Singular Vectors for Barotropic, Hurricane-Like Vortices in Horizontal Shear: Structure and Perturbation Growth Mechanisms

Abstract

Abstract In this study the structure and evolution of singular vectors (SVs) for stable and unstable hurricane-like vortices in background flows with horizontal shear are investigated on f and β planes using a nondivergent barotropic model. With increasing shear strength, the singular values for stable vortices increase and the sensitive regions extend farther away from the vortex. The formation of β gyres leads to significant changes in the SV structure but has only weak influence on the singular values. For sufficiently strong anticyclonic shear, the initial SVs are aligned with streamlines connected to stagnation points. The evolved SVs are dominated by dipole structures, indicating a displacement of the vortex. The displacement is caused by the circulation associated with the initial SV perturbation outside of the vortex core, which grows by untilting and unshielding. This process is strongly enhanced by anticyclonic background shear. For both cyclonic and anticyclonic shear, the displacement by the perturbation circulation causes an additional displacement that is proportional to the shear strength. The shear-enhanced barotropic growth mechanism in stable vortices results in singular values that are comparable to those for unstable vortices without background shear. Perturbation growth involving the normal mode in barotropically unstable vortices suffers from background shear. The shear-induced modifications of the outer vortex regions cause a strong decrease of the singular value with increasing shear. For sufficiently strong shear, the SVs for unstable vortices grow by the same mechanism as for stable vortices.