scholarly journals Asymmetries in vertical vorticity and vertical velocity arising during nonlinear homogeneous spindown

2012 ◽  
Vol 24 (7) ◽  
pp. 076601 ◽  
Author(s):  
J. A. Benthuysen ◽  
L. N. Thomas
Keyword(s):  
Vertical Velocity ◽  
Vertical Vorticity

Experimental and numerical investigation of turbulent convection in a rotating cylinder

2009 ◽  
Vol 642 ◽  
pp. 445-476 ◽  
Author(s):  
R. P. J. KUNNEN ◽  
B. J. GEURTS ◽  
H. J. H. CLERCX
Keyword(s):  
Temperature Gradient ◽  
Boundary Layers ◽  
Power Law ◽  
Vertical Velocity ◽  
Stereoscopic Particle Image Velocimetry ◽  
Turbulent Heat Transfer ◽  
Bulk Temperature ◽  
Rossby Number ◽  
Cyclonic Vorticity ◽  
Vertical Vorticity

The effects of an axial rotation on the turbulent convective flow because of an adverse temperature gradient in a water-filled upright cylindrical vessel are investigated. Both direct numerical simulations and experiments applying stereoscopic particle image velocimetry are performed. The focus is on the gathering of turbulence statistics that describe the effects of rotation on turbulent Rayleigh–Bénard convection. Rotation is an important addition, which is relevant in many geophysical and astrophysical flow phenomena.A constant Rayleigh number (dimensionless strength of the destabilizing temperature gradient) Ra = 109 and Prandtl number (describing the diffusive fluid properties) σ = 6.4 are applied. The rotation rate, given by the convective Rossby number Ro (ratio of buoyancy and Coriolis force), takes values in the range 0.045 ≤ Ro ≤ ∞, i.e. between rotation-dominated flow and zero rotation. Generally, rotation attenuates the intensity of the turbulence and promotes the formation of slender vertical tube-like vortices rather than the global circulation cell observed without rotation. Above Ro ≈ 3 there is hardly any effect of the rotation on the flow. The root-mean-square (r.m.s.) values of vertical velocity and vertical vorticity show an increase when Ro is lowered below Ro ≈ 3, which may be an indication of the activation of the Ekman pumping mechanism in the boundary layers at the bottom and top plates. The r.m.s. fluctuations of horizontal and vertical velocity, in both experiment and simulation, decrease with decreasing Ro and show an approximate power-law behaviour of the shape Ro0.2 in the range 0.1 ≲ Ro ≲ 2. In the same Ro range the temperature r.m.s. fluctuations show an opposite trend, with an approximate negative power-law exponent Ro−0.32. In this Rossby number range the r.m.s. vorticity has hardly any dependence on Ro, apart from an increase close to the plates for Ro approaching 0.1. Below Ro ≈ 0.1 there is strong damping of turbulence by rotation, as the r.m.s. velocities and vorticities as well as the turbulent heat transfer are strongly diminished. The active Ekman boundary layers near the bottom and top plates cause a bias towards cyclonic vorticity in the flow, as is shown with probability density functions of vorticity. Rotation induces a correlation between vertical vorticity and vertical velocity close to the top and bottom plates: near the top plate downward velocity is correlated with positive/cyclonic vorticity and vice versa (close to the bottom plate upward velocity is correlated with positive vorticity), pointing to the vortical plumes. In contrast with the well-mixed mean isothermal bulk of non-rotating convection, rotation causes a mean bulk temperature gradient. The viscous boundary layers scale as the theoretical Ekman and Stewartson layers with rotation, while the thermal boundary layer is unaffected by rotation. Rotation enhances differences in local anisotropy, quantified using the invariants of the anisotropy tensor: under rotation there is strong turbulence anisotropy in the centre, while near the plates a near-isotropic state is found.

