Surface Vorticity Research Articles

Bottom pressure torque and the vorticity balance from observations in Drake Passage

AbstractThe vorticity balance of the Antarctic Circumpolar Current in Drake Passage is examined using 4 years of observations from current‐ and pressure‐recording inverted echo sounders. The time‐varying vorticity, planetary and relative vorticity advection, and bottom pressure torque are calculated in a two‐dimensional array in the eddy‐rich Polar Frontal Zone (PFZ). Bottom pressure torque is also estimated at sites across Drake Passage. Mean and eddy nonlinear relative vorticity advection terms dominate over linear advection in the local (50‐km scale) vorticity budget in the PFZ, and are balanced to first order by the divergence of horizontal velocity. Most of this divergence comes from the ageostrophic gradient flow, which also provides a second‐order adjustment to the geostrophic relative vorticity advection. Bottom pressure torque is approximately one‐third the size of the local depth‐integrated divergence. Although the cDrake velocity fields exhibit significant turning with depth throughout Drake Passage even in the mean, surface vorticity advection provides a reasonable representation of the depth‐integrated vorticity balance. Observed near‐bottom currents are strongly topographically steered, and bottom pressure torques grow large where strong near‐bottom flows cross steep topography at small angles. Upslope flow over the northern continental slope dominates the bottom pressure torque in cDrake, and the mean across this Drake Passage transect, 3 to m s−2, exceeds the mean wind stress curl by a factor of 15–20.

The effect of a uniform through-surface flow on a cylinder and sphere

The effect of a uniform through-surface flow (velocity$U_{b}$) on a rigid and stationary cylinder and sphere (radius$a$) fixed in a free stream (velocity$U_{\infty }$) is analysed analytically and numerically. The flow is characterised by a dimensionless blow velocity${\it\Lambda}\,(=U_{b}/U_{\infty })$and Reynolds number$Re\,(=2aU_{\infty }/{\it\nu}$, where${\it\nu}$is the kinematic viscosity). High resolution numerical calculations are compared against theoretical predictions over the range$-3\leqslant {\it\Lambda}\leqslant 3$and$Re=1,10,100$for planar flow past a cylinder and axisymmetric flow past a sphere. For$-{\it\Lambda}\gg 1$, the flow is viscously dominated in a thin boundary layer of thickness${\it\nu}/|U_{b}|$adjacent to the rigid surface which develops in a time${\it\nu}/U_{b}^{2}$; the surface vorticity scales as$Re|{\it\Lambda}|U_{\infty }/a$for a cylinder and sphere. A boundary layer analysis is developed to analyse the unsteady viscous forces. Numerical results show that the surface pressure and vorticity distribution within the boundary layer agrees with a steady state analysis. The flow downstream of the body is irrotational so the wake volume flux,$Q_{w}$, is zero and the drag force is$F_{D}=-{\it\rho}U_{\infty }Q_{b}$, where${\it\rho}$is the density of the fluid and$Q_{b}$is the normal flux through the body surface. The drag coefficient is therefore$-2{\rm\pi}{\it\Lambda}$or$-8{\it\Lambda}$for a cylinder or sphere, respectively. A dissipation argument is applied to analyse the drag force; the rate of working of the drag force is balanced by viscous dissipation, flux of stagnation pressure and rate of work by viscous stresses due to sucking. At large$Re|{\it\Lambda}|$, the drag force is largely determined by viscous dissipation for a cylinder, with a weak contribution by the normal viscous stresses, while for a sphere, only$3/4$of the drag force is determined by viscous dissipation with the remaining$1/4$due to the flux of stagnation pressure through the sphere surface. When${\it\Lambda}\gg 1$, the boundary layer thickness initially grows linearly with time as vorticity is blown away from the rigid surface. The vorticity in the boundary layer is weakly dependent on viscous effects and scales as$U_{\infty }/a{\it\Lambda}$or$U_{\infty }/a{\it\Lambda}^{3/2}$for a cylinder and sphere, respectively. For large blow velocity, the vorticity is swept into two well-separated shear layers and the maximum vorticity decreases due to diffusion. The drag force is related to the vorticity distribution on the body surface and an approximate expression can be derived by considering the first term of a Fourier expansion in the surface vorticity. It is found that the drag coefficient$C_{D}$for a cylinder (corrected for flow boundedness) is weakly dependent on${\it\Lambda}$while for a sphere,$C_{D}$decreases with${\it\Lambda}$.

