Two-dimensional turbulence above topography: Vortices and potential vorticity homogenization.

The evolution of unforced and weakly damped two-dimensional turbulence over random rough topography presents two extreme states. If the initial kinetic energy [Formula: see text] is sufficiently high, then the topography is a weak perturbation, and evolution is determined by the spontaneous formation and mutual interaction of coherent axisymmetric vortices. High-energy vortices roam throughout the domain and mix the background potential vorticity (PV) to homogeneity, i.e., in the region between vortices, which is most of the domain, the relative vorticity largely cancels the topographic PV. If [Formula: see text] is low, then vortices still form but they soon become locked to topographic features: Anticyclones sit above topographic depressions and cyclones above elevated regions. In the low-energy case, with topographically locked vortices, the background PV retains some spatial variation. We develop a unified framework of topographic turbulence spanning these two extreme states of low and high energy. A main organizing concept is that PV homogenization demands a particular kinetic energy level [Formula: see text]. [Formula: see text] is the separator between high-energy evolution and low-energy evolution.

Mechanism of vorticity amplification by elastic waves in a viscoelastic channel flow.

Inertia-less viscoelastic channel flow displays a supercritical nonnormal mode elastic instability due to finite-size perturbations despite its linear stability. The nonnormal mode instability is determined mainly by a direct transition from laminar to chaotic flow, in contrast to normal mode bifurcation leading to a single fastest-growing mode. At higher velocities, transitions to elastic turbulence and further drag reduction flow regimes occur accompanied by elastic waves in three flow regimes. Here, we demonstrate experimentally that the elastic waves play a key role in amplifying wall-normal vorticity fluctuations by pumping energy, withdrawn from the mean flow, into wall-normal fluctuating vortices. Indeed, the flow resistance and rotational part of the wall-normal vorticity fluctuations depend linearly on the elastic wave energy in three chaotic flow regimes. The higher (lower) the elastic wave intensity, the larger (smaller) the flow resistance and rotational vorticity fluctuations. This mechanism was suggested earlier to explain elastically driven Kelvin-Helmholtz-like instability in viscoelastic channel flow. The suggested physical mechanism of vorticity amplification by the elastic waves above the elastic instability onset recalls the Landau damping in magnetized relativistic plasma. The latter occurs due to the resonant interaction of electromagnetic waves with fast electrons in the relativistic plasma when the electron velocity approaches light speed. Moreover, the suggested mechanism could be generally relevant to flows exhibiting both transverse waves and vortices, such as Alfven waves interacting with vortices in turbulent magnetized plasma, and Tollmien-Schlichting waves amplifying vorticity in both Newtonian and elasto-inertial fluids in shear flows.

Four-dimensional flow cardiovascular magnetic resonance aortic cross-sectional pressure changes and their associations with flow patterns in health and ascending thoracic aortic aneurysm.

