Are the Beta Gyres Really Normal Modes?
Hugh E. Willoughby, NOAA/AOML/HRD, Miami, FL; and R. W. Jones When an axisymmetric vortex is represented in a cylindrical coordinate system whose origin is displaced from the axis of rotation, some of the flow projects onto wavenumber 1. The apparent asymmetry is a normal mode of the linearized governing equations. It is sometimes called the “pseudo-mode” since it represents invariance of the vortex under relocation of the reference frame. Because a gradient-balance vortex is a steady solution of the governing equations, the mode’s natural frequency is zero. Growth of the “pseudo-mode” as a result of asymmetric forcing is also the way that the linearized equations represent translation of the vortex. Thus, “translational mode (TM)” is a more apt term than “pseudo-mode”. The TM vorticity is the radial gradient of axisymmetric vorticity dotted into the displacement of the vortex axis from the origin. In a hurricane-like vortex, its magnitude is greatest just inward from the Radius of Max
Hugh E. Willoughby, NOAA/AOML/HRD, Miami, FL; and R. W. Jones When an axisymmetric vortex is represented in a cylindrical coordinate system whose origin is displaced from the axis of rotation, some of the flow projects onto wavenumber 1. The apparent asymmetry is a normal mode of the linearized governing equations. It is sometimes called the “pseudo-mode” since it represents invariance of the vortex under relocation of the reference frame. Because a gradient-balance vortex is a steady solution of the governing equations, the mode’s natural frequency is zero. Growth of the “pseudo-mode” as a result of asymmetric forcing is also the way that the linearized equations represent translation of the vortex. Thus, “translational mode (TM)” is a more apt term than “pseudo-mode”. The TM vorticity is the radial gradient of axisymmetric vorticity dotted into the displacement of the vortex axis from the origin. In a hurricane-like vortex, its magnitude is greatest just inward from the Radius of Max
