Hydrodynamic stability

Ghil, Michael. “The wind-driven ocean circulation: Applying dynamical systems theory to a climate problem.” Discrete and Continuous Dynamical Systems - A 37, no. 1 (2017): 189-228. Abstract

The large-scale, near-surface flow of the mid-latitude oceans is dominated by the presence of a larger, anticyclonic and a smaller, cyclonic gyre. The two gyres share the eastward extension of western boundary currents, such as the Gulf Stream or Kuroshio, and are induced by the shear in the winds that cross the respective ocean basins. This physical phenomenology is described mathematically by a hierarchy of systems of nonlinear partial differential equations (PDEs). We study the low-frequency variability of this wind-driven, double-gyre circulation in mid-latitude ocean basins, subject to time-constant, purely periodic and more general forms of time-dependent wind stress. Both analytical and numerical methods of dynamical systems theory are applied to the PDE systems of interest. Recent work has focused on the application of non-autonomous and random forcing to double-gyre models. We discuss the associated pullback and random attractors and the non-uniqueness of the invariant measures that are obtained. The presentation moves from observations of the geophysical phenomena to modeling them and on to a proper mathematical understanding of the models thus obtained. Connections are made with the highly topical issues of climate change and climate sensitivity.

Ghil, Michael, Tian Ma, and Shouhong Wang. “Structural Bifurcation of 2-D Nondivergent Flows with Dirichlet Boundary Conditions: Applications to Boundary-Layer Separation.” SIAM J. Appl. Math. 65, no. 5 (2005): 1576–1596.
Ghil, Michael, Jian-Guo Liu, Cheng Wang, and Shouhong Wang. “Boundary-layer separation and adverse pressure gradient for 2-D viscous incompressible flow.” Physica D: Nonlinear Phenomena 197, no. 1-2 (2004): 149–173.
Simonnet, Eric, Michael Ghil, Shouhong Wang, and Zhi-Min Chen. “Hopf Bifurcation in Quasi-geostrophic Channel Flow.” SIAM J. Appl. Math. 64, no. 1 (2003): 343–368.
Ghil, Michael, Tian Ma, and Shouhong Wang. “Structural bifurcation of 2-D incompressible flows.” Indiana University Mathematics Journal 50 (2001): 159–180.