BACKGROUND: Ascending thoracic aortic aneurysm (ATAA) is a silent and threatening dilation of the ascending aorta (AscAo). Maximal aortic diameter which is currently used for ATAA patients management and surgery planning has been shown to inadequately characterize risk of dissection in a large proportion of patients. Our aim was to propose a comprehensive quantitative evaluation of aortic morphology and pressure-flow-wall associations from four-dimensional (4D) flow cardiovascular magnetic resonance (CMR) data in healthy aging and in patients with ATAA. METHODS: We studied 17 ATAA patients (64.7 ± 14.3 years, 5 females) along with 17 age- and sex-matched healthy controls (59.7 ± 13.3 years, 5 females) and 13 younger healthy subjects (33.5 ± 11.1 years, 4 females). All subjects underwent a CMR exam, including 4D flow and three-dimensional anatomical images of the aorta. This latter dataset was used for aortic morphology measurements, including AscAo maximal diameter (iDMAX) and volume, indexed to body surface area. 4D flow MRI data were used to estimate 1) cross-sectional local AscAo spatial (∆PS) and temporal (∆PT) pressure changes as well as the distance (∆DPS) and time duration (∆TPT) between local pressure peaks, 2) AscAo maximal wall shear stress (WSSMAX) at peak systole, and 3) AscAo flow vorticity amplitude (VMAX), duration (VFWHM), and eccentricity (VECC). RESULTS: Consistency of flow and pressure indices was demonstrated through their significant associations with AscAo iDMAX (WSSMAX:r = -0.49, p < 0.001; VECC:r = -0.29, p = 0.045; VFWHM:r = 0.48, p < 0.001; ∆DPS:r = 0.37, p = 0.010; ∆TPT:r = -0.52, p < 0.001) and indexed volume (WSSMAX:r = -0.63, VECC:r = -0.51, VFWHM:r = 0.53, ∆DPS:r = 0.54, ∆TPT:r = -0.63, p < 0.001 for all). Intra-AscAo cross-sectional pressure difference, ∆PS, was significantly and positively associated with both VMAX (r = 0.55, p = 0.002) and WSSMAX (r = 0.59, p < 0.001) in the 30 healthy subjects (48.3 ± 18.0 years). Associations remained significant after adjustment for iDMAX, age, and systolic blood pressure. Superimposition of ATAA patients to normal aging trends between ∆PS and WSSMAX as well as VMAX allowed identifying patients with substantially high pressure differences concomitant with AscAo dilation. CONCLUSION: Local variations in pressures within ascending aortic cross-sections derived from 4D flow MRI were associated with flow changes, as quantified by vorticity, and with stress exerted by blood on the aortic wall, as quantified by wall shear stress. Such flow-wall and pressure interactions might help for the identification of at-risk patients.

Numerical Investigation on the Effect of Section Width on the Performance of Air Ejector with Rectangular Section.

Due to its simple structure and lack of moving parts, the supersonic air ejector has been widely applied in the fields of machinery, aerospace, and energy-saving. The performance of the ejector is influenced by the flow channel structure and the velocity of the jet, thus the confined jet is an important limiting factor for the performance of the supersonic air ejector. In order to investigate the effect of the confined jet on the performance of the ejector, an air ejector with a rectangular section was designed. The effects of the section width (Wc) on the entrainment ratio, velocity distribution, turbulent kinetic energy distribution, Mach number distribution, and vorticity distribution of the rectangular section air ejector were studied numerically. The numerical results indicated that the entrainment ratio of the rectangular section air ejector increased from 0.34 to 0.65 and the increment of the ER was 91.2% when the section width increased from 1 mm to 10 mm. As Wc increased, the region of the turbulent kinetic energy gradually expanded. The energy exchange between the primary fluid and the secondary fluid was mainly in the form of turbulent diffusion in the mixing chamber. In addition to Wc limiting the fluid flow in the rectangular section air ejector, the structure size of the rectangular section air ejector in the XOY plane also had a limiting effect on the internal fluid flow. In the rectangular section air ejector, the streamwise vortices played an important role in the mixing process. The increase of Wc would increase the distribution of the streamwise vortices in the constant-area section. Meanwhile, the distribution of the spanwise vortices would gradually decrease.

Energy balance for forced two-dimensional incompressible ideal fluid flow.

Cheskidov et al. (2016 Commun. Math. Phys. 348, 129-143. (doi:10.1007/s00220-016-2730-8)) proved that physically realizable weak solutions of the incompressible two-dimensional Euler equations on a torus conserve kinetic energy. Physically realizable weak solutions are those that can be obtained as limits of vanishing viscosity. The key hypothesis was boundedness of the initial vorticity in [Formula: see text], [Formula: see text]. In this work, we extend their result, by adding forcing to the flow. This article is part of the theme issue 'Scaling the turbulence edifice (part 2)'.

Convergence to precipitating quasi-geostrophic equations with phase changes: asymptotics and numerical assessment.

