Helicity, superhelicity and weighted relative potential vorticity: Useful diagnostic pseudoscalars?

Hide, R.

doi:10.1002/qj.200212858318

Cited by 44 publications

(9 citation statements)

References 24 publications

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“…This coincidence is not only the result of shear-enhanced secondary circulation, as noted in Vollaro (2008, 2010), but also comes from a balance adjustment because of the vortex tilt. This is consistent with theoretical studies of helicity dynamics suggesting that helicity is closely related with temperature advection (Tan and Wu 1994) and upward motion (Hide 2002).…”

Section: Discussionsupporting

confidence: 91%

“…This confirms that the positive local helicity not only coincides with upward motion but is also in phase with warm advection in the framework of balanced dynamics. Hide (2002) derived a relationship between helicity and vertical motion for geostrophic adiabatic flows. This relationship relates helicity H directly with vertical motion w according to H 5 N 2 w/(2f ), in which N is the Brunt-Väisälä frequency and f is the vertical component of planetary rotation.…”

Section: B Kinematic and Thermodynamic Structurementioning

confidence: 99%

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The Evolution of Vortex Tilt and Vertical Motion of Tropical Cyclones in Directional Shear Flows

Tan

Qiu

2018

J. Atmos. Sci.

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Recent studies have demonstrated the importance of moist dynamics on the intensification variability of tropical cyclones (TCs) in directional shear flows. Here, we propose that dry dynamics can account for many aspects of the structure change of TCs in moist simulations. The change of vortex tilt with height and time essentially determines the kinematic and thermodynamic structure of TCs experiencing directional shear flows, depending on how the environmental flow rotates with height, that is, in a clockwise (CW) or counterclockwise (CC) fashion. The vortex tilt precesses faster and is closer to the left-of-shear (with respect to the deep-layer shear) region, with a smaller magnitude at equilibrium in CW hodographs than in CC hodographs. The low-level vortex tilt and accordingly more low-level upward motions are ahead of the overall vortex tilt in CW hodographs but are behind the overall vortex tilt in CC hodographs. Such a configuration of vortex tilt in CW hodographs is potentially favorable for the continuous precession of convection into the upshear region but in CC hodographs it is unfavorable. Most of the upward motions within a TC undergoing CW shear are concentrated in the downshear-left region, whereas those in the CC shear are located in the downshear-right region. Moreover, the upward (downward) motions are in phase with positive (negative) local helicity in both CW and CC hodographs. Here, we present an alternative mechanism that is associated with balanced dynamics in response to vortex tilt to explain the coincidence and also the distribution variability of vertical motions, as well as local helicity in directional shear flows. The balanced dynamics could explain the overlap of positive helicity and convection in both moist simulations and observations.

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Section: Discussionsupporting

confidence: 91%

Section: B Kinematic and Thermodynamic Structurementioning

confidence: 99%

The Evolution of Vortex Tilt and Vertical Motion of Tropical Cyclones in Directional Shear Flows

Tan

Qiu

2018

J. Atmos. Sci.

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“…Furthermore, stratification is seen as playing an essential role in the formation and structure of submarine turbidity currents, as measured and analyzed in Azpiroz‐Zabala et al (), leading to sediment suspension and transport for long distances. Helicity is produced by hydrostatic and geostrophic balance between the Coriolis force, gravity, and pressure gradients, while neglecting the nonlinear advection term (Hide, ; Marino et al, ). In tropical storms, helicity is associated with the presence of coherent structures in the form of roll vortices in the boundary layer of typhoons, structures which are linked with inflection point shear instabilities (Morrison et al, ).…”

Section: The Role Of Kinetic Helicitymentioning

confidence: 99%

Helicity Dynamics, Inverse, and Bidirectional Cascades in Fluid and Magnetohydrodynamic Turbulence: A Brief Review