Eddy–Wind Interaction in the California Current System: Dynamics and Impacts

AbstractThe summertime California Current System (CCS) is characterized by energetic mesoscale eddies, whose sea surface temperature (SST) and surface current can significantly modify the wind stress and Ekman pumping. Relative importance of the eddy–wind interactions via SST and surface current in the CCS is examined using a high-resolution (7 km) regional coupled model with a novel coupling approach to isolate the small-scale air–sea coupling by SST and surface current. Results show that when the eddy-induced surface current is allowed to modify the wind stress, the spatially averaged surface eddy kinetic energy (EKE) is reduced by 42%, and this is primarily due to enhanced surface eddy drag and reduced wind energy transfer. In contrast, the eddy-induced SST–wind coupling has no significant impact on the EKE. Furthermore, eddy-induced SST and surface current modify the Ekman pumping via their crosswind SST gradient and surface vorticity gradient, respectively. The resultant magnitudes of the Ekman pumping velocity are comparable, but the implied feedback effects on the eddy statistics are different. The surface current-induced Ekman pumping mainly attenuates the amplitude of cyclonic and anticyclonic eddies, acting to reduce the eddy activity, while the SST-induced Ekman pumping primarily affects the propagation. Time mean–rectified change in SST is determined by the altered offshore temperature advection by the mean and eddy currents, but the magnitude of the mean SST change is greater with the eddy-induced current effect. The demonstrated remarkably strong dynamical response in the CCS system to the eddy-induced current–wind coupling indicates that eddy-induced current should play an important role in the regional coupled ocean–atmosphere system.

Estimation of Time-Averaged Surface Divergence and Vorticity from Satellite Ocean Vector Winds

Abstract Two methods of computing the time-mean divergence and vorticity from satellite vector winds in rain-free (RF) and all-weather (AW) conditions are investigated. Consequences of removing rain-contaminated winds on the mean divergence and vorticity depend strongly on the order in which the time-average and spatial derivative operations are applied. Taking derivatives first and averages second (DFAS_RF) incorporates only those RF winds measured at the same time into the spatial derivatives. While preferable mathematically, this produces mean fields biased relative to their AW counterparts because of the exclusion of convergence and cyclonic vorticity often associated with rain. Conversely, taking averages first and derivatives second (AFDS_RF) incorporates all RF winds into the time-mean spatial derivatives, even those not measured coincidentally. While questionable, the AFDS_RF divergence and vorticity surprisingly appears qualitatively consistent with the AW means, despite using only RF winds. The analysis addresses whether the AFDS_RF method accurately estimates the AW mean divergence and vorticity. Model simulations indicate that the critical distinction between these two methods is the inclusion of typically convergent and cyclonic winds bordering rain patches in the AFDS_RF method. While this additional information removes some of the sampling bias in the DFAS_RF method, it is shown that the AFDS_RF method nonetheless provides only marginal estimates of the mean AW divergence and vorticity given sufficient time averaging and spatial smoothing. Use of the AFDS_RF method is thus not recommended.

Modulational instability in the Whitham equation with surface tension and vorticity

We study modulational stability and instability in the Whitham equation, combining the dispersion relation of water waves and a nonlinearity of the shallow water equations, and modified to permit the effects of surface tension and constant vorticity. When the surface tension coefficient is large, we show that a periodic traveling wave of sufficiently small amplitude is unstable to long wavelength perturbations if the wave number is greater than a critical value, and stable otherwise, similarly to the Benjamin–Feir instability of gravity waves. In the case of weak surface tension, we find intervals of stable and unstable wave numbers, whose boundaries are associated with the extremum of the group velocity, the resonance between the first and second harmonics, the resonance between long and short waves, and a resonance between dispersion and the nonlinearity. For each constant vorticity, we show that a periodic traveling wave of sufficiently small amplitude is unstable if the wave number is greater than a critical value, and stable otherwise. Moreover it can be made stable for a sufficiently large vorticity. The results agree with those based upon numerical computations or formal multiple-scale expansions to the physical problem.