The quasi-geostrophic (QG) equations play a crucial role in our understanding of atmospheric and oceanic fluid dynamics. Nevertheless, the traditional QG equations describe 'dry' dynamics that do not account for moisture and clouds. To move beyond the dry setting, precipitating QG (PQG) equations have been derived recently using formal asymptotics. Here, we investigate whether the moist Boussinesq equations with phase changes will converge to the PQG equations. A priori, it is possible that the nonlinearity at the phase interface (cloud edge) may complicate convergence. A numerical investigation of convergence or non-convergence is presented here. The numerical simulations consider cases of [Formula: see text], 0.01 and 0.001, where [Formula: see text] is proportional to the Rossby and Froude numbers. In the numerical simulations, the magnitude of vertical velocity [Formula: see text] (or other measures of imbalance and inertio-gravity waves) is seen to be approximately proportional to [Formula: see text] as [Formula: see text] decreases, which suggests convergence to PQG dynamics. These measures are quantified at a fixed time [Formula: see text] that is [Formula: see text], and the numerical data also suggests the possibility of convergence at later times. This article is part of the theme issue 'Mathematical problems in physical fluid dynamics (part 2)'.

Hemodynamic interplay of vorticity, viscous energy loss, and kinetic energy from 4D Flow MRI and link to cardiac function in healthy subjects and Fontan patients.

The purpose of this study was to directly assess (patho)physiology of intraventricular hemodynamic interplay between four-dimensional flow cardiovascular magnetic resonance imaging (4D Flow MRI)-derived vorticity with kinetic energy (KE) and viscous energy loss (EL) over the cardiac cycle and their association to ejection fraction (EF) and stroke volume (SV). Fifteen healthy subjects and thirty Fontan patients underwent whole heart 4D Flow MRI. Ventricular vorticity, KE, and EL were computed over systole (vorticity_volavg systole, KEavg systole, and ELavg systole) and diastole (vorticity_volavg diastole, KEavg diastole, and ELavg diastole). The association between vorticity_vol and KE and EL was tested by Spearman correlation. Fontan patients were grouped to normal and impaired EF groups. A significant correlation was found between SV and vorticity in healthy subjects (systolic: ρ = 0.84, P < 0.001; diastolic: ρ = 0.81, P < 0.001) and in Fontan patients (systolic: ρ = 0.61, P < 0.001; diastolic: ρ = 0.54, P = 0.002). Healthy subjects showed positive correlation between vorticity_vol versus KE (systole: ρ = 0.96, P < 0.001; diastole: ρ = 0.90, P < 0.001) and EL (systole: ρ = 0.85, P < 0.001; diastole: ρ = 0.84, P < 0.001). Fontan patients showed significantly elevated vorticity_vol compared with healthy subjects (vorticity_volavg systole: 3.1 [2.3-3.9] vs. 1.7 [1.3-2.4] L/s, P < 0.001; vorticity_volavg diastole: 3.1 [2.0-3.7] vs. 2.1 [1.6-2.8] L/s, P = 0.002). This elevated vorticity in Fontan patients showed strong association with KE (systole: ρ = 0.91, P < 0.001; diastole: ρ = 0.85, P < 0.001) and EL (systole: ρ = 0.82, P < 0.001; diastole: ρ = 0.89, P < 0.001). Fontan patients with normal EF showed significantly higher vorticity_volavg systole and ELavg systole, but significantly decreased KE avg diastole, in the presence of normal SV, compared with healthy subjects. Healthy subjects show strong physiological hemodynamic interplay between vorticity with KE and EL. Fontan patients demonstrate a pathophysiological hemodynamic interplay characterized by correlation of elevated vorticity with KE and EL in the presence of maintained normal stroke volume. Altered vorticity and energetic hemodynamics are found in the presence of normal EF in Fontan patients.NEW & NOTEWORTHY Physiologic intraventricular hemodynamic interplay/coupling is present in the healthy left ventricle between vorticity versus viscous energy loss and kinetic energy from four-dimensional flow cardiovascular magnetic resonance imaging (4D Flow MRI). Conversely, Fontan patients present compensatory pathophysiologic hemodynamic coupling by an increase in intraventricular vorticity that positively correlates to viscous energy loss and kinetic energy levels in the presence of maintained normal stroke volume. Altered vorticity and energetics are found in the presence of normal ejection fraction in Fontan patients.

