Title: An adjoint description of geostrophic adjustment

Authors: Michael C. Morgan (University of Wisconsin - Madison)

The notion of geostrophic adjustment is an important concept in geophysical fluid dynamics as it offers insight into the relationship between the slowly evolving dynamics of rapidly revolving fluid flows (i.e., low Rossby number flows) and the potential vorticity distribution (the conserved dynamical variable for rotating fluids) of those flows. Further it provides a means of addressing the scale-dependence of the evolution of mass and wind perturbations to rotating fluids, and the emergence of a nearly balanced wind and mass field. Many extant adjoint sensitivity studies have revealed that over sufficiently long integrations of adjoint models, a relationship, resembling geostrophic balance, emerges between sensitivities to mass and sensitivities to wind. In this presentation, an analytical and numerical study of the linearized shallow water system is discussed and the conserved dynamical variables of the adjoint to the shallow water system are revealed. The scale-dependence of this "adjoint adjustment" is also explored. The implications of these results to sensitivity studies and data assimilation are discussed.

GMAO Head: Michele Rienecker Global Modeling and Assimilation Office NASA Goddard Space Flight Center

Curator: Nikki Privé Last Updated: May 27 2011