Vorticity transport and the leading-edge vortex of a plunging airfoil

The three-dimensional flow field was experimentally characterized for a nominally two-dimensional flat-plate airfoil plunging at large amplitude and reduced frequencies, using three-dimensional reconstructions of planar PIV data at a chord-based Reynolds number of 10,000. Time-resolved, instantaneous PIV measurements reveal that secondary vorticity, of opposite sign to the primary vortex, is intermittently entrained into the leading-edge vortex (LEV) throughout the downstroke, with the rate of entrainment increasing toward the end of the stroke when the leading-edge shear layer weakens. A planar vorticity transport analysis around the LEV indicated that, during the downstroke, the surface vorticity flux due to the pressure gradient is consistently about half that due to the leading-edge shear layer for all parameter values investigated, demonstrating that production and entrainment of secondary vorticity is an important mechanism regulating LEV strength. A small but non-negligible vorticity source was also attributed to spanwise flow toward the end of the downstroke. Aggregate vortex tilting is notably more significant for higher plunge frequencies, suggesting that the vortex core is more three-dimensional.

Impacts of Increasing Low-Level Shear on Supercells during the Early Evening Transition*

Abstract The dynamical response of simulated supercells to temporally increasing lower-tropospheric vertical wind shear is investigated using idealized simulations. These simulations are based upon observed soundings from two cases that underwent an early evening transition during the Second Verification of the Origins of Rotation in Tornadoes Experiment (VORTEX2). Mature supercells were simulated in observed afternoon environments with moderate vertical wind shear and then compared to simulated supercells experiencing observed evening increases in lower-tropospheric shear. The primary effect of the increase in low-level shear is to establish larger values of vertical vorticity at lower altitudes in the storm’s updraft. In turn, this leads to a nonlinear increase in the updraft strength due to the enhanced dynamic pressure minimum associated with larger vorticity in the storm’s mesocyclone. This is particularly important at low levels, where it increases the storm's ability to lift cool surface air (including outflow). Trajectories launched in developing vortices show that, despite comparable buoyant accelerations, parcels experience greater vertical velocity and stretching of vertical vorticity due to increased dynamic accelerations when the low-level shear is increased. Thus, even as low-level stability gradually increases in the early evening, the supercells’ low-level updraft intensity and surface vorticity production can increase. These results are consistent with climatological observations of a supercell’s likelihood of tornadogenesis during the early evening hours.

The Vorticity Balance of the Ocean Surface in Hawaii from a Regional Reanalysis

AbstractThe ocean surface vorticity budget around the Hawaiian Islands is examined using an 18-month model reanalysis generated using four-dimensional variational state estimation with all available observations (satellite, in situ, and high-frequency radio). To better resolve the ocean surface currents and reduce the representation error of the radio-measured surface currents, this study developed a new vertical scheme for the Regional Ocean Modeling System. A new, detailed description of the ocean surface vorticity is created, revealing a region dominated by cyclonic (anticyclonic) vorticity to the north (south) of the mean position of the Hawaii Lee Countercurrent. Advection of vorticity is the primary process that transports the vorticity generated in the lee of the islands by the wind wake. In this island lee, the zonal wavenumber spectra show a cascade of vorticity/energy from the submesoscale toward the larger scales. Latitudinal differences in the advection of vorticity spectra indicate the propagation of a first baroclinic mode Rossby wave in the region dominated by anticyclonic vorticity to the west of the island of Hawaii, while the region dominated by cyclonic vorticity is disrupted by the wake of the smaller islands.

The other optimal Stokes drag profile

AbstractThe lowest drag shape of fixed volume in Stokes flow has been known for some 40 years. It is front–back symmetric and similar to an American football with ends tangent to a cone of $60^{\circ }$. The analogous convex axisymmetric shape of fixed surface area, which may be of interest for particle design in chemistry and colloidal science, is characterised in this paper. This ‘other’ optimal shape has a surface vorticity proportional to the mean surface curvature, which is used with a local analysis of the flow near the tip to show that the front and rear ends are tangent to a cone of angle $30.8^{\circ }$. Using the boundary element method, we numerically represent the shape by expanding its tangent angle in terms decaying odd Legendre modes, and show that it has 11.3 % lower drag than a sphere of equal surface area, significantly more pronounced than for the fixed-volume optimal.