Impact of Thoracic Endografting on the Hemodynamics of the Native Aorta: Pre- and Postoperative Assessments of Wall Shear Stress and Vorticity Using Computational Fluid Dynamics.

PURPOSE: To quantify the hemodynamic consequences of thoracic endovascular aortic repair (TEVAR) by comparing the preoperative and postoperative wall shear stress (WSS) and vorticity profiles on computational fluid dynamics (CFD) simulations. MATERIALS AND METHODS: The pre- and postoperative computed tomography (CT) scans from 20 consecutive patients (median age 69 years, range 20-87) treated for different thoracic aortic pathologies (11 aneurysms, 5 false aneurysms, 3 penetrating ulcers, and 1 traumatic aortic rupture) were segmented to construct patient-specific CFD models using a meshless code. The simulations were run over the cardiac cycle, and the WSS and vorticity values measured at the proximal and distal landing zones were compared. RESULTS: The CFD runs provided 4-dimensional simulations of blood flow in all patients. WSS and vorticity profiles at the proximal landing zone (located in zones 0-3 in 15 patients) varied in 18 and 20 of the cases, respectively; WSS was increased in 11 cases and the vorticity in 9. Pre- and postoperative WSS median values were 4.19 and 4.90 Pa, respectively. Vorticity median values were 40.38 and 39.17 Hz, respectively. CONCLUSION: TEVAR induces functional alterations in the native thoracic aorta, though the prognostic significance of these changes is still unknown. CFD appears to be a valuable tool to explore aortic hemodynamics, and its application in a larger series would help define a predictive role for these hemodynamic assessments.

Moving beyond size: vorticity and energy loss are correlated with right ventricular dysfunction and exercise intolerance in repaired Tetralogy of Fallot.

BACKGROUND: The global effect of chronic pulmonary regurgitation (PR) on right ventricular (RV) dilation and dysfunction in repaired Tetralogy of Fallot (rTOF) patients is well studied by cardiovascular magnetic resonance (CMR). However, the links between PR in the RV outflow tract (RVOT), RV dysfunction and exercise intolerance are not clarified by conventional measurements. Not all patients with RV dilation share the same intracardiac flow characteristics, now measurable by time resolved three-dimensional phase contrast imaging (4D flow). In our study, we quantified regional vorticity and energy loss in rTOF patients and correlated these parameters with RV dysfunction and exercise capacity. METHODS: rTOF patients with 4D flow datasets were retrospectively analyzed, including those with transannular/infundibular repair and conduit repair. Normal controls and RV dilation patients with atrial-level shunts (Qp:Qs > 1.2:1) were included for comparison. 4D flow was post-processed using IT Flow (Cardioflow, Japan). Systolic/diastolic vorticity (ω, 1/s) and viscous energy loss (VEL, mW) in the RVOT and RV inflow were measured. To characterize the relative influence of diastolic vorticity in the two regions, an RV Diastolic Vorticity Quotient (ωRVOT-Diastole/ωRV Inflow-Diastole, RV-DVQ) was calculated. Additionally, RVOT Vorticity Quotient (ωRVOT-Diastole/ωRVOT-Systole, RVOT-VQ) and RVOT Energy Quotient (VELRVOT-Diastole/VELRVOT-Systole, RVOT-EQ) was calculated. In rTOF, measurements were correlated against conventional CMR and exercise stress test results. RESULTS: 58 rTOF patients, 28 RV dilation patients and 12 controls were included. RV-DVQ, RVOT-VQ, and RVOT-EQ were highest in rTOF patients with severe PR compared to rTOF patients with non-severe PR, RV dilation and controls (p < 0.001). RV-DVQ positively correlated with RV end-diastolic volume (0.683, p < 0.001), PR fraction (0.774, p < 0.001) and negatively with RV ejection fraction (- 0.521, p = 0.003). Both RVOT-VQ, RVOT-EQ negatively correlated with VO2-max (- 0.587, p = 0.008 and - 0.617, p = 0.005) and % predicted VO2-max (- 0.678, p = 0.016 and - 0.690, p = 0.001). CONCLUSIONS: In rTOF patients, vorticity and energy loss dominate the RVOT compared to tricuspid inflow, correlating with RV dysfunction and exercise intolerance. These 4D flow-based measurements may be sensitive biomarkers to guide surgical management of rTOF patients.

