Dissipative Quasigeostrophic Motion under Temporally Almost Periodic Forcing

The full nonlinear dissipative quasigeostrophic model is shown to have a unique temporally almost periodic solution when the wind forcing is temporally almost periodic under suitable constraints on the spatial square-integral of the wind forcing and the $\beta$ parameter, Ekman number, viscosity and the domain size. The proof involves the pullback attractor for the associated nonautonomous dynamical system

Noise-Sustained currents in quasigeostrophic turbulence over topography

We study the development of mean structures in a nonlinear model of large scale ocean dynamics with bottom topography and dissipation, and forced with a noise term. We show that the presence of noise in this nonlinear model leads to persistent average currents directed along isobaths. At variance with previous works we use a scale unselective dissipation, so that the phenomenon can not be explained in terms of minimum enstrophy states. The effect requires the presence of both the nonlinear and the random terms, and can be though of as an ordering of the stochastic energy input by the combined effect of nonlinearity and topography. The statistically steady state is well described by a generalized canonical equilibrium with mean energy and enstrophy determined by a balance between random forcing and dissipation. This result allows predicting the strengh of the noise-sustained currents. Finally we discuss the relevance that these noise-induced currents could have on real ocean circulation.Comment: 11 pages REVTeX. Includes 4 figures using epsf. Related material in http://www.imedea.uib.es/Nonlinear and http://www.imedea.uib.es/Oceanograph

Local and Nonlocal Dispersive Turbulence

We consider the evolution of a family of 2D dispersive turbulence models. The members of this family involve the nonlinear advection of a dynamically active scalar field, the locality of the streamfunction-scalar relation is denoted by $\alpha$, with smaller $\alpha$ implying increased locality. The dispersive nature arises via a linear term whose strength is characterized by a parameter $\epsilon$. Setting $0 < \epsilon \le 1$, we investigate the interplay of advection and dispersion for differing degrees of locality. Specifically, we study the forward (inverse) transfer of enstrophy (energy) under large-scale (small-scale) random forcing. Straightforward arguments suggest that for small $\alpha$ the scalar field should consist of progressively larger eddies, while for large $\alpha$ the scalar field is expected to have a filamentary structure resulting from a stretch and fold mechanism. Confirming this, we proceed to forced/dissipative dispersive numerical experiments under weakly non-local to local conditions. For $\epsilon \sim 1$, there is quantitative agreement between non-dispersive estimates and observed slopes in the inverse energy transfer regime. On the other hand, forward enstrophy transfer regime always yields slopes that are significantly steeper than the corresponding non-dispersive estimate. Additional simulations show the scaling in the inverse regime to be sensitive to the strength of the dispersive term : specifically, as $\epsilon$ decreases, the inertial-range shortens and we also observe that the slope of the power-law decreases. On the other hand, for the same range of $\epsilon$ values, the forward regime scaling is fairly universal.Comment: 19 pages, 8 figures. Significantly revised with additional result

Intergyre transport in a wind-driven, quasigeostrophic double gyre: An application of lobe dynamics

We study the flow obtained from a three-layer, eddy-resolving quasigeostrophic ocean circulation model subject to an applied wind stress curl. For this model we will consider transport between the northern and southern gyres separated by an eastward jet. We will focus on the use of techniques from dynamical systems theory, particularly lobe dynamics, in the forming of geometric structures that govern transport. By “govern”, we mean they can be used to compute Lagrangian transport quantities, such as the flux across the jet. We will consider periodic, quasiperiodic, and chaotic velocity fields, and thus assess the effectiveness of dynamical systems techniques in flows with progressively more spatio-temporal complexity. The numerical methods necessary to implement the dynamical systems techniques and the significance of lobe dynamics as a signature of specific “events”, such as rings pinching off from a meandering jet, are also discussed

Predictability of the Burgers dynamics under model uncertainty

Complex systems may be subject to various uncertainties. A great effort has been concentrated on predicting the dynamics under uncertainty in initial conditions. In the present work, we consider the well-known Burgers equation with random boundary forcing or with random body forcing. Our goal is to attempt to understand the stochastic Burgers dynamics by predicting or estimating the solution processes in various diagnostic metrics, such as mean length scale, correlation function and mean energy. First, for the linearized model, we observe that the important statistical quantities like mean energy or correlation functions are the same for the two types of random forcing, even though the solutions behave very differently. Second, for the full nonlinear model, we estimate the mean energy for various types of random body forcing, highlighting the different impact on the overall dynamics of space-time white noises, trace class white-in-time and colored-in-space noises, point noises, additive noises or multiplicative noises