LOW-ORDER MODELS, INITIALIZATION, AND THE SLOW MANIFOLD

A nine equation low-order model of the shallow water equations is used as a testbed to compare several initialization strategies and to find points satisfying conditions of ''slowness.'' Several methods are exp lored to initialize the low order model: (1) Lorenz's method of succes sively zeroing tendencies; (2) minimization of the sum of the squares of the tendencies; (3) use of a balance condition. We find that the ba lance condition produces the smoothest solution on a consistent basis. In addition, Lorenz initialization, the Newton-Kantorovich Theorem, a nd the Nested Interval Property are used to compute points devoid of g ravity waves to order N for low values of the forcing (F-1 less than o r equal to 0.1). Several of these points are calculated.