resulting from vortex stretching and tilting is found to have a significant advantage in the interaction region. Based on these results, the threshold required for a bubble vortex breakdown was theoretically derived as an inequality. The numerical simulation results support the theoretical criterion obtained from the proposed inequality. Therefore, a streamwise vortex breakdown resulting from the interaction between the vortex and intersecting oblique-shocks should be reasonably predicted.

RETRACTED ARTICLE: Assessment of fetal intraventricular diastolic fluid dynamics using ultrasound vector flow mapping

ObjectiveThe purpose of this study was to investigate the feasibility of visualizing and quantifying the normal pattern of vortex formation in the left ventricle (LV) and right ventricle (RV) of the fetal heart during diastole using vector flow mapping (VFM).MethodsA total of 36 healthy fetuses in the second trimester (mean gestational age: 23 weeks, 2 days; range: 22–24 weeks) were enrolled in the study. Color Doppler signals were recorded in the four-chamber view to observe the phase of the diastolic vortices in the LV and RV. The vortex area and circulation were measured, and parameters such as intraventricular pressure difference (IVPD), intraventricular pressure gradient (IVPG), and average energy loss (EL_AVG) were evaluated at different diastolic phases, including isovolumic relaxation (D1), early diastole (D2), and late diastole (D3).ResultsHealthy second-trimester fetal vortex formations were observed in both the LV and RV at the end of diastole, with the vortices rotating in a clockwise direction towards the outflow tract. There were no significant differences in vortex area and circulation between the two ventricles (p > 0.05). However, significant differences were found in IVPD, IVPG, and EL_AVG among the diastolic phases (D1, D2, and D3) (p < 0.05). Trends in IVPD, IVPG, and EL_AVG during diastole (D1-D2-D3) revealed increasing IVPD and EL_AVG values, as well as decreasing IVPG values. Furthermore, during D3, the RV exhibited significantly higher IVPD, IVPG, and EL_AVG compared to the LV (p > 0.05).ConclusionVFM is a valuable technique for analyzing the formation of vortices in the left and right ventricles during fetal diastole. The application of VFM technology has the potential to enhance the assessment of fetal cardiac parameters.

Mitigating PM2.5 exposure with vegetation barrier and building designs in urban open-road environments based on numerical simulations

Vegetation barriers (VB) are commonly regarded as an effective strategy in urban planning for mitigating traffic-induced airborne pollutants and associated exposure of road-users and nearby urban dwellers. Locally verified evidence is needed to better understand the nexus between VB designs and PM2.5 dispersion and provide practical insights for the creation of a healthy urban environment. This study constructs a 3D numerical model using in-situ measurements via field campaign, and then simulates PM2.5 dispersion in an open-road environment in Shanghai, China, characterized by varying VB designs (short vs. tall bushes in different location and coverage) and building structure (present vs. absent). The simulation results reveal the effectiveness of VB in PM2.5 mitigation in the sidewalk canyon, regardless the presence of building structure. Bushes at the windward side, regardless their size, tend to be more effective than arbors. The building structure flanked the sidewalk also contribute to PM2.5 mitigation in the sidewalk canyon. Various scenarios using short bushes consistently reduce PM2.5 concentrations along building façade, which might be attributed to the formation of vortex circulations in the sidewalk canyon. In contrast, a greater tall-bush coverage (2/3 and above, regardless of their location) tends to exacerbate PM2.5 pollution along building façade. Thus, constructing VB with a large proportion of short bushes could be a practical solution to minimizing the exposure of both sidewalk users and building inhabitants to traffic-induced PM2.5 in open-road environments.

