The Response of Balanced Hurricanes to Local Sources of Heat and Momentum

Shapiro, Lloyd J.; Willoughby, H. E.

doi:10.1175/1520-0469(1982)039<0378:trobht>2.0.co;2

Cited by 476 publications

(505 citation statements)

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“…The features of the contraction are in general agreement with the observations of Hurricane Gilbert (Black & Willoughby, 1992). While the outer band contracting dynamics is often argued to be an axisymmetric gradient-balanced process involving advection by the divergent part of the flow (Shapiro & Willoughby, 1982), Fig. 12 suggests that vorticity advection by the nondivergent part of the flow can also contribute to the contraction dynamics in the concentric eyewalls formation.…”

Section: Concentric Eyewall Cyclessupporting

confidence: 81%

Barotropic Aspects of Hurricane Structural and Intensity Variability

Hendricks¹,

Kuo²,

Peng³

et al. 2011

Recent Hurricane Research - Climate, Dynamics, and Societal Impacts

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and Intensity Variability 3 Diagnostic balance equationBy setting ∂δ/∂t = 0 in (4), and neglecting terms involving the velocity potential χ,t h e relationship between ψ and h is obtained. This is the nonlinear balance equation in polar coordinates. Equation (9) indicates that given ψ or h with appropriate boundary conditions, the other field which is in quasi-balance with that field may be obtained. Since P =(∇ 2 ψ + f )/h, equations (8) and (9) are sufficient to describe the quasi-balanced evolution of a shallow water vortex. By substituting h =( ∇ 2 ψ + f )/P into the right hand side of (9), an invertibility relationship is obtained, where ψ, h, ζ, u and v may be obtained diagnostically, given P. This invertibility principle is the reason P is such a useful dynamical quantity. The shallow water dynamics can be succintly speficied by one prognostic PV equation and a diagnostic relationship for the other quasi-balanced fields. For the special case of axisymmetric flow in which v = ∂ψ/∂r and u = −∂ψ/r∂φ = 0, equation (9) reduces toimplying that, when enforcing the boundary conditions,which is the gradient wind balance equation. In this context, (9) is a more general formulation of the gradient wind balance equation when the flow is both asymmetric and balanced. LinearizationEquations (3)-(5) cannot be solved analytically due to the nonlinear terms. However, under the assumption that perturbations are small in comparison to their means, a modified set of equations can be obtained that can be solved analytically. This process is referred to as linearization. In order to linearize (3)-(5), a basic state chosen here is that of an arbitrary axisymmetric vortexω(r)=v(r)/r that is in gradient balance with the heighth(r). While our basic state vortex is prescribed to be axisymmetric, the basic state could similarly be obtained by taking an azimuthal mean, i.e.,vand similar definitions hold for the other variables. ′ (r, φ, t), χ(r, φ, t)=χ ′ (r, φ, t),andψ(r, φ, t)=ψ ′ (r, φ, t). The perturbations u ′ , v ′ , ζ ′ ,andδ ′ are related to ψ ′ and χ ′ as above. Upon substituting the decomposed variables into (3)-(5), enforcing the gradient balance constraint, and neglecting higher order terms involving multiplication of perturbation quantities, we obtain the linearized versions of (3)-(5) which govern small amplitude disturbances about the basic state vortex, The decomposition for all variables is as follows: h(r)=h(r)+h ′ (r, φ, t), v(r)=v(r)+v ′ (r, φ, t), u(r)=u ′ (r, φ, t), ζ(r)=ζ(r)+ ζ ′ (r, φ, t), δ(r)=δwhereη = f +ζ is the basic state absolute vertical vorticity. We wish to understand the nature and behavior of small disturbances (i.e., waves) on this basic state vortex. Using the Wentzel-Kramers-Brillouin (WKB) approximation, we assume normal mode solutions of the form ψ ′ (r, φ, t)=ψ exp[i(kr + mφ − νt)], χ ′ (r, φ, t)=χ exp[i(kr + mφ − νt)],a n d h ′ (r, φ, t)=ĥ exp[i(kr + mφ − νt)],w h e r ek is the radial wavenumber (i.e., the number of wave crests per unit radial distance), m is the azimuthal wave number (i.e.,...

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Section: Concentric Eyewall Cyclessupporting

confidence: 81%

Barotropic Aspects of Hurricane Structural and Intensity Variability

Hendricks¹,

Kuo²,

Peng³

et al. 2011

Recent Hurricane Research - Climate, Dynamics, and Societal Impacts

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“…More general derivations of this equation are found, for example, in Willoughby (1979), Shapiro and Willoughby (1982) and Smith et al (2005). The SE equation is elliptic if the vortex is symmetrically stable (i.e.…”

Section: Balanced Hurricane Modelsmentioning

confidence: 98%

Balanced boundary layers used in hurricane models

Smith¹,

Montgomery

2008

Quart J Royal Meteoro Soc

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ABSTRACT:We examine the formulation and accuracy of various approximations made in representing the boundary layer in simple axisymmetric hurricane models, especially those that assume strict gradient wind balance in the radial direction. Approximate solutions for a steady axisymmetric slab boundary-layer model are compared with a full model solution. It is shown that the approximate solutions are generally poor in the inner core region of the vortex, where the radial advection term in the radial momentum equation is important and cannot be neglected. These results affirm some prior work and have implications for a range of theoretical studies of hurricane dynamics, including theories of potential intensity, that employ balanced boundary-layer formulations.

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“…Un formalisme reposant sur l'hypothèse de l'équilibre du « vent gradient » entre le champ de température et le vent tangentiel permet de rendre compte de la structure axisymétrique du coeur du cyclone (Shapiro et Willoughby, 1982). On distingue la circulation primaire (tangentielle) et la circulation secondaire (radiale et verticale), cette dernière étant moins intense d'un ordre de grandeur environ.…”

Section: Structure à Maturité Et éVolutionunclassified

Les cyclones tropicaux

Roux¹,

Viltard²

1997

Météorologie

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The Response of Balanced Hurricanes to Local Sources of Heat and Momentum

Cited by 476 publications

References 0 publications

Barotropic Aspects of Hurricane Structural and Intensity Variability

Barotropic Aspects of Hurricane Structural and Intensity Variability

Balanced boundary layers used in hurricane models

Les cyclones tropicaux

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