Left atrial 4D flow cardiovascular magnetic resonance: a reproducibility study in sinus rhythm and atrial fibrillation.

BACKGROUND: Four-dimensional (4D) flow cardiovascular magnetic resonance (CMR) allows sophisticated quantification of left atrial (LA) blood flow, and could yield novel biomarkers of propensity for intra-cardiac thrombus formation and embolic stroke. As reproducibility is critically important to diagnostic performance, we systematically investigated technical and temporal variation of LA 4D flow in atrial fibrillation (AF) and sinus rhythm (SR). METHODS: Eighty-six subjects (SR, n = 64; AF, n = 22) with wide-ranging stroke risk (CHA2DS2VASc 0-6) underwent LA 4D flow assessment of peak and mean velocity, vorticity, vortex volume, and stasis. Eighty-five (99%) underwent a second acquisition within the same session, and 74 (86%) also returned at 30 (27-35) days for an interval scan. We assessed variability attributable to manual contouring (intra- and inter-observer), and subject repositioning and reacquisition of data, both within the same session (same-day scan-rescan), and over time (interval scan). Within-subject coefficients of variation (CV) and bootstrapped 95% CIs were calculated and compared. RESULTS: Same-day scan-rescan CVs were 6% for peak velocity, 5% for mean velocity, 7% for vorticity, 9% for vortex volume, and 10% for stasis, and were similar between SR and AF subjects (all p > 0.05). Interval-scan variability was similar to same-day scan-rescan variability for peak velocity, vorticity, and vortex volume (all p > 0.05), and higher for stasis and mean velocity (interval scan CVs of 14% and 8%, respectively, both p < 0.05). Longitudinal changes in heart rate and blood pressure at the interval scan in the same subjects were associated with significantly higher variability for LA stasis (p = 0.024), but not for the remaining flow parameters (all p > 0.05). SR subjects showed significantly greater interval-scan variability than AF patients for mean velocity, vortex volume, and stasis (all p < 0.05), but not peak velocity or vorticity (both p > 0.05). CONCLUSIONS: LA peak velocity and vorticity are the most reproducible and temporally stable novel LA 4D flow biomarkers, and are robust to changes in heart rate, blood pressure, and differences in heart rhythm.

Aortic Vorticity, Helicity, and Aortopathy in Adult Patients with Tetralogy of Fallot: Pilot Study Using Four-Dimensional Flow Magnetic Resonance Images.

To employ quantitative analysis in the vorticity and helicity of the aortic root and the ascending aorta (AAo) in adults with tetralogy of Fallot (TOF), and to evaluate aortopathy and the relevant factors. Prospectively, 51 consecutive adults with TOF underwent 4 dimensional flow magnetic resonance imaging study for the assessment of vorticity and helicity of the aortic root and AAo, wall shear stress (WSS), viscous energy loss (EL), and the left ventricular outflow tract - aortic root (LVOT-Ao) angle. Patients were divided into the two groups: dilated aortic root and/or AAo (indexed diameter > 25 mm/cm2), Group A (15 patients); non-dilated aortic patients, Group B (36 patients). Ten age-matched controls were also enrolled. Group A showed more acute LVOT-Ao angle, higher incidence of aortic regurgitation, and initial anatomy of pulmonary atresia, compared to Group B (P < 0.0001, 0.02, 0.043). Group A showed greater clockwise vorticity at the level of Valsalva, AAo, and proximal arch, sagittal vorticity, AAo helicity, WSS, and EL than in Group B (P < 0.001, < 0.001, < 0.001, 0.045, 0.049, 0.02, 0.026). More acute LVOT-Ao angle correlated with the diameter of the aortic root and AAo, AAo vorticity, helicity, WSS, and EL (P = 0.004, 0.023, 0.045, 0.004, 0.0004, 0.017). On a univariate logistic analysis, more acute LVOT-Ao angle, AAo vorticity, AAo helicity, and maximum WSS were relevant factors of AAo dilatation (P = 0.02, 0.02, 0.045, 0.03, 0.046). On a multivariate logistic analysis, more acute LVOT-Ao angle was the most important factor of AAo dilatation (odds ratio 0.66, 95% CI 0.46-0.95, P < 0.024). TOF adults presenting dilated AAo have greater vorticity, helicity, and acute LVOT-Ao angle. Flow eccentricity and these flow hemodynamic parameters may be adjunctive predictions of aortopathy in this population.

