The Tropical Cyclone Boundary Layer 2: Dynamics

The Centre for Australian Weather and Climate ResearchA partnership between CSIRO and the Bureau of Meteorology

The Tropical Cyclone Boundary Layer2: Dynamics

Jeff Kepert

Head, High Impact Weather Research

Oct 2013

www.cawcr.gov.au

The Centre for Australian Weather and Climate Research A partnership between CSIRO and the Bureau of Meteorology

• Turbulence time scales are short (< 1 hour)• Cyclone evolves slowly (~ 10 hours to days)• Assume that boundary layer flow in tropical cyclones is the response to

• Conditions above the boundary layer (gradient wind, stability structure)

• Surface conditions (roughness, fluxes)

• One side of two-way interaction• Approach successful for marine boundary layer theory

• except for strong horizontal advection

• needs modification over land where diurnal effects are strong


Theoretical framework

BL affects the TC:• distribution of updraft• thermodynamic properties of updraft• dynamic properties of updraft

TC affects the BL:• distribution of gradient wind / pressure• large-scale divergence asymmetry• turbulent fluxes through top• convective downdrafts

Ignore Keep (some of)



Types of models

• Full nonlinear equations, asymmetric (Kepert and Wang 2001)• Linearised equations, asymmetric (Rosenthal 1962, Kepert 2001)• Depth-averaged equations, nonlinear, asymmetric (Shapiro 1983,

Smith 2003, Smith and Vogl 2008)• Depth-averaged equations, nonlinear, symmetric (Smith 2003, Smith

and Vogl 2008)• Depth-averaged equations, linear, symmetric (Ooyama 1969, Emanuel

1986)• Prescribed vertical structure, symmetric (Smith 1968, Kuo 1971, Kepert

2010)• One-dimensional (Moss and Rosenthal 1975, Powell 1980)

• Most of these models study the response to an imposed, steady, tropical cyclone-like pressure field.

• See Kepert (2010, QJRMS) for additional references.


Angular momentum

axisy

mm

etric

axisy

mm

etric

invisc

id

Absolute angular momentum is conserved for inviscid flow


The full BL model

• Solves the thermodynamic and momentum budget equations over a domain that is hundreds of km across and a few km deep

• Upper boundary conditions represent all the effects of the TC on the BL

• Prescribed pressure / gradient wind

• Storm motion

• Convection

• Turbulent transfer

• Asymmetries (including environmental)

• Lower boundary condition has sophisticated air-sea interaction, etc• Includes suitable turbulence closure, other parameterisations• Model described in Kepert and Wang (2001, JAS) and Kepert (2012,

MWR)


Symmetric Structure


Symmetric structure

Radial

Azimuthal

Vertical


Comparison to observations

Obs in H. Isabel (Bell 2010) Typical model run


Flow summary diagram

vgr

104ζ

100w

-u10

v10


Supergradient flow

• fig

Black contours: vShading: v – vgr, zero contour whiteVectors u-w


Supergradient flow

• Inflow produces an azimuthal acceleration (by conservation of angular momentum)

• Supergradient flow implies that there is an outwards acceleration • Centrifugal force (outwards) + Coriolis (outwards) > pressure gradient

(inwards)

• The jet maximum occurs within the inflow layer

• What maintains the inflow in the presence of this outwards acceleration?


u

gradient windresidual

friction

verticaladvection

radial advection

v

angularmomentum advection

friction

verticaladvection

Contours: 0, +/-{1,2,3…128}*1e-4 m s-2


Supergradient flow

• Inflow produces an azimuthal acceleration (by conservation of angular momentum)

• Supergradient flow implies that there is an outwards acceleration • Centrifugal force (outwards) > Coriolis (inwards) + pressure gradient

(inwards)

• The jet maximum occurs within the inflow layer

• What maintains the inflow in the presence of this outwards acceleration?

• Diffusion and advection of inflow from below, plus self-advection of inflow (less important)


Radial wind Azimuthal wind

Inside RMW

Outside RMW

Same above BL

Large Variation in Nearby Wind Profiles


Hurricane Guillermo (1997)


Radial Flow Azimuthal Flow

Strongest winds in right forward quadrant

Strongest inflow to right

5 m/s

Near-Surface Earth-Relative Flow


Surface winds

Powell (1982, MWR)


Asymmetries (earth-relative)

Total flow

Asymmetric

Wavenumber-1

Radial (10 m) Azimuthal (10 m) Vertical (400 m)


Asymmetries (storm-relative)

Total flow

Asymmetric

Wavenumber-1

Radial (10 m) Azimuthal (10 m) Vertical (400 m)


5 m/s• Surface wind factor is 0.6 to 0.8 in

outer part of storm.

• It increases towards the centre and is 0.8 to 1.0 near the RMW.

• It is larger on the left than on the right (in the NH).

Surface Wind Reduction Factor -Ratio of surface wind speed to gradient wind


• Objective analysis, observations plotted as percentage, black ring shows RMW.

• No shading => not enough data for analysis.

|V50| / |V1500|

• Largest values (~1) in left eye-wall.

• Smallest values to right.

• Secondary max associated with outer rainband.

|V50| / |V2500|

H. Georges: Observed Surface Wind Factor


• Track of Andrew at landfall over Miami in 1992, with positions of surface wind observations for which co-located aircraft data (at altitude ~ 3 km) were available.

Hurricane Andrew


• From tabulated aircraft-surface wind speed comparison in Powell and Houston (Weather & Forecasting, 1996)

Hurricane Andrew


Hurricane Mitch (1998)


• Convection biased towards left rear of slowly moving storm.

• Data courtesy of NOAA/HRD

Hurricane Mitch


Hurricane Mitch - Comparison of gradient and observed winds

GPS dropsonde data from NOAA/HRD

• Pressure profiles were fitted to observations at 100, 200 … 3000 m (left).

• Black = Holland• Red = Willoughby

• Gradient wind compared to observed storm-relative azimuthal flow (right)

• Super-gradient near eye-wall from about 500 m to 2 km.

100 m

3 km

1.5 km

500 m


• Best track from NOAA/NHC

Hurricane Georges


Hurricane Georges

• From NOAA/NHC reconnaissance aircraft.


• Data from NOAA/HRD

H. Georges – Observed eyewall wind profiles


Georges : Observations and model wind speed


• Nonlinear model predicts• Supergradient flow in upper

boundary layer• Inflow layer becomes shallower

towards centre• Surface wind factor increases

towards centre, higher on left• Strongest surface winds in right

front quadrant• Wind profile variation between

storms

• Observational evidence for all of this

Conclusions

Documents

The Tropical Cyclone Boundary Layer 2: Dynamics