We show that, under reasonably mild hypotheses, the solution of the forced–dissipative rotating primitive equations of the ocean loses most of its fast, inertia–gravity, component in the small Rossby number limit as t → ∞. At leading order, the solution approaches what is known as “geostrophic balance” even under ageostrophic, slowly time-dependent forcing. Higherorder results can be obtained i...

We investigate the effect of adding a single real (for various forcing notions adding reals) on cardinal invariants associated with the continuum. We show: (1) adding an eventually different or a localization real adjoins a Luzin set of size continuum and a mad family of size ω1; (2) Laver and Mathias forcing collapse the dominating number to ω1, and thus two Laver or Mathias reals added iterat...

We prove various theorems about the preservation and destruction of the tree property at ω2. Working in a model of Mitchell [9] where the tree property holds at ω2, we prove that ω2 still has the tree property after ccc forcing of size א1 or adding an arbitrary number of Cohen reals. We show that there is a relatively mild forcing in this same model which destroys the tree property. Finally we ...

We study the stability of the steady waves forced by a moving localised pressure disturbance in water of finite depth. The steady waves take the form of a downstream wavetrain for subcritical flow, but for supercritical flow there is a solution branch for each specified forcing term, which has two localised solitarylike solutions for each Froude number, a small-amplitude and a large-amplitude s...

The notion of forcing pairs is located in the study of quasi-random graphs. Roughly speaking, a pair of graphs (F, F ′) is called forcing if the following holds: Suppose for a sequence of graphs (Gn) there is a p > 0 such that the number of copies of F and the number of copies of F ′ in every graph Gn of the sequence (Gn) is approximately the same as the expected value in the random graph G(n, ...

It is argued that a major fundamental limitation on the predictability of the El Niño–Southern Oscillation phenomenon is provided by the stochastic forcing of the tropical coupled ocean–atmosphere system by atmospheric transients. A new theoretical framework is used to analyze in detail the sensitivity of a skillful coupled forecast model to this stochastic forcing. The central concept in this ...

Numerical simulations of forced isotropic turbulence are most often formulated in Fourier space, where forcing is applied to low-wavenumber modes. For applications in physical space, low-wavenumber forcing is difficult to implement. The linear forcing recently proposed by Lundgren “Linearly forced isotropic turbulence,” in Annual Research Briefs Center for Turbulence Research, Stanford, 2003 , ...

The tradition in Navier-Stokes analysis of finding estimates in terms of the Grashof number Gr , whose character depends on the ratio of the forcing to the viscosity ν, means that it is difficult to make comparisons with other results expressed in terms of Reynolds number Re, whose character depends on the fluid response to the forcing. The first task of this paper is to apply the approach of D...