Secondary circulations in rotating-flow boundary layers

Rotunno, Richard

doi:10.22499/2.6401.004

Cited by 14 publications

(7 citation statements)

References 28 publications

(40 reference statements)

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“…In the case of tropical cyclones, such an eye is readily identified in satellite images by the absence of cloud cover. Despite their common appearance, there is still little agreement as to the mechanisms of eye formation [3][4][5], and indeed it is not even clear that the same basic mechanisms are responsible in different classes of atmospheric vortices [6]. In the absence of such a fundamental understanding, one cannot reliably predict when eyes should, or should not, form.…”

Section: Introductionmentioning

confidence: 99%

Formation of eyes in large-scale cyclonic vortices

2018

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We present numerical simulations of steady, laminar, axisymmetric convection of a Boussinesq fluid in a shallow, rotating, cylindrical domain. The flow is driven by an imposed vertical heat flux and shaped by the background rotation of the domain. The geometry is inspired by that of tropical cyclones and the global flow pattern consists of a shallow, swirling vortex combined with a poloidal flow in the r − z plane which is predominantly inward near the bottom boundary and outward along the upper surface. Our numerical experiments confirm that, as suggested by [1], an eye forms at the centre of the vortex which is reminiscent of that seen in a tropical cyclone and is characterised by a local reversal in the direction of the poloidal flow. We establish scaling laws for the flow and map out the conditions under which an eye will, or will not, form. We show that, to leading order, the velocity scales with V = (αgβ) 1/2 H, where g is gravity, α the expansion coefficient, β the background temperature gradient, and H is the depth of the domain. We also show that the two most important parameters controlling the flow are Re = V H/ν and Ro = V / (ΩH), where Ω is the background rotation rate and ν the viscosity. The Prandtl number and aspect ratio also play an important, if secondary, role. Finally, and most importantly, we establish the criteria required for eye formation. These consist of a lower bound on Re, upper and lower bounds on Ro, and an upper bound on Ekman number.

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Section: Introductionmentioning

confidence: 99%

Formation of eyes in large-scale cyclonic vortices

2018

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“…3c,3d,8c,and 8d in LWL20. This alternative inflow-outflow-inflow (and the associated subgradient-supergradient-subgradient wind) structure is the well-known inertial oscillation of a rotating flow with a frictional boundary layer or a process related to the gradient wind adjustment comprehended in the literature (e.g., Rotunno 2014;Stern et al 2020). Since the outflowing supergradient air becomes subgradient near the RMW and thus does not spin up the tangential wind therein.…”

Section: Main Mechanism For Axisymmetric Tc Intensificationmentioning

confidence: 97%

Reply to “Comments on ‘How Much Does the Upward Advection of the Supergradient Component of Boundary Layer Wind Contribute to Tropical Cyclone Intensification and Maximum Intensity?’”

Wang

2020

Journal of the Atmospheric Sciences

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This is a reply to the comments by Smith et al. (2020, hereafter SGM20) on the work of Li et al. (2020, hereafter LWL20) recently published in the Journal of the Atmospheric Sciences. All the comments and concerns by SGM20 have been well addressed or clarified. We think that most of the comments by SGM20 are not in line with the intention of LWL20 and provide one-sided and thus little scientifically meaningful arguments. Regarding the comment on the adequacy of the methodology adopted in LWL20, we believe that the design of the thought (sensitivity) experiment is adequate to address the scientific issue under debate and helps quantify the contribution by the upward advection of the supergradient component of boundary layer wind to tropical cyclone intensification, which is shown to be very marginal. Note that we are open to accept any alternative, better methods to be used to further address this scientific issue.

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“…[1,2] make three additional assumptions. We will make the same assumptions here so as not to introduce additional complexity when comparing with their published solutions: (1) in evaluating V(r, z) from the azimuthally-averaged tangential wind in the WRF model, we take its value at 490 m altitude and extend that value downward so as to be independent of z below 490 m; (2) we assume a stress-free boundary condition on the disturbance horizontal velocity at z = 0; (3) we neglect the F r forcing term, and its vertical counterpart F z , keeping only F λ and Q, i.e., using only Equations (6) and (10).…”

Section: A Forced Axisymmetric Convective Ring Model Revisitedmentioning

confidence: 99%

“…The time derivatives are computed as centered differences using data at hours 28 and 26. No formal accuracy is lost here by using the residual method because it has the same accuracy as a direct evaluation of F λ and Q from Equations (5), (6) and (10). (To address a possible question about the potential inaccuracy of the residual method, for obtaining the partial time derivative terms using relatively coarse (1 h) model output, we have found that in Equations (12) and (13), the forcing terms F λ and Q are dominated by the vertical and horizontal advection terms, and are relatively insensitive to the time derivatives and therefore still less sensitive to the precise time interval used to evaluate the finite differences.…”

Section: A Forced Axisymmetric Convective Ring Model Revisitedmentioning

confidence: 99%

On the Applicability of Linear, Axisymmetric Dynamics in Intensifying and Mature Tropical Cyclones

Montgomery

Smith

2017

Fluids

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Abstract:The applicability of linearized axisymmetric dynamics to the intensification and structure change of tropical cyclones is investigated. The study is motivated by recent work that presented axisymmetric solutions to the linearized, non-hydrostatic, vortex-anelastic equations of motion (the so-called 3DVPAS model). The work called into question the importance of a recently proposed nonlinear, system-scale boundary-layer spinup mechanism both in intensifying storms and in mature storms undergoing secondary eyewall formation. The issue is examined using a three-dimensional mesoscale simulation of an intensifying tropical cyclone, alongside the linear 3DVPAS model. Solutions to the linear model, for imposed eddy forcing terms derived from the mesoscale simulation, are shown to be valid only for short times (t < 1 h) in the inner-core region of the vortex. At later times, the neglected nonlinear terms become significant and the linear results invalid. It follows that the linear results cannot be used to describe all aspects of the tropical cyclone dynamics at later times. In particular, they cannot be used (a) to dismiss the importance of the nonlinear boundary-layer spinup mechanism, nor (b) to isolate the separate effects of diabatic heating from those of friction, within the nonlinear boundary layer at least. Such separation depends on the linear superposition principle, which fails whenever nonlinearity is important. Similar caveats apply to the use of another linear model, the traditional Sawyer-Eliassen balance model. Its applicability is limited not only by linearity, but also by its assumption of strictly balanced motion. Both are incompatible with nonlinear spinup.

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Secondary circulations in rotating-flow boundary layers

Cited by 14 publications

References 28 publications

Formation of eyes in large-scale cyclonic vortices

Formation of eyes in large-scale cyclonic vortices

Reply to “Comments on ‘How Much Does the Upward Advection of the Supergradient Component of Boundary Layer Wind Contribute to Tropical Cyclone Intensification and Maximum Intensity?’”

On the Applicability of Linear, Axisymmetric Dynamics in Intensifying and Mature Tropical Cyclones

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