5:15 PM - 7:15 PM
[MIS16-P05] Numerical simulations of the interaction of vortex pair and movement of single vortex on a two-dimensional β plane
Keywords:vortex, numerical model
When multiple typhoons occur within a short distance (approximately 1000 km), they can interact with each other and take complex paths. The behavior of these vortices is known as the Fujiwara effect (Fujiwara, 1923), but its details are not fully understood. Here, we constructed a numerical model of the vorticity equation for a horizontally two-dimensional, incompressible fluid on a β-plane to investigate interactions of vortices. We also investigate factors that determine the direction of movement of a single vortex.
A numerical model of the vorticity equation for a horizontally two-dimensional, incompressible fluid on the β-plane is constructed using the finite difference method. Both the east-west and north-south boundaries are taken as periodic boundaries, and the model consists of 512 × 512 grid points. Experiments were conducted to investigate vortex interaction, with parameters including vortex strength and the distance between the centers of binary vortices. In the experiment to analyze the factors that determine the direction of movement of a single vortex, the north-south boundary was set as a free-slip rigid wall (zero gradient of the stream function). The initial distribution of vorticity was given with reference to Kitade (1981).
For the case of β = 0 investigating the interaction of two vortices, they initially rotated counterclockwise and then merged together, as if attracted to each other. The merged vortices stably stayed in the center between the two vortices. This result was qualitatively similar to that of Rasmussen et al. (2002), showing that there were no major issues with the calculation of our constructed model. For the case of β > 0 with two vortices, a vorticity gradient appeared due to the beta term, resulting in the vortex pair rotating counterclockwise and moving northwestward. However, the two vortices did not merge and eventually moved separately. It is known that for a single vortex in a rotating system, the Rossby wave generated by the effect of beta term causes the vortex to propagate westward. In addition, counterclockwise flow on the left side of the vortex and clockwise flow on the right side of it cause the vortex to move northward. These effects cause the vortex to move northwestward (beta drift). In this experiment, we confirmed that beta drift occurs in the case of the vortex pair as well as in the case of a single vortex.
To investigate factors that determine the direction of movement of a single vortex, we conducted a series of numerical experiments applying an arbitrary negative vorticity outside of the initial vortex. We found that the smaller the vorticity around the initial vortex, the more it was prevented from moving westward and the more it moved northward. Following the analyzing method of Elsberry (1986), we divided the flow field into the following three components: (i) axial symmetric circulation, (ii) axial asymmetric circulation resulting from the interaction between the axial symmetric circulation and the environment, and (iii) large-scale steering flow that is uniform in the horizontal direction. This separation analysis of the stream function into axial symmetric and asymmetric components suggests that the direction of vortex movement may be determined by the direction of rotation of the axial asymmetric component.
A numerical model of the vorticity equation for a horizontally two-dimensional, incompressible fluid on the β-plane is constructed using the finite difference method. Both the east-west and north-south boundaries are taken as periodic boundaries, and the model consists of 512 × 512 grid points. Experiments were conducted to investigate vortex interaction, with parameters including vortex strength and the distance between the centers of binary vortices. In the experiment to analyze the factors that determine the direction of movement of a single vortex, the north-south boundary was set as a free-slip rigid wall (zero gradient of the stream function). The initial distribution of vorticity was given with reference to Kitade (1981).
For the case of β = 0 investigating the interaction of two vortices, they initially rotated counterclockwise and then merged together, as if attracted to each other. The merged vortices stably stayed in the center between the two vortices. This result was qualitatively similar to that of Rasmussen et al. (2002), showing that there were no major issues with the calculation of our constructed model. For the case of β > 0 with two vortices, a vorticity gradient appeared due to the beta term, resulting in the vortex pair rotating counterclockwise and moving northwestward. However, the two vortices did not merge and eventually moved separately. It is known that for a single vortex in a rotating system, the Rossby wave generated by the effect of beta term causes the vortex to propagate westward. In addition, counterclockwise flow on the left side of the vortex and clockwise flow on the right side of it cause the vortex to move northward. These effects cause the vortex to move northwestward (beta drift). In this experiment, we confirmed that beta drift occurs in the case of the vortex pair as well as in the case of a single vortex.
To investigate factors that determine the direction of movement of a single vortex, we conducted a series of numerical experiments applying an arbitrary negative vorticity outside of the initial vortex. We found that the smaller the vorticity around the initial vortex, the more it was prevented from moving westward and the more it moved northward. Following the analyzing method of Elsberry (1986), we divided the flow field into the following three components: (i) axial symmetric circulation, (ii) axial asymmetric circulation resulting from the interaction between the axial symmetric circulation and the environment, and (iii) large-scale steering flow that is uniform in the horizontal direction. This separation analysis of the stream function into axial symmetric and asymmetric components suggests that the direction of vortex movement may be determined by the direction of rotation of the axial asymmetric component.