Workshops

Dynamic Transitions in Climate Dynamics

100
reads
Workshops

Shouhong Wang

2012-09-18
13:50:00 - 14:40:00

101 , Mathematics Research Center Building (ori. New Math. Bldg.)

The main objective of this article is to develop a systematic dynamic transition theory for low frequency variability of the large-scale atmospheric and oceanic flows. The primary goal of this proposed effort is to document, through careful theoretical and numerical studies, the presence of climate low frequency variability, to verify the robustness of this variability's characteristics to changes in model parameters, and to help explain its physical mechanisms. The main focus is on a few typical sources of atmospheric and oceanic variability, including in particular the wind driven ocean circulation, the thermohaline circulation (THC) and the tropical atmosphere-ocean modes associated with the El Nino Southern Oscillations (ENSO). The wind-driven circulation plays a role mostly in the oceans' subannual-to-interannual variability, while the THC is most important in decadal-to-millenial variability.

There are two types of nonlinear systems in nature: conservative and dissipative. A systematic dynamic transition theory for dissipative systems is established recently by the authors. The key philosophy of the theory is to search for the full set of transition states, giving a complete characterization of stability and transition. The set of transition states is represented by a local attractor near or away from the basic state. The central theme of the theory is to establish a general principle that transitions for all dissipative systems consists of only three types: continuous, catastrophic, and mixed (random).

For ENSO, we derive a new mechanism of the ENSO, as a self-organizing and self-excitation system, with two highly coupled processes. The first is the oscillation between the two metastable warm (El Ni\~no phase) and cold events (La Nina phase), and the second is the spatiotemporal oscillation of the sea surface temperature (SST) field. The interplay between these two processes gives rises the climate variability associated with the ENSO, leads to both the random and deterministic features of the ENSO, and defines a new natural feedback mechanism, which drives the sporadic oscillation of the ENSO. The randomness is closely related to the uncertainty/fluctuations of the initial data between the narrow basins of attractions of the corresponding metastable events, and the deterministic feature is represented by a deterministic coupled atmospheric and oceanic model predicting the basins of attraction and the sea-surface temperature (SST). It is hoped this mechanism based on a rigorous mathematical theory could lead to a better understanding and prediction of the ENSO phenomena.

For the THC, a mathematical theory is derived. In particular, we obtain a general transition and stability theory for the Boussinesq system, governing the motion and states of the large-scale ocean circulation. First, it is shown that the first transition is either to multiple steady states or to oscillations (periodic solutions), determined by the sign of a nondimensional parameter $K$, depending on the geometry of the physical domain and the thermal and saline Rayleigh numbers. Second, for both the multiple equilibria and periodic solutions transitions, both Type-I (continuous) and Type-II (jump) transitions can occur, and precise criteria are derived in terms of two computable nondimensional parameters $b_1$ and $b_2$. Associated with Type-II transitions are the hysteresis phenomena, and the physical reality is represented by either metastable states or by a local attractor away from the basic solution, showing more complex dynamical behavior. Third, a convection scale law is introduced, leading to an introduction of proper friction terms in the model in order to derive the correct circulation length scale. In particular, the dynamic transitions of the model with the derived friction terms suggest that the THC favors the continuous transitions to stable multiple equilibria.

For material related to this talk, click here.