Pouquet

Rosenberg

Stawarz

et al. 2019

Earth and Space Science

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We briefly review helicity dynamics, inverse and bidirectional cascades in fluid and magnetohydrodynamic (MHD) turbulence, with an emphasis on the latter. The energy of a turbulent system, an invariant in the nondissipative case, is transferred to small scales through nonlinear mode coupling. Fifty years ago, it was realized that, for a two‐dimensional fluid, energy cascades instead to larger scales and so does magnetic excitation in MHD. However, evidence obtained recently indicates that, in fact, for a range of governing parameters, there are systems for which their ideal invariants can be transferred, with constant fluxes, to both the large scales and the small scales, as for MHD or rotating stratified flows, in the latter case including quasi‐geostrophic forcing. Such bidirectional, split, cascades directly affect the rate at which mixing and dissipation occur in these flows in which nonlinear eddies interact with fast waves with anisotropic dispersion laws, due, for example, to imposed rotation, stratification, or uniform magnetic fields. The directions of cascades can be obtained in some cases through the use of phenomenological arguments, one of which we derive here following classical lines in the case of the inverse magnetic helicity cascade in electron MHD. With more highly resolved data sets stemming from large laboratory experiments, high‐performance computing, and in situ satellite observations, machine learning tools are bringing novel perspectives to turbulence research. Such algorithms help devise new explicit subgrid‐scale parameterizations, which in turn may lead to enhanced physical insight, including in the future in the case of these new bidirectional cascades.

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“…with Z H the helical enstrophy (sometimes called superhelicity [44]), a pseudoscalar as helicity itself. Note that, locally (as opposed to globally), helicity can be produced through alignment of vorticity and shear [45].…”

Section: A the Temporal Decay Of Helicitymentioning

confidence: 99%

Helicity dynamics in stratified turbulence in the absence of forcing

et al. 2013

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A numerical study of decaying stably stratified flows is performed. Relatively high stratification (Froude number ≈ 10 −2 -10 −1 ) and moderate Reynolds (Re) numbers (Re ≈ 3-6 × 10 3 ) are considered and a particular emphasis is placed on the role of helicity (velocity-vorticity correlations), which is not an invariant of the nondissipative equations. The problem is tackled by integrating the Boussinesq equations in a periodic cubical domain using different initial conditions: a nonhelical Taylor-Green (TG) flow, a fully helical Beltrami [ArnoldBeltrami-Childress (ABC)] flow, and random flows with a tunable helicity. We show that for stratified ABC flows helicity undergoes a substantially slower decay than for unstratified ABC flows. This fact is likely associated to the combined effect of stratification and large-scale coherent structures. Indeed, when the latter are missing, as in random flows, helicity is rapidly destroyed by the onset of gravitational waves. A type of large-scale dissipative "cyclostrophic" balance can be invoked to explain this behavior. No production of helicity is observed, contrary to the case of rotating and stratified flows. When helicity survives in the system, it strongly affects the temporal energy decay and the energy distribution among Fourier modes. We discover in fact that the decay rate of energy for stratified helical flows is much slower than for stratified nonhelical flows and can be considered with a phenomenological model in a way similar to what is done for unstratified rotating flows. We also show that helicity, when strong, has a measurable effect on the Fourier spectra, in particular at scales larger than the buoyancy scale, for which it displays a rather flat scaling associated with vertical shear, as observed in the planetary boundary layer.

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Helicity, superhelicity and weighted relative potential vorticity: Useful diagnostic pseudoscalars?

Cited by 44 publications

References 24 publications

The Evolution of Vortex Tilt and Vertical Motion of Tropical Cyclones in Directional Shear Flows

The Evolution of Vortex Tilt and Vertical Motion of Tropical Cyclones in Directional Shear Flows

Helicity Dynamics, Inverse, and Bidirectional Cascades in Fluid and Magnetohydrodynamic Turbulence: A Brief Review

Helicity dynamics in stratified turbulence in the absence of forcing

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