## Experiment design

A core vortex is specified initially, which has a hurricane-like tangential wind profile (see Fig. 2) defined as follows:

where the maximum tangential wind Vmax = 0.5(25m/s), and the radius of maximum wind Rmax = 0.1(100km). The vorticity of the core vortex has a maximum at the center of the vortex (as seen in Fig. 1(c)) and decreases

Fig. 2. Radial profiles of the hurricane-like vortex for nondimensional (a) tangential wind, (b) angular velocity, (c) vorticity, and (d) vorticity gradient. To obtain tangential wind in ms_1, multiply by 50. To obtain angular velocity or vorticity in s~1, multiply by 5 X 10_5. To obtain vorticity gradient in m~1 s~1, multiply by 5 X 10_11. To obtain radial displacement in km, multiply by 1000.

monotonically with radius, with a maximum vorticity gradient located at r = 0.044 (Fig. 2(d)).

Different from the vortex-vortex interaction scenario in Kuo et al.,2 we focus on the interaction between the asymmetric disturbances and symmetric core vortex flows. The initial asymmetry specified contains either a wavenumber 2 or a wavenumber 3 structure in the azimuthal direction. (To avoid the movement of the core vortex, a wavenumber-one asymmetry is not considered.) The initial asymmetry is prescribed by a vorticity perturbation with the following expression:

5 exp

where r is the radial distance; A the azimuthal angle; k, the azimuthal wavenumber (k = 2 or k = 3) and the radial scale (or size) of the asymmetry a = 0.025. The radial parameter Rp controls the position of the initial asymmetry.

To investigate how the initial asymmetry position might affect the formation of the second peak of the symmetric tangential wind, five experiments have been designed for the wavenumber 2 perturbations. In the first experiment the initial perturbation is placed at the radius of 0.2 (Rp = 0.2, hereafter denoted as T20, see Fig. 3(a)). In the second

Wavenumber two Wavenumber three

Wavenumber two Wavenumber three

-0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4

Fig. 3. The initial non-dimensional barotropic asymmetric vorticity with the maximum center located at the radius of 0.2 for (a) wavenumber 2 case T20 and (b) wavenumber 3 case H20. The contour interval is 1. To obtain vorticity in s~1, multiply by 5 X 10_5. To obtain radial displacement in km, multiply by 1000. Only the inner 400 km X 400 km model domain is shown.

-0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4

Fig. 3. The initial non-dimensional barotropic asymmetric vorticity with the maximum center located at the radius of 0.2 for (a) wavenumber 2 case T20 and (b) wavenumber 3 case H20. The contour interval is 1. To obtain vorticity in s~1, multiply by 5 X 10_5. To obtain radial displacement in km, multiply by 1000. Only the inner 400 km X 400 km model domain is shown.

experiment the initial asymmetry is placed at the radius of 0.25 (Rp = 0.25, hereafter denoted as T25); the third one at the radius of 0.3 (Rp = 0.3, denoted as T30); the fourth at the radius of 0.1 (Rp = 0.1, denoted as T10); and the fifth at the radius of 0.15 (Rp = 0.15, denoted as T15). The similar five sensitivity experiments with the wavenumber 3 disturbances are denoted as H20 (Rp = 0.2), H25 (Rp = 0.25), H30 (Rp = 0.3), H10 (Rp = 0.1), and H15 (Rp = 0.15) respectively (Fig. 3(b)).