Velocity field, surface profile and curvature resolution of steep and short free-surface waves

On steep, millimeter-scale, 2D water waves, surface profile, and subsurface velocity field are measured with high-spatio-temporal resolution. This allows resolving surface vorticity, which is captured in the surface boundary layer and compared with its direct computation from interface curvature and velocity. Data are obtained with a combination of high-magnification time-resolved particle image velocimetry (PIV) and planar laser-induced fluorescence. The latter is used to resolve the surface profile and serves as a processing mask for the former. PIV processing schemes are compared to optimize accuracy locally, and profilometry data are treated to obtain surface curvature. This diagnostic enables new insights into free-surface dynamic, in particular, wave growth and surface vorticity generation, for flow regimes not studied previously. The technique is demonstrated on a high-speed water jet discharging in quiescent air at a Reynolds number of 4.8 × 104. Shear-layer instability below the surface leads to streamwise traveling waves with wavelength λ ~ 2 mm and steepness \(2\pi a / \lambda \ge 2.0\), where a is the crest to trough amplitude. Flow structures are resolved at these scales by recording at 16 kHz with a magnification of 4.

The Effects of Gap-Wind-Induced Vorticity, the Monsoon Trough, and the ITCZ on East Pacific Tropical Cyclogenesis

Abstract Tropical cyclogenesis in the eastern North Pacific (EPAC) basin is related to gap-wind-induced surface relative vorticity, the monsoon trough, and the intertropical convergence zone (ITCZ). There are several gaps in the Central American mountains, on the eastern edge of the EPAC basin, through which wind can be funneled to generate surface wind jets (gap winds). This study focuses on gap winds that occur over the Gulf of Papagayo and Gulf of Tehuantepec. Quick Scatterometer (QuikSCAT) 10-m equivalent neutral winds are used to identify gap wind events that occur during May through November of 2002–08. Dvorak fix locations, Gridded Satellite (GridSat) infrared (IR) data, and National Hurricane Center (NHC) tropical cyclone (TC) reports are used to track the disturbances during the study period. Surface vorticity is tracked using the QuikSCAT winds and the contribution of surface vorticity from the gap winds to the development of each disturbance is categorized as small, medium, or large. Cross-calibrated multiplatform surface wind data are used to verify the tracking of QuikSCAT-computed surface vorticity and to identify when the monsoon trough and the ITCZ are present. It is found that gap winds are present over the Gulf of Papagayo and Gulf of Tehuantepec for about 50% of the QuikSCAT coverage days and that these gap winds appear to contribute to the development of disturbances in the EPAC. Considerably more TCs form when the monsoon trough is present versus the ITCZ and the majority of the contributions from the gap winds also occur when the monsoon trough is present.

Steady flow past a sphere in an aligned magnetic field at high Reynolds numbers

The flow of steady, incompressible, viscous, electrically conducting fluid past a sphere in the presence of an uniform magnetic field parallel to the undisturbed flow is investigated using the finite difference method. The multigrid method with defect correction technique is used to achieve the second order accurate solution. The Hartmann number, M is used as the perturbation parameter. It is found that the increase of magnetic field decreases the wake length and increases the drag coefficient. The graphs of streamlines, vorticity lines, drag coefficient, surface pressure and surface vorticity are presented and discussed. Keywords: Navier-Stokes equations, MHD, Hartmann number, Multigrid method, Defect correctionInternational Journal of Engineering, Science and Technology, Vol. 6, No. 1, 2014, pp

Vortical Inviscid Flows with Two-Way Solid-Fluid Coupling

Vortex methods increasingly receive attention from the computer graphics community for simple and direct modeling of complex flow phenomena such as turbulence. The coupling between free-form solids, represented by arbitrary surface meshes, and fluids simulated with vortex methods, leads to visually rich simulations. In this paper, we introduce a novel approach for simulating the interaction between solids and inviscid fluids for high-quality simulations using Lagrangian vortex particles. The key aspect of our method is simulating the creation of vorticity at a solid's surface. While previous vortex simulators only focus on modeling the solid as a boundary for the fluid, our approach allows the accurate simulation of two processes of visual interest. The first is the introduction of surface vorticity in the main flow as turbulence (vortex shedding). The second is the motion of the solid induced by fluid forces. We also introduce to computer graphics the concept of source panels to model nonturbulent flow around objects. To the best of our knowledge, this is the first work on two-way coupling of 3D solids and fluids using Lagrangian vortex methods in computer graphics.