On the unsteady interactions between a sweeping jet and afterbody vortices

In this paper, a sweeping jet was applied to control the afterbody vortices behind a 30° slanted-base cylinder at a Reynolds number of 87 000. Phase-locked stereo particle image velocimetry measurements were conducted during a sweeping jet actuation cycle, and insights of the complex three-dimensional interaction process between the sweeping jet and the afterbody vortices have been obtained for the first time. It is found that in the near-field of the jet orifice (x/c &amp;lt; 0.3), the jet swings from side to side over the endplate between the afterbody vortex pair. An intersection between them around x/c = 0.3 causes the sweeping jet to take on a zigzag pattern as it propagates downstream along the slanted surface. From x/c = 0.6 onwards, the intensity of this interaction decreases as the afterbody vortices become detached from the base. Nevertheless, the sweeping jet continues invading the afterbody vortices from their inner side and pushes its way outwards from the underside of the afterbody vortices causing them to weaken further. Furthermore, the interaction between sweeping jets and afterbody vortices results in a cyclic variation in the circulation of afterbody vortices, which increases in magnitude at downstream locations. Except for the phases where a merger between the afterbody vortex and the sweeping occurs, a reduction in the circulation is observed. Finally, the level of interaction between sweeping jets and afterbody vortices intensifies as the strength of the sweeping jet increases resulting in the afterbody vortices being penetrated by the sweeping jet and their regular shape being momentarily destroyed.

Large Eddy Simulation for Empirical Modeling of the Wake of Three Urban Air Mobility Vehicles

Recent advances in urban air mobility have driven the development of many new vertical take-off and landing (VTOL) concepts. These vehicles often feature original designs departing from the conventional helicopter configuration. Due to their novelty, the characteristics of the supervortices forming in the wake of such aircraft are unknown. However, these vortices may endanger any other vehicle evolving in their close proximity, owing to potentially large induced velocities. Therefore, improved knowledge about the wakes of VTOL vehicles is needed to guarantee safe urban air mobility operations. In this work, we study the wake of three VTOL aircraft in cruise by means of large eddy simulation. We present a two-stage numerical procedure that enables the simulation of long wake ages at a limited computational cost. Our simulations reveal that the wakes of rotary vehicles (quadcopter and side-by-side helicopter) feature larger wake vortex cores than an isolated wing. Their decay is also accelerated due to self-induced turbulence generated during the wake roll-up. A tilt-wing wake, on the other hand, is moderately turbulent and has smaller vortex cores than the wing. Finally, we introduce an empirical model of the vortex circulation distribution that enables fast prediction of wake-induced velocities, within a 2% error of the simulation results on average.

Benchtop Models of Patient-Specific Intraventricular Flow During Heart Failure and LVAD Support.

The characterization of intraventricular flow is critical to evaluate the efficiency of fluid transport and potential thromboembolic risk but challenging to measure directly in advanced heart failure (HF) patients with left ventricular assist device (LVAD) support. The study aims to validate an in-house mock loop (ML) by simulating specific conditions of HF patients with normal and prosthetic mitral valves (MV) and LVAD patients with small and dilated left ventricle volumes, then comparing the flow-related indices result of vortex parameters, residence time (RT), and shear-activation potential (SAP). Patient-specific inputs for the ML studies included heart rate, end-diastolic and end-systolic volumes, ejection fraction, aortic pressure, E/A ratio, and LVAD speed. The ML effectively replicated vortex development and circulation patterns, as well as RT, particularly for HF patient cases. The LVAD velocity fields reflected altered flow paths, in which all or most incoming blood formed a dominant stream directing flow straight from the mitral valve to the apex. RT estimation of patient and ML compared well for all conditions, but SAP was substantially higher in the LVAD cases of the ML. The benchtop system generated comparable and reproducible hemodynamics and fluid dynamics for patient-specific conditions, validating its reliability and clinical relevance. This study demonstrated that ML is a suitable platform to investigate the fluid dynamics of HF and LVAD patients and can be utilized to investigate heart-implant interactions.

