D. EXPERIMENT DESIGN
IV. UNCOUPLED CONTROL SIMULATION
The axisymmetric and asymmetric structure of the TC kinematic and thermodynamic responses to the cold wake will be described in this chapter. Discussion of the control (uniform and constant SST) experiment will be given in Chapter IV and the five cold wake experiments with variable SST but fixed in time will be described in Chapter V.
To remove transient features, an azimuthal- and time-mean composite in radial-height coordinates is used to examine the axisymmetric structures. The asymmetric deviations relative to the axisymmetric vortex are revealed by a wavenumber decomposition using the discretized Fast Fourier Transform (FFT). First, the model field is transformed from the Cartesian to cylindrical coordinates. Next, the perturbation is obtained by removing the azimuthal mean at each vertical level and radius. Finally, an azimuthal 1-D FFT is applied. By filtering the FFT series using a box window in the middle of the FFT series (i.e., set the coefficients of higher wave numbers to zero inside the box), discretized wave 1-5 fields are obtained after inverting the FFT of the filtered field back to the original field.
The intensification of the TC in the uncoupled control (CNTL) experiment is with a time invariant 303K SST. The maximum wind speed increases rapidly from Saffir-Simpson category (CAT) 1 at 12 h forecast time to a CAT5 by 42 h (Figure 16). After 42 h, the maximum wind speed oscillates between 80-90 m s-1. The maximum wind speed and minimum SLP at 72 h are 95 m s-1 and 936 hPa, respectively (Figure 16).
The relationship between surface pressure (P) and maximum sustained surface wind speed (W) has been studied frequently, and numerous P-W relationships have been developed (Knaff and Zehr 2007, Holland 2008). A polynomial fit of degree 2 calculated for the CNTL SLP and maximum 10 m wind Vmax (Figure 17) gives the relation
2
max 0.01(1010 ) 2.5(1010 ) 45
V = − −P + −P + (3)
This nonlinear equation predicts 98% of the CNTL maximum 10 m wind variance. Compared with previous W relationships using the CNTL SLP, the CNTL P-W curve lies to the right side of P-P-W curves derived from observations. The maximum wind predicted by the P-W relationship is larger than the P-W derived from a dataset that includes both the Atlantic and eastern North Pacific (Knaff and Zehr 2007: Holland 2008). Since no environmental vertical wind shear is imposed in the CNTL experiment, a stronger TC intensity is expected. Although the maximum wind from the CNTL P-W relationship is larger than suggested by Knaff and Zehr and Holland, the COAMPS P-W curve has a similar slope as the Knaff and Zehr curve.
One effect of vertical wind shear is to decrease the TC intensity by inducing a vertical tilt of the vortex in the downshear left direction (Jones 1995, 2000a,b: Frank and Ritchie 1999, 2001). Since no background vertical wind shear is imposed in the CNTL experiment, any vertical tilt of CNTL vortex may be attributed to the local shear produced by internal vortex dynamics. During the CAT3 - CAT5 stage intensification, the magnitude of the vertical tilt below 5 km height is small (~ 4 km in the horizontal).
The vorticity maxima at 400 hPa and 850 hPa are almost vertically aligned until 72 h (Figure 18).
Figure 16. Maximum 10 m wind speed (m s-1, blue dashed line) and minimum SLP (hPa, green line) during the first 72 h of the CNTL experiment.
Figure 17. Minimum SLP (hpa) and maximum 10 m wind (kt) relationship for the CNTL experiment (blue circles). These data are fitted with a polynomial of 2 degree (black line) for comparison with other P-W relationships (see inset for sources).
Similar to previous studies (Montgomery and Kallenbach 1997: Carr and Williams 1989), the model-simulated vortex ring is not in a steady state; rather, the vortex alternates between axisymmetrization processes and asymmetric structures. Due to these asymmetries, the center of the vortex that was initially at the center of grid 3 has moved 55 km northwestward at 72 h (Figure 18). The movement initially starts around 36 h, when the TC reaches CAT4 intensity. After this time, the vorticity ring continuously evolves from triangular to elliptical and finally to a monopole vortex between 36-48 h.
After 48 h, the vortex maintains a monopole structure. During this trochoidal oscillation period, 3-4 smaller mesovortices developed within the eye (Figure 19). These polygonal
studies (Schubert et al. 1999: Kossin and Schubert 2001, 2004: Montgomery et al. 2002:
Hendricks et al. 2008). These studies attributed the inner-core vortex features to the asymmetric dynamics of potential vorticity (PV) mixing in the hurricane inner core, because PV is not conserved in the presence of diabatic heating. The PV mixing causes the vortex ring to become barotropically unstable, which destabilizes the vortex.
Figure 18. Time evolution (forecast hour at top) of the relative vorticity (s-1) at 400 hPa (blue) and at 850 hPa (red) in the CNTL experiment on a 200 km x 200 km. The contour interval is 0.05 s-1 and 0.01 s-1 for the 850 hPa and 400 hPa vorticity, respectively.
The barotropic instability is evident from the time evolution of the azimuthal- mean 400 hPa vorticity (Figure 20). There is a steady increase of vorticity with time except between 42-48 h, when a reversal in the sign of the vorticity gradient is simulated.
The radial gradient of vorticity changes sign twice, which is an indication of the development of barotropic instability and possible exponential growth in the inner-core region. This period is also the time of the trochoidal oscillation. The location of maximum vorticity is around 10 km from the center of the eye. After 60 h, the axis of maximum vorticity moves inward, which indicates a contraction of the eyewall. Outside the eyewall, a band of a small mean positive vorticity associated with the outer rainbands extends to about 70 km. The vorticity is predicted to approach zero at larger radius (> 100 km). The vortex center used to compute the azimuthal-mean vorticity for forecast times prior to 24 h is the center of the third nest. After 24 h, the location of minimum SLP is used to define the vortex center.
Figure 19. Predicted 400 hPa vorticity (s-1, scale on right) at 38 h, 41 h, 43 h, and 46 in the CNTL experiment. At these four times, the vortex was undergoing trochoidal oscillations, and the vortex had multiple mesovortices and a polygonal eyewall.
Figure 20. Azimuthal and vertical average of the vorticity (10-3 s-1) with radius at various times (see inset) in the CNTL experiment.
The axisymmetric structures of the kinematic and thermodynamics fields in the CNTL experiment are investigated using composites obtained by first computing the azimuthal mean of each field at each forecast time. A time average of the azimuthal-mean fields is calculated over 24-72 h, which is the time period that the TC spins-up to CAT3-CAT5 intensity. In these composites of tangential and radial winds, the horizontal axis is normalized with mean radius of maximum tangential wind (RMW) in the vertical, which has a value of 30.3 km.