Gravitomagnetic Stern-Gerlach Force.

A heuristic description of the spin-rotation-gravity coupling is presented and the implications of the corresponding gravitomagnetic Stern-Gerlach force are briefly mentioned. It is shown, within the framework of linearized general relativity, that the gravitomagnetic Stern-Gerlach force reduces in the appropriate correspondence limit to the classical Mathisson spin-curvature force.

Transient pressure modeling in jetting animals.

There are many marine animals that employ a form of jet propulsion to move through the water, often creating the jets by expanding and collapsing internal fluid cavities. Due to the unsteady nature of this form of locomotion and complex body/nozzle geometries, standard modeling techniques prove insufficient at capturing internal pressure dynamics, and hence swimming forces. This issue has been resolved with a novel technique for predicting the pressure inside deformable jet producing cavities (M. Krieg and K. Mohseni, J. Fluid Mech., 769, 2015), which is derived from evolution of the surrounding fluid circulation. However, this model was only validated for an engineered jet thruster with simple geometry and relatively high Reynolds number (Re) jets. The purpose of this manuscript is twofold: (i) to demonstrate how the circulation based pressure model can be used to analyze different animal body motions as they relate to propulsive output, for multiple species of jetting animals, (ii) and to quantitatively validate the pressure modeling for biological jetting organisms (typically characterized by complicated cavity geometry and low/intermediate Re flows). Using jellyfish (Sarsia tubulosa) as an example, we show that the pressure model is insensitive to complex cavity geometry, and can be applied to lower Re swimming. By breaking down the swimming behavior of the jellyfish, as well as that of squid and dragonfly larvae, according to circulation generating mechanisms, we demonstrate that the body motions of Sarsia tubulosa are optimized for acceleration at the beginning of pulsation as a survival response. Whereas towards the end of jetting, the velar morphology is adjusted to decrease the energetic cost. Similarly, we show that mantle collapse rates in squid maximize propulsive efficiency. Finally, we observe that the hindgut geometry of dragonfly larvae minimizes the work required to refill the cavity. Date Received: 10-18-2019, Date Accepted: 99-99-9999 *kriegmw@hawaii.edu, UHM Ocean and Res Eng, 2540 Dole St, Honolulu, HI 96822.

Vorticity in lower urinary tract can be assessed and associates with urinary tract morphology in men.

OBJECTIVES: The aim of this study is to develop a method to evaluate the fluid dynamics of urine flow in the lower urinary tract (LUT), especially that of vorticity. MATERIALS AND METHODS: This investigation included three sub-studies to demonstrate urine flow in the entire LUT. First, we attempted to observe vorticity generation in the urinary bladder during spontaneous voiding using transabdominal color Doppler ultrasonography (CDUS). Second, we performed transrectal CDUS to evaluate the vorticity of urine flow in the prostatic urethra. Patients with prostate cancer were enrolled before robotic surgery and divided into the vorticity and non-vorticity groups based on CDUS findings for comparisons of longitudinal urethral diameter and prostatic urethral angle. Third, the vorticity of the voided urine stream was observed using a high-speed video-camera. Micturition was done in a standing position while synchronously monitored for urine flow using uroflowmetry. RESULTS: Vorticity formation could be dynamically demonstrated in the urinary bladder and prostatic urethra using CDUS. The prostatic urethral angle of the vorticity group was more than that of the non-vorticity group. High-speed video recording could clearly capture vorticity and spiral shape generation in voided urine. The distance from the external urethral orifice to the first twist changed in accordance with urine flow rate. CONCLUSIONS: In a series of sub-studies, this investigation proved vorticity generation in the LUT and voided urine. Vorticity was detectable in the LUT and in voided urine using CDUS and a high-speed video-camera. Vorticity generation might be associated with urethral morphology.