Influence of Underlying Topography on Post-Monsoon Cyclonic Systems over the Indian Peninsula

During the post-monsoon cyclone season, the landfalls of westward-moving cyclonic systems often lead to extreme rainfall over the east coast of the Indian peninsula. A stationary cyclonic system over the coast can produce heavy rainfall for several days and cause catastrophic flooding. This study analyzes the dynamics of a propagating and stationary cyclonic system over the east coast, highlighting the possible cause behind the stagnation. The vorticity budgets of these two systems are presented using a reanalysis dataset. Vortex stretching and horizontal vorticity advection were the dominant terms in the budget. Vertical advection and tilting terms were significant over the orography. The horizontal advection of vorticity was positive (negative) on the western (eastern) side of the systems and, thus, favored westward propagation. Vortex stretching was confined to the upstream of orography in the stationary vortex. In the propagating vortex, the vortex stretching occurred over the orography during its passage. Data from the radiosonde soundings over a coastal station showed orographic blocking of the low-level winds in the stationary case. Conversely, the flow crossed the orographic barrier in the propagating case. Thus, the predominance of the upstream orographic convergence over the vortex circulation can be the reason for system stagnation over the coast.

Stability of Hill's spherical vortex

AbstractWe study stability of a spherical vortex introduced by M. Hill in 1894, which is an explicit solution of the three‐dimensional incompressible Euler equations. The flow is axi‐symmetric with no swirl, the vortex core is simply a ball sliding on the axis of symmetry with a constant speed, and the vorticity in the core is proportional to the distance from the symmetry axis. We use the variational setting introduced by A. Friedman and B. Turkington (Trans. Amer. Math. Soc., 1981), which produced a maximizer of the kinetic energy under constraints on vortex strength, impulse, and circulation. We match the set of maximizers with the Hill's vortex via the uniqueness result of C. Amick and L. Fraenkel (Arch. Rational Mech. Anal., 1986). The matching process is done by an approximation near exceptional points (so‐called metrical boundary points) of the vortex core. As a consequence, the stability up to a translation is obtained by using a concentrated compactness method.

Aspects of potential vorticity circulation in the Northern Hemisphere: climatology and variation

This study revisits the concept of potential vorticity (PV) circulation (PVC) and presents new findings. Results suggest that PVC can cross the isentropic surface. The gross PV in the Northern Hemisphere (NH) depends solely on the total flux of PVC crossing the atmospheric upper boundary, bottom, and cross-section along the equator. In terms of climate, the cross-upper boundary PVC flux is critical for forming the positive basic state of the gross PV in the NH. In terms of variation, a cancelation intrinsically rooted in the PV dynamics between the cross-upper boundary PVC flux and cross-equator PVC flux means that the NH’s gross PV anomaly is largely determined by the cross-bottom PVC flux. Further analysis sheds light on a seminal atmospheric process in which anomalous PVC inflowing from the NH’s upper boundary outflows from the cross-section along the equator and vice versa. An analysis of the quasi-biennial oscillation verifies the process. All results imply that the PVC is a novel tool for examining the interaction between the upper and lower levels of the atmosphere and the interaction between hemispheres.

Vortex structure and fluid force changed by altering whole-body kinematic parameters during underwater undulatory swimming

ABSTRACT Swimmers generate vortices around their bodies during underwater undulatory swimming (UUS). Alteration of UUS movement would induce changes in vortex structure and fluid force. This study investigated whether a skilled swimmer’s movement generated an effective vortex and fluid force for increasing the UUS velocity. A three-dimensional digital model and kinematic data yielded during UUS with maximum effort were collected for one skilled and one unskilled swimmer. The skilled swimmer’s UUS kinematics were input into the skilled swimmer’s model (SK-SM) and unskilled swimmer’s model (SK-USM), followed by the kinematics of the unskilled swimmer (USK-USM and USK-SM, respectively). The vortex area, circulation, and peak drag force were determined using computational fluid dynamics. A larger vortex with greater circulation at the ventral side of the trunk and a greater circulation vortex behind the swimmer were observed in SK-USM compared to USK-USM. USK-SM generated a smaller vortex on the ventral side of the trunk and behind the swimmer, with a weaker circulation behind the swimmer compared to SK-SM. The peak drag force was larger for SK-USM than for USK-USM. Our results indicate that an effective vortex for propulsion was generated when a skilled swimmer’s UUS kinematics was input in the other swimmer’s model.