Decay laws, anisotropy and cyclone–anticyclone asymmetry in decaying rotating turbulence

2010 ◽  
Vol 666 ◽  
pp. 5-35 ◽  
Author(s):  
F. MOISY ◽  
C. MORIZE ◽  
M. RABAUD ◽  
J. SOMMERIA
Keyword(s):  
Vertical Velocity ◽  
Large Scale ◽  
Large Time ◽  
Initial Conditions ◽  
Shear Instability ◽  
Vorticity Field ◽  
Rotating Platform ◽  
Velocity Fluctuations ◽  
Vertical Vorticity ◽  
Rotating Turbulence

The effect of a background rotation on the decay of grid-generated turbulence is investigated from experiments using the large-scale ‘Coriolis’ rotating platform. A first transition occurs at 0.4 tank rotation (instantaneous Rossby number Ro ≃ 0.25), characterized by a t−6/5 → t−3/5 transition of the energy-decay law. After this transition, anisotropy develops in the form of vertical layers, where the initial vertical velocity fluctuations remain trapped. The vertical vorticity field develops a cyclone–anticyclone asymmetry, reproducing the growth law of the vorticity skewness, Sω(t) ≃ (Ωt)0.7, reported by Morize, Moisy & Rabaud (Phys. Fluids, vol. 17 (9), 2005, 095105). A second transition is observed at larger time, characterized by a return to vorticity symmetry. In this regime, the layers of nearly constant vertical velocity become thinner as they are advected and stretched by the large-scale horizontal flow, and eventually become unstable. The present results indicate that the shear instability of the vertical layers contributes significantly to the re-symmetrization of the vertical vorticity at large time, by re-injecting vorticity fluctuations of random sign at small scales. These results emphasize the importance of the nature of the initial conditions in the decay of rotating turbulence.

scholarly journals Observing and quantifying ocean flow properties using drifters with drogues at different depths

2021 ◽  
Author(s):  
Irina I. Rypina ◽  
Timothy R. Getscher ◽  
Larry J. Pratt ◽  
Baptiste Mourre
Keyword(s):  
Vertical Velocity ◽  
Finite Size ◽  
Vertical Shear ◽  
Vertical Vorticity ◽  
Significant Term ◽  
True Model ◽  
Different Depths ◽  
Multi Level ◽  
True Values ◽  
Vorticity Balance

<p>We present analyses of drifters with drogues at 1, 10, 30 and 50 m, which were deployed in the Mediterranean Sea to investigate subduction and upwelling processes. Drifter trajectories were used to estimate divergence, vorticity, vertical velocity, and finite-size Lyapunov exponents (FTLEs), and to investigate the magnitudes of terms in the vertical vorticity equation. The divergence and vorticity are O(f) and change sign along trajectories. Vertical velocity is O(1 mm/s), is larger at depth, indicates predominant upwelling with isolated downwelling events, and sometimes changes sign between 1 and 50 m. Vortex stretching is one of, but not the only, significant term in the vertical vorticity balance. 2D FTLEs are 2x10^(-5) 1/s after 1 day, about twice larger than in a 400-m-resolution numerical model. 3D FTLEs are 50% larger than 2D FTLEs and are dominated by the vertical shear of horizontal velocity. Bootstrapping-based uncertainty for both divergence and vorticity is ~10% of the time-mean absolute values. Simulated drifters in a model suggest that drifter-based divergence and vorticity are close to true model values, except when drifters get aligned into long and narrow filaments. Drifter-based vertical velocity is close to true values in the model at 1 m but differs from the true model values at deeper depths. The errors in the vertical velocity are largely due to the lateral separation between drifters at different depths, and partially due to having drifters at only 4 depths. Overall, multi-level drifters provided useful information about the 3D flow structure.</p>

scholarly journals Diagnosing Mesoscale Vertical Motion from Horizontal Velocity and Density Data

2005 ◽  
Vol 35 (10) ◽  
pp. 1744-1762 ◽  
Author(s):  
Enric Pallàs Sanz ◽  
Álvaro Viúdez
Keyword(s):  
Vertical Velocity ◽  
Extreme Values ◽  
Vertical Motion ◽  
Shear Velocity ◽  
Horizontal Velocity ◽  
Vertical Shear ◽  
Coriolis Parameter ◽  
Vertical Vorticity ◽  
Omega Equation ◽  
Q Vector