Modeling of ocean–atmosphere interaction phenomena during the breaking of modulated wave trains

Air water interaction phenomena taking place during the breaking of ocean waves are investigated here. The study is carried out by exploiting the combination between a potential flow method, which is used to describe the evolution of the wave system up to the onset of the modulational instability, and a two-fluids Navier–Stokes solver which describes the strongly non-linear air–water interaction taking place during breaking events. The potential flow method is based on a fully non-linear mixed Eulerian–Lagrangian approach, whereas the two-fluid model uses a level-set method for the interface capturing. The method is applied to study the evolution of a modulated wave train composed by a fundamental wave component with two side band disturbances. It is shown that breaking occurs when the initial steepness exceed a threshold value. Once the breaking starts, it is not just a single event but it is recurrent with a period associated to the group velocity. Results are presented in terms of free surface shapes, velocity and vorticity fields, energy and viscous dissipation. The analysis reveals the formation of large vortex structures in the air domain which are originated by the separation of the air flow at the crest of the breaking wave. The form drag associated to the flow separation process significantly contributes to the dissipation of the energy content of the wave system. The energy fraction dissipated by each breaking event is distinguished.

Numerical solutions for steady viscous flow past a circular cylinder in an aligned magnetic field

The steady incompressible Magneto-Hydrodynamic (MHD) flow past a circular cylinder with an aligned magnetic field is studied for the Reynolds number (Re) up to 100, using the Hartmann number M, as the perturbation parameter. The multigrid method with defect correction technique is used to achieve the second order accurate solution of complete nonlinear Navier-Stokes equations. The magnetic Reynolds number is assumed to be small. It is observed that the volume of the separation bubble decreases and drag coefficient increases as M is increased. The graphs of streamlines, vorticity lines, surface pressure, surface vorticity and drag coefficient are presented and the effect of magnetic field is discussed.

Diagnosis of high‐resolution upper ocean dynamics from noisy sea surface temperatures

The noise present in infrared satellite measurements of sea surface temperature (SST) hampers the use of surface quasi‐geostrophic (SQG) equations to diagnose ocean dynamics at high resolutions. Here we propose a methodology to reduce the contribution of noise when diagnosing surface vorticity, divergence, and vertical velocity from SST able to retain the dynamics at scales of a few kilometers. It is based on the use of denoising techniques with curvelets as basis functions and the application of a selective low‐pass filters to improve the reconstruction of surface upwelling/downwelling patterns. First, it is tested using direct numerical simulations of SQG turbulence and then applied to diagnose low‐frequency vertical velocity patterns from real MODIS (Moderate Resolution Imaging Spectroradiometer) images. The methodology here presented, which is not tied to the validity of SQG equations nor to the use of SST, is quite general and can be applied to a wide range of measurements and dynamical frameworks.

Weighted ensemble transform Kalman filter for image assimilation

ABSTRACTThis study proposes an extension of the Weighted Ensemble Kalman filter (WEnKF) proposed by Papadakis et al. (2010) for the assimilation of image observations. The main focus of this study is on a novel formulation of the Weighted filter with the Ensemble Transform Kalman filter (WETKF), incorporating directly as a measurement model a non-linear image reconstruction criterion. This technique has been compared to the original WEnKF on numerical and real world data of 2-D turbulence observed through the transport of a passive scalar. In particular, it has been applied for the reconstruction of oceanic surface current vorticity fields from sea surface temperature (SST) satellite data. This latter technique enables a consistent recovery along time of oceanic surface currents and vorticity maps in presence of large missing data areas and strong noise.