Liquid entrainment of the toroidal bubble crossing the interface between two immiscible liquids

We experimentally investigate the transport of liquid by a toroidal bubble that rises vertically and penetrates a horizontal interface between two immiscible liquids. Experiments are conducted with various strengths of vortex circulation in the bubble, and with different liquid densities and viscosities. In contrast to a spherical bubble, a rising toroidal bubble carries a great amount of the lower liquid by virtue of the self-induction of circulating flow. The lower liquid is entrained by the toroidal bubble and forms an ellipsoidal body enclosing the bubble after it penetrates the interface. The downward net force acting on the ellipsoidal body results in the radial contraction of the bubble, reducing the volume of the entrained lower liquid. As the entrained volume decreases, the nearby upper liquid eventually pierces the ellipsoidal body, making the bubble unstable. At this instant, the net force acting on the ellipsoidal body approaches zero, and the volume ratio of the entrained lower liquid and bubble converges to a specific value. For smaller vortex circulation and larger density difference between the liquids, the volume of the entrained lower liquid within the ellipsoidal body becomes smaller and the travel distance of the bubble from the initial interface until it becomes unstable decreases. The effective Froude number, which accounts for both the inertial effect of vortex circulation and the gravitational effect of liquid density difference, is found to characterise the temporal changes in the ring radius, propagation speed and entrained volume.

Measuring the 3D wake of swimming snakes (Natrix tessellata) using volumetric particle image velocimetry.

We describe a method for measuring the 3D vortical structures produced by an anguilliform swimmer using volumetric velocimetry. The wake of freely swimming dice snakes (Natrix tessellata) was quantified, revealing the creation of multiple vortices along the body of the snake due to its undulation. The 3D structure of the vortices generally consisted of paired vortex tubes, some of which were linked together to form a hairpin structure. The observations match predictions from computational fluid dynamic studies of other anguilliform swimmers. Quantitative measurements allowed us to study vortex circulation and size, and global kinetic energy of the flow, which varied with swimming speed, vortex topology and individual characteristics. Our findings provide a baseline for comparing wake structures of snakes with different morphologies and ecologies and investigating the energetic efficiency of anguilliform swimming.

A numerical examination on the use of phase change materials to improve the sun-tracking photovoltaic panels' performance

The power generation of a photovoltaic (PV) panel is inherently affected by the amount of solar radiation striking the panel and the PV temperature. Tracking PV panels reach higher temperature than fixed panels due to more received radiation. Phase change materials (PCMs) are widely used as a passive method for cooling fixed PV panels. The melting dynamics of the PCM is very different during tracking compared to previous research carried out on fixed panels due to the changing orientation. A tracking PV-PCM system is numerically modeled in this research, and the temperature distribution and convection in the PCM are analyzed. The numerical results are presented as temperature-time curves for several different positions inside the PCM container, liquid fraction and streamlines in melted PCM, and isothermal curves. The temperature variation shows that the temperature of solid PCM increases rapidly in the initial time, reaching the melting temperature. The PCM changes from the solid phase to the liquid phase at a constant temperature. After complete melting, the PCM temperature increases over time. The PCM temperature changes were compared at two different distances from the photovoltaic panel. The streamlines show that the PCM starts to melt near the heated wall at the container's top corner. The melted PCM expands toward the down of the container due to vortex circulation created in the molten material. It is observed that the increase in PV panel temperature between 1.5 and 7 h is only 5.3 K, showing that using PCM is an effective method for absorbing heat from the PV panels during melting. Results show that the temperature of PV panel with PCM is on average 6.9 K lower than that without PCM.