Abstract The mesoscale vertical velocity is obtained by solving a generalized omega equation (ω equation) using density and horizontal velocity data from three consecutive quasi-synoptic high-resolution surveys in the Alboran Sea. The Atlantic Jet (AJ) and the northern part of the Western Alboran Gyre (WAG) were observed as a large density anticyclonic front extending down to 200–230 m. The horizontal velocity uh in the AJ reached maxima of 1.2 m s−1 for the three surveys, with extreme Rossby numbers of ζ/f ≈ −0.9 in the WAG and +0.9 in the AJ (where ζ is the vertical vorticity and f is the Coriolis parameter). The generalized ω equation includes the ageostrophic horizontal flow. It is found that the most important “forcing” term in this equation is ( fζph + ∇hϱ) · ∇2huh, where ζph is the horizontal (pseudo) vorticity and ϱ is the buoyancy. This term is related to the horizontal advection of vertical vorticity by the vertical shear velocity, uhz · ∇hζ. Extreme values of the diagnosed vertical velocity w were located at 80–100 m with max{w} ⊂ [34, 45] and min{w} ⊂ [−64, −34] m day−1. Comparison with the quasigeostrophic (QG) ω equation shows that, because of the large Rossby numbers, non-QG terms are important. The differences between w and the QG vertical velocity are mainly related to the divergence of the ageostrophic part of the total Q vector (Qh ≡ ∇huh · ∇hϱ) in the ω equation.

Impact of a Vertical Vorticity Constraint in Variational Dual-Doppler Wind Analysis: Tests with Real and Simulated Supercell Data

2012 ◽  
Vol 29 (1) ◽  
pp. 32-49 ◽  
Author(s):  
Corey K. Potvin ◽  
Alan Shapiro ◽  
Ming Xue
Keyword(s):  
Vertical Velocity ◽  
Three Dimensional ◽  
Mass Conservation ◽  
Vorticity Equation ◽  
Vertical Vorticity ◽  
Advanced Regional Prediction System ◽  
Supercell Storm ◽  
Radar Networks ◽  
Regional Prediction ◽  
The Impact

Abstract One of the greatest challenges to dual-Doppler retrieval of the vertical wind is the lack of low-level divergence information available to the mass conservation constraint. This study examines the impact of a vertical vorticity equation constraint on vertical velocity retrievals when radar observations are lacking near the ground. The analysis proceeds in a three-dimensional variational data assimilation (3DVAR) framework with the anelastic form of the vertical vorticity equation imposed along with traditional data, mass conservation, and smoothness constraints. The technique is tested using emulated radial wind observations of a supercell storm simulated by the Advanced Regional Prediction System (ARPS), as well as real dual-Doppler observations of a supercell storm that occurred in Oklahoma on 8 May 2003. Special attention is given to procedures to evaluate the vorticity tendency term, including spatially variable advection correction and estimation of the intrinsic evolution. Volume scan times ranging from 5 min, typical of operational radar networks, down to 30 s, achievable by rapid-scan mobile radars, are considered. The vorticity constraint substantially improves the vertical velocity retrievals in our experiments, particularly for volume scan times smaller than 2 min.

scholarly journals Multiple-Doppler Radar Observations of the Evolution of Vorticity Extrema in a Convective Boundary Layer

2006 ◽  
Vol 134 (1) ◽  
pp. 355-374 ◽  
Author(s):  
Paul Markowski ◽  
Christina Hannon
Keyword(s):  
Boundary Layer ◽  
Vertical Velocity ◽  
Convective Boundary Layer ◽  
Doppler Radar ◽  
Vertical Wind Shear ◽  
Evolutionary Stage ◽  
Convective Boundary ◽  
Vertical Vorticity ◽  
Complex Interactions ◽  
Convection Initiation