Influence of the hydrodynamic conditions on the accessibility of Aristeus antennatus and other demersal species to the deep water trawl fishery off the Balearic Islands (western Mediterranean)

Monthly catches per unit of effort (CPUE) of adult red shrimp (Aristeus antennatus), reported in the deep water bottom trawl fishery developed on the Sóller fishing ground off northern Mallorca (Western Mediterranean), and the mean ocean surface vorticity in the surrounding areas are compared between 2000 and 2010. A good correlation is found between the rises in the surrounding surface vorticity and the drops in the CPUE of the adult red shrimp. This correlation could be explained by assuming that most of the surface vorticity episodes could reach the bottom, increasing the seabed velocities and producing sediment resuspension, which could affect the near bottom water turbidity. A. antennatus would respond to this increased turbidity disappearing from the fishing grounds, probably moving downwards to the deeper waters. This massive displacement of red shrimp specimens away from the fishing grounds would consequently decrease their accessibility to fishing exploitation. Similar although more intense responses have been observed during the downslope shelf dense water current episodes that occurred in a submarine canyon, northeast of the Iberian peninsula. The proposed mechanism suggesting how the surface vorticity observed can affect the bottom sediments is investigated using a year-long moored near-bottom current meter and a sediment trap moored near the fishing grounds.The relationship between vorticity and catches is also explored for fish species (Galeus melastomus, Micromesistius poutassou, Phycis blennoides) and other crustacean (Geryon longipes and Nephrops norvegicus), considered as by-catch of the deep water fishery in the area. Results appear to support the suggestion that the water turbidity generated by the vorticity episodes is significant enough to affect the dynamics of the demersal species.

Controlled transitory stall on a pitching airfoil using pulsed actuation

Transitory separation control of a static and pitching 2-D airfoil is investigated in wind tunnel experiments using pulsed actuation on time scales that are an order of magnitude shorter than the characteristic convective time scale Tconv. Actuation is provided by momentary [O(0.05Tconv)] pulsed jets that are generated by a spanwise array of combustion-based actuators integrated in the center segment of the airfoil. The flow field in the center plane above the airfoil and in its near wake is computed from high-resolution PIV measurements in multiple overlapping cross-stream frames that are obtained phase-locked to the actuation and allow for tracking of vorticity concentrations. A single actuation pulse leads to a strong transitory increase in the circulation about the airfoil that is manifested by a partial collapse of the separated flow domain and is accompanied by the shedding of a large-scale clockwise vortex, and the attachment and accumulation of the surface vorticity layer behind it. The slow relaxation of the flow following termination of pulsed actuation returns the airfoil to full stall within 10Tconv. It is shown that repetition of actuation pulses within Tconv can increase the streamwise extent of the attached flow domain, and the trapped vorticity leads to a substantial increase in the peak transitory circulation before the flow separates again when the actuation is terminated. The coupling of the pulsed actuation to the airfoil’s motion enhances the actuation’s control authority. Single pulse can significantly increase the lift over most of the oscillation cycle both at post-stall and at angles of attack that are below stall. Several actuation pulses distributed during the pitch oscillation cycle can momentarily extend the accumulation of vorticity and thus increase the transitory and cycle-averaged lift, and improve the airfoil’s pitch stability.

Development of gas entrainment mitigation devices for PFBR hot pool

The phenomenon of argon gas entrainment into primary sodium in the hot pool of a liquid Sodium cooled Fast Reactor (SFR) is investigated. A combined experimental and computational approach is proposed. Physical entrainment of argon into sodium is highly geometry dependent and the present study is focused on the Indian Prototype Fast Breeder Reactor (PFBR). The computational model which is used for parametric studies is validated against a 1/4 scale water model tests. Based on systematic experiments, the free surface velocity for onset of gas entrainment is determined to be 0.32m/s, and the corresponding threshold value for the surface vorticity has been estimated as 8.3s−1.A horizontal baffle plate attached to inner vessel is found to reduce the free surface velocity/vorticity effectively. The radial width of the baffle plate and its elevation has been optimized to be 0.125m and 0.315m from free surface by computational studies. The optimized device has been tested in the water model to confirm its satisfactory performance before its recommendation for PFBR.