The Impact of Orographic Forcing on Barotropic Unstable Singular Vectors

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  • 1 European Centre for Medium-Range Weather Forecasts, Shinfield Park, Reading, United Kingdom
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Abstract

The influence of topography on fluid instability has been studied in literature both in the beta-channel approximation and on the sphere mainly using normal modes. A different approach recently proposed is based on the identification of unstable singular vectors (i.e., structures that have the fastest growth over finite-time intervals). Systems characterized by neutral or damped normal modes have been shown to have singular vectors growing (e.g., in terms of kinetic energy) over finite-time intervals. Singular vectors do not conserve their shape during time evolution as normal modes do. Various aspects related to the identification of singular vectors of a barotropic flow are analyzed in this paper, with the final goal of studying the impact of the orography on these structures.

First, the author focuses on very idealized situations to verify if neutral and damped flows can sustain structures growing over finite-time intervals. Then, the author studies singular vectors of basic states defined as the super-position of a superrotation and a Rossby-Haurwitz wave forced by orographies that project onto one spectral component only or forced by very simple orographies with longitudinally or latitudinally elongated shapes. This first part shows that orography can alter the unstable subspace generated by the most unstable singular vectors, either directly through the action of the orographic term in the linear equation or indirectly by modifying the evolution of the basic state.

In the second part, the author considers a realistic basic state, defined as a mean winter flow computed from 3 months of observed vorticity field, forced by a realistic orography. It is shown that the orographic forcing can indirectly modify the singular vector structures. In fact, “orographically induced” instabilities can be identified only when considering time-evolving basic states.

These results show that unstable structures related to physical processes can be captured by the adjoint technique.

Abstract

The influence of topography on fluid instability has been studied in literature both in the beta-channel approximation and on the sphere mainly using normal modes. A different approach recently proposed is based on the identification of unstable singular vectors (i.e., structures that have the fastest growth over finite-time intervals). Systems characterized by neutral or damped normal modes have been shown to have singular vectors growing (e.g., in terms of kinetic energy) over finite-time intervals. Singular vectors do not conserve their shape during time evolution as normal modes do. Various aspects related to the identification of singular vectors of a barotropic flow are analyzed in this paper, with the final goal of studying the impact of the orography on these structures.

First, the author focuses on very idealized situations to verify if neutral and damped flows can sustain structures growing over finite-time intervals. Then, the author studies singular vectors of basic states defined as the super-position of a superrotation and a Rossby-Haurwitz wave forced by orographies that project onto one spectral component only or forced by very simple orographies with longitudinally or latitudinally elongated shapes. This first part shows that orography can alter the unstable subspace generated by the most unstable singular vectors, either directly through the action of the orographic term in the linear equation or indirectly by modifying the evolution of the basic state.

In the second part, the author considers a realistic basic state, defined as a mean winter flow computed from 3 months of observed vorticity field, forced by a realistic orography. It is shown that the orographic forcing can indirectly modify the singular vector structures. In fact, “orographically induced” instabilities can be identified only when considering time-evolving basic states.

These results show that unstable structures related to physical processes can be captured by the adjoint technique.

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