Stress increases intracardiac 4D flow cardiovascular magnetic resonance -derived energetics and vorticity and relates to VO2max in Fontan patients.

BACKGROUND: We hypothesize that dobutamine-induced stress impacts intracardiac hemodynamic parameters and that this may be linked to decreased exercise capacity in Fontan patients. Therefore, the purpose of this study was to assess the effect of pharmacologic stress on intraventricular kinetic energy (KE), viscous energy loss (EL) and vorticity from four-dimensional (4D) Flow cardiovascular magnetic resonance (CMR) imaging in Fontan patients and to study the association between stress response and exercise capacity. METHODS: Ten Fontan patients underwent whole-heart 4D flow CMR before and during 7.5 µg/kg/min dobutamine infusion and cardiopulmonary exercise testing (CPET) on the same day. Average ventricular KE, EL and vorticity were computed over systole, diastole and the total cardiac cycle (vorticity_volavg cycle, KEavg cycle, ELavg cycle). The relation to maximum oxygen uptake (VO2 max) from CPET was tested by Pearson's correlation or Spearman's rank correlation in case of non-normality of the data. RESULTS: Dobutamine stress caused a significant 88 ± 52% increase in KE (KEavg cycle: 1.8 ± 0.5 vs 3.3 ± 0.9 mJ, P < 0.001), a significant 108 ± 49% increase in EL (ELavg cycle: 0.9 ± 0.4 vs 1.9 ± 0.9 mW, P < 0.001) and a significant 27 ± 19% increase in vorticity (vorticity_volavg cycle: 3441 ± 899 vs 4394 ± 1322 mL/s, P = 0.002). All rest-stress differences (%) were negatively correlated to VO2 max (KEavg cycle: r = - 0.83, P = 0.003; ELavg cycle: r = - 0.80, P = 0.006; vorticity_volavg cycle: r = - 0.64, P = 0.047). CONCLUSIONS: 4D flow CMR-derived intraventricular kinetic energy, viscous energy loss and vorticity in Fontan patients increase during pharmacologic stress and show a negative correlation with exercise capacity measured by VO2 max.

Electron Vorticity Indicative of the Electron Diffusion Region of Magnetic Reconnection.

While vorticity defined as the curl of the velocity has been broadly used in fluid and plasma physics, this quantity has been underutilized in space physics due to low time resolution observations. We report Magnetospheric Multiscale (MMS) observations of enhanced electron vorticity in the vicinity of the electron diffusion region of magnetic reconnection. On 11 July 2017 MMS traversed the magnetotail current sheet, observing tailward-to-earthward outflow reversal, current-carrying electron jets in the direction along the electron meandering motion or out-of-plane direction, agyrotropic electron distribution functions, and dissipative signatures. At the edge of the electron jets, the electron vorticity increased with magnitudes greater than the electron gyrofrequency. The out-of-plane velocity shear along distance from the current sheet leads to the enhanced vorticity. This, in turn, contributes to the magnetic field perturbations observed by MMS. These observations indicate that electron vorticity can act as a proxy for delineating the electron diffusion region of magnetic reconnection.

Three-dimensional quantification of vorticity and helicity from 3D cine PC-MRI using finite-element interpolations.

