By Boris A. Kagan, Mikhail Hazin
This ebook goals to acquaint readers with the new advances in experimental and theoretical investigations of ocean-atmosphere interactions, a swiftly constructing box in earth sciences. specific consciousness is paid to the scope and views for satellite tv for pc measurements and mathematical modeling. present ways to the development of coupled ocean-atmosphere versions (from the easiest one-dimensional to complete 3-dimensional ones) for the answer of key difficulties in weather idea are mentioned intimately. box measurements and the result of numerical weather simulations are offered and aid to provide an explanation for weather variability that arises from a variety of average and anthropogenic components.
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Extra resources for Ocean Atmosphere Interaction and Climate Modeling (Cambridge Atmospheric and Space Science Series)
5), reject the terms containing the products and squares of perturbations y\ and V2 and subtract the equations for i^(100) and i^^. As a result we obtain the following equations: ^ / \ ^ l , ^ / d i = 0. 10) r\ = iTM exp(f"(2GO)T/2), ( 0) where we have taken into account the fact that f"\ = *r 1 at x = 0. 10) it follows that deviations from the state (0,1) increase exponentially, and deviations from the state (0,-1) decrease exponentially, with time. In other words, the first of these two steady states is unstable, and the second is stable.
5). )/2. 6) this expression yields 1 where 1Tf] = (I - r cosh(r/2) - rf sinh(r/2)' rf)2)1/2. 9) that ^ = 0 and 1T2 = -1, that is, on a phase plane (a plane whose coordinates are the state parameters f"i, t~2) the asymptotic behaviour of the system is presented as a point with coordinates (0, — I). 5), this equilibrium state is non-unique: there is one more point, with coordinates (0,1). Let us clarify which of the above is stable. For this purpose we use the perturbation method, and write rTl9 Y2 in the vicinity of steady states ( O ^ ^ ) as iTx = 1T^ + ir\, iT2 = 1T2^ + TT^ where 1T™ = 0 and iT(2G0) = 1.
Thus, it turns out that the ocean thermohaline circulation may have four stable states: two two-cell and two single-cell states with opposite directions of rotation. In practice, as was established by Welander (1986), within the framework of a three-box ocean model there are nine steady states, but only four of them are stable, the others being unstable. However, if we reject this three-box model and replace it by a more realistic model representing the ocean as a system of three ventilated (participating in heat and moisture exchange with the atmosphere) layers - the surface layer, the intermediate layer and the bottom layer - then, according to Kagan and Maslova (1991), the number of steady states will be equal to 81, including 16 stable states.