Abstract Overdetermined, dual-Doppler wind syntheses are used to document the evolution, structure, and dynamics of vertical vorticity extrema observed in a convective boundary layer during the 12 June 2002 International H2O Project (IHOP) mission. Discrete vertical vorticity extrema having horizontal scales of 1–2 km can be observed continuously for periods exceeding an hour. The evolution of the vorticity field is characterized by complex interactions among vorticity extrema and between the vertical vorticity and vertical velocity fields. The most prominent vorticity maxima have amplitudes of approximately 0.01 s−1 and are associated with retrieved pressure deficits of order 0.1 mb. The vorticity extrema weaken with height and tilt in the presence of vertical wind shear. Advection and propagation both contribute substantially to the motion of the vorticity extrema. Amplifications of vertical vorticity are closely linked to the intensification of updrafts. Both stretching and tilting can contribute significantly to the vorticity budgets of the air parcels comprising the vorticity extrema, and their relative importance varies with elevation, evolutionary stage, and from one vorticity extremum to another. It is therefore difficult to generalize about the dynamics of the vorticity extrema. It also is difficult to generalize about the helicity of the vorticity maxima and suppression of mixing for similar reasons. The weakening of vertical vorticity extrema is closely tied to the weakening of updrafts. In some cases, downward-directed vertical pressure gradient forces due to vertical gradients of rotation bring about updraft weakening and vorticity demise. An improved understanding of the nature of boundary layer vortices could have large relevance to convection initiation owing to feedbacks between vertical velocity and vorticity.

The Origins of Vortex Sheets in a Simulated Supercell Thunderstorm

2014 ◽  
Vol 142 (11) ◽  
pp. 3944-3954 ◽  
Author(s):  
Paul Markowski ◽  
Yvette Richardson ◽  
George Bryan
Keyword(s):  
Vertical Velocity ◽  
Large Body ◽  
Lower Boundary ◽  
Vortex Sheet ◽  
Horizontal Gradient ◽  
Vortex Sheets ◽  
Vertical Vorticity ◽  
Supercell Storms ◽  
Gust Fronts ◽  
Homogeneous Environment

Abstract This paper investigates the origins of the (cyclonic) vertical vorticity within vortex sheets that develop within a numerically simulated supercell in a nonrotating, horizontally homogeneous environment with a free-slip lower boundary. Vortex sheets are commonly observed along the gust fronts of supercell storms, particularly in the early stages of storm development. The “collapse” of a vortex sheet into a compact vortex is often seen to accompany the intensification of rotation that occasionally leads to tornadogenesis. The vortex sheets predominantly acquire their vertical vorticity from the tilting of horizontal vorticity that has been modified by horizontal buoyancy gradients associated with the supercell’s cool low-level outflow. If the tilting is within an ascending airstream (i.e., the horizontal gradient of vertical velocity responsible for the tilting resides entirely within an updraft), the vertical vorticity of the vortex sheet nearly vanishes at the lowest model level for horizontal winds (5 m). However, if the tilting occurs within a descending airstream (i.e., the horizontal gradient of vertical velocity responsible for tilting includes a downdraft adjacent to the updraft within which the majority of the cyclonic vorticity resides), the vortex sheet extends to the lowest model level. The findings are consistent with the large body of prior work that has found that downdrafts are necessary for the development of significant vertical vorticity at the surface.

Combining SAR interferometry and the equation of continuity to estimate the three-dimensional glacier surface-velocity vector

1999 ◽  
Vol 45 (151) ◽  
pp. 533-538 ◽  
Author(s):  
Niels Reeh ◽  
Søren Nørvang Madsen ◽  
Johan Jakob Mohr
Keyword(s):  
Steady State ◽  
Mass Balance ◽  
Vertical Velocity ◽  
Velocity Vector ◽  
Thickness Distribution ◽  
Vertical Surface ◽  
Horizontal Velocity ◽  
Sar Interferometry ◽  
Surface Velocity ◽  
Ice Thickness

AbstractUntil now, an assumption of surface-parallel glacier flow has been used to express the vertical velocity component in terms of the horizontal velocity vector, permitting all three velocity components to be determined from synthetic aperture radar interferometry. We discuss this assumption, which neglects the influence of the local mass balance and a possible contribution to the vertical velocity arising if the glacier is not in steady state. We find that the mass-balance contribution to the vertical surface velocity is not always negligible as compared to the surface-slope contribution. Moreover, the vertical velocity contribution arising if the ice sheet is not in steady state can be significant. We apply the principle of mass conservation to derive an equation relating the vertical surface velocity to the horizontal velocity vector. This equation, valid for both steady-state and non-steady-state conditions, depends on the ice-thickness distribution. Replacing the surface-parallel-flow assumption with a correct relationship between the surface velocity components requires knowledge of additional quantities such as surface mass balance or ice thickness.

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