PURPOSE: We propose a 3D finite-element method for the quantification of vorticity and helicity density from 3D cine phase-contrast (PC) MRI. METHODS: By using a 3D finite-element method, we seamlessly estimate velocity gradients in 3D. The robustness and convergence were analyzed using a combined Poiseuille and Lamb-Ossen equation. A computational fluid dynamics simulation was used to compared our method with others available in the literature. Additionally, we computed 3D maps for different 3D cine PC-MRI data sets: phantom without and with coarctation (18 healthy volunteers and 3 patients). RESULTS: We found a good agreement between our method and both the analytical solution of the combined Poiseuille and Lamb-Ossen. The computational fluid dynamics results showed that our method outperforms current approaches to estimate vorticity and helicity values. In the in silico model, we observed that for a tetrahedral element of 2 mm of characteristic length, we underestimated the vorticity in less than 5% with respect to the analytical solution. In patients, we found higher values of helicity density in comparison to healthy volunteers, associated with vortices in the lumen of the vessels. CONCLUSIONS: We proposed a novel method that provides entire 3D vorticity and helicity density maps, avoiding the used of reformatted 2D planes from 3D cine PC-MRI. Magn Reson Med 79:541-553, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Jet-paddling jellies: swimming performance in the Rhizostomeae jellyfish Catostylus mosaicus.

Jellyfish are a successful and diverse class of animals that swim via jet propulsion, with swimming performance and propulsive efficiency being related to the animal's feeding ecology and body morphology. The Rhizostomeae jellyfish lack tentacles but possess four oral lobes and eight trailing arms at the centre of their bell, giving them a body morphology quite unlike that of other free-swimming medusae. The implications of this body morphology on the mechanisms by which thrust is produced are unknown. Here, we determined the wake structure and propulsive efficiency in the blue-blubber jellyfish Catostylus mosaicus (order: Rhizostomeae). The animal is propelled during both bell contraction and bell relaxation by different thrust-generating mechanisms. During bell contraction, a jet of fluid is expelled from the subumbrellar cavity, which results from the interaction between the counter-rotating stopping (from the preceding contraction cycle) and starting vortices, creating a vortex superstructure and propulsion. This species is also able to utilise passive energy recapture, which increases the animal's swimming velocity towards the end of the bell expansion phase when the bell diameter is constant. The thrust produced during this phase is the result of the flexible bell margin manoeuvring the stopping vortex into the subumbrellar cavity during bell relaxation, enhancing its circulation, and creating a region of high pressure on the inner surface of the bell and, consequently, thrust. These mechanisms of thrust generation result in C. mosaicus having a relatively high propulsive efficiency compared with other swimmers, indicating that economical locomotion could be a contributing factor in the ecological success of these medusan swimmers.

New approaches for assessing squid fin motions: coupling proper orthogonal decomposition with volumetric particle tracking velocimetry.

Squid, which swim using a coupled fin/jet system powered by muscular hydrostats, pose unique challenges for the study of locomotion. The high flexibility of the fins and complex flow fields generated by distinct propulsion systems require innovative techniques for locomotive assessment. For this study, we used proper orthogonal decomposition (POD) to decouple components of the fin motions and defocusing digital particle tracking velocimetry (DDPTV) to quantify the resultant 3D flow fields. Kinematic footage and DDPTV data were collected from brief squid, Lolliguncula brevis [3.1-6.5 cm dorsal mantle length (DML)], swimming freely in a water tunnel at speeds of 0.39-7.20 DML s-1 Both flap and wave components were present in all fin motions, but the relative importance of the wave components was higher for arms-first swimming than for tail-first swimming and for slower versus higher speed swimming. When prominent wave components were present, more complex interconnected vortex ring wakes were observed, while fin movements dominated by flapping resulted in more spatially separated vortex ring patterns. Although the jet often produced the majority of the thrust for steady rectilinear swimming, our results demonstrated that the fins can contribute more thrust than the jet at times, consistently produce comparable levels of lift to the jet during arms-first swimming, and can boost overall propulsive efficiency. By producing significant drag signatures, the fins can also aid in stabilization and maneuvering. Clearly, fins play multiple roles in squid locomotion, and when coupled with the jet, allow squid to perform a range of swimming behaviors integral to their ecological success.

Analytical approximation and numerical simulations for periodic travelling water waves.

We present recent analytical and numerical results for two-dimensional periodic travelling water waves with constant vorticity. The analytical approach is based on novel asymptotic expansions. We obtain numerical results in two different ways: the first is based on the solution of a constrained optimization problem, and the second is realized as a numerical continuation algorithm. Both methods are applied on some examples of non-constant vorticity.This article is part of the theme issue 'Nonlinear water waves'.