Impacts of the Surface Potential Vorticity Circulation over the Tibetan Plateau on the East Asian Monsoon in July

Based on the definition of potential vorticity substance (W) and its equation, an index “iPV” representing the leading mode of the surface potential vorticity circulation (PVC) over the Tibetan Plateau is defined to characterize the orographic potential vorticity (PV) forcing on the atmospheric general circulation. The relationships between the iPV index and the East Asian monsoon in July, as well as the Silk Road pattern in Eurasia, are investigated on an interannual time scale. Results show that the iPV in July is closely related to the interannual variability of the East Asian monsoon. Corresponding to the positive phase of iPV with negative (positive) PVC over the north (south) of the plateau, strong positive PV anomalies and westerly flows develop in the troposphere over the plateau. Consequently, in the downstream region, the zonal PV advection increases with height just above the Jianghuai Meiyu front, which is conducive to the generation of upward movement. Over the East Asian area, the upper troposphere is controlled by the eastward shifted South Asian High. In the lower troposphere, the southwesterly flow anomaly on the northwestern side of the strengthened western Pacific subtropical high transports abundant water vapor to the north, forming a convergence in the Jianghuai area, leading to the formation of large-scale precipitation along the Meiyu front. Results from partial correlation analysis also demonstrate that the link between the variability of the East Asian monsoon in July and the plateau PV forcing is affected very little by the Silk Road pattern, whereas the plateau PV forcing plays a key “bridging” role in the influence of the Silk Road pattern on the East Asian monsoon.

Decomposition of airflow over topography and its application to a topographic blizzard event in central Asia

To better understand the triggering mechanisms of extreme precipitation events in Central Asia due to the complex terrain, a case study of a topographic blizzard that occurred in Xinjiang Province on 30 November 2018 is conducted. The near-surface wind field is decomposed into flow-around and flow-over components to analyze the dynamic and thermodynamic effects of the flow around and over the topography in the Ili River valley and the northern slope of the Tianshan Mountains. The results reveal that the flow around the topography is the dominant component of the flow field that transports water vapor and causes moisture convergence. The symmetric instability observed at the lower level of the snowfall area is attributed to the flow-around wind field, which leads to advective transport of generalized potential temperature and causes changes in potential vorticity, ultimately resulting in symmetric instability. The local variation of stratified instability in the snowfall area is caused by flow-over potential divergence, specifically, the advection of the flow-over wind vertical shear to equivalent potential temperature causes the change of flow-over potential divergence, thus promotes stratified instability. Moreover, the flow-over potential divergence is negatively correlated with the amount of topographic snowfall to a certain extent, which can provide reference for topographic snowfall forecast in the future. Additionally, the cyclonic vorticity in the snowfall area is mainly caused by the flow around topography and flow-around wind produces favorable vortical circulation conditions for snowfall, while the vertical movement near the ground at the snowfall triggering stage is mainly caused by the flow-over component. Furthermore, the flow-over kinetic energy in the snow area is stronger and the work done by the pressure gradient force caused by flow over terrain drives kinetic energy changes.

Rotation effects on turbulence features of viscoelastic spanwise-rotating plane Couette flows

Rotation effects on turbulence features have been examined in viscoelastic spanwise-rotating plane Couette flows (RPCF) at the Reynolds number Re = 1300 and the Weissenberg number Wi = 5, by using of direct numerical simulations for the rotation number Ro=0.02–0.9. Here, Re represents the ratio of inertial forces to viscous forces, and Wi and Ro quantify the strength of fluid elasticity and system rotation, respectively. Based on the detailed examinations of the turbulent kinetic energy and Reynolds stress budgets as well as vortical structures, the viscoelastic RPCF can be classified roughly into three regimes: weak rotation for Ro≤0.1, intermediate rotation for 0.1&amp;lt;Ro&amp;lt;0.4, and strong rotation for Ro≥0.4. Essentially, the comprehensive rotation effects are inherent to the rotation-driven vortical change characterized by an enhancement as Ro is changed from weak to intermediate rotation and a followed suppression at the elasto-inertial turbulence (EIT) state of strong rotation. Specifically, the turbulent kinetic energy and Reynolds stress at Ro = 0.9 are found less than 10% of those at Ro = 0.2. Of particular interest, at weak and intermediate rotation, intense polymer–turbulence interaction is found to occur primarily in the extensional flows between two neighboring roll cells, whereas for the high-Ro EIT state, it happens in the bulk region as the small-scale turbulent vortices serve to homogenize the polymer dynamics via their vortical circulations. The present finding has shed some new light onto the polymer–turbulence interaction under system rotation.