Nonlinear stability of the Sverdrup flow against mesoscale disturbances

In the framework of the homogeneous model of ocean circulation, we prove the nonlinear asymptotic stability, in the energy norm, of the Sverdrup flow against mesoscale disturbances. Stability holds in the same parameter condition that the Sverdrup theory itself requires for validity

A note on the full non-linear stability of inviscid, planar flows with constant relative vorticity

The non-linear stability of inviscid, planar flows with constant relative vorticity is proved in the context of the quasi-geostrophic shallow-water theory, for simply connected fluid domains of arbitrary shape. First, the result is obtained relative to the enstrophy and kinetic energy norms and, then, it is extended to a “generalised energy” norm which is expressed through the former

An inner additional condition for solving Munk-like ocean circulation models

The problem of determining the additional boundary conditions, in the framework of the wind-driven single-gyre ocean circulation with lateral diffusion of relative vorticity, is explored with reference to the western boundary and in the context of the classical linear Munk model. As, of necessity, each model solution satisfies a certain inner additional condition, the latter is used to select special kinds of partial-slip boundary conditions, one of which assures the dynamic stability of the linear solution. Moreover, as the boundary conditions are left unaffected by nonlinearity, the same condition can be applied also to the nonlinear model. In particular, an open question about the flow energetics, reported in the literature, is solved by using the present results

Quasi-geostrophic equations revisited: The case of the ocean

Oceanic circulation on the beta-plane demands the presence of (at least) two scales of the motion to describe completely the flow structure and evolution both in the central-eastern area of the basin and in the western boundary layer. In each of the two regions of the basin, well-established quasi-geostrophic vorticity equations govern the flow. However, since these two regions are physically connected, a single and general vorticity equation is requested to hold in the Whole basin. In the present investigation, the inference of this last equation is analysed by comparing some methods found in the literature with another which is put forward by the authors

Frictional dissipation at the interface of a two-layer quasi-geostrophic flow

In two-layer ocean circulation models the possible dissipation mechanism arising at the interface between the layers is parameterised in terms of the difference between the horizontal velocities of the flow in each layer. We explain and derive such parameterisation by extending the classical Ekman theory, which originally refers to the surface and to the benthic boundary layers, to the interface of a quasi-geostrophic, two-layered flow

On the benthic Ekman layer

A review of the standard model of the benthic Ekman layer is presented and reformulated in terms of relative vorticity in place of horizontal current. In this context, the possibility to use mixed boundary conditions to model this layer is explored. The related model solutions can be cast into two main groups: the first is a generalization of the classical Ekman result, while the second one has some unexpected features which are problematic with respect to the Ekman pumping process. An investigation on the finite amplitude stability via the Lyapunov method shows that solutions belonging to the first group are stable while, in the second group, solutions are unstable. This fact poses a physical constraint to the set of the admissible boundary conditions. Finally, a connection between mass transport and boundary condition at the sea floor is numerically investigated

Analisi del fenomeno di blocco atmosferico osservato a Trieste tra agosto 2003 ed agosto 2018

Il blocco atmosferico \ue8 una configurazione dell'atmosfera particolarmente stabile, caratterizzata dalla persistenza di alta pressione (anticiclone di blocco) che interrompe la propagazione delle perturbazioni atlantiche provenienti da ovest. L'analisi matematica mostra che generalmente un blocco pu\uf2 essere ottenuto dalla sovrapposizione di un opportuno usso medio zonale e un'onda di Rossby e che ha un decorso di circa 15 giorni, periodo ben pi\uf9 alto dei tipici pochi giorni di alternanza "bel tempo-brutto tempo"

The carbonate system in the Gulf of Trieste: a two years time series at PALOMA station

In the framework of VECTOR project (activity 6.2.2), pH, Total Alkalinity (AT) and physical/chemical parameters were acquired on a monthly basis since January 2008, in the water column at the PALOMA site (Advanced Oceanic Laboratory PlatforM for the Adriatic sea, Gulf of Trieste, 25m depth ). The pH was measured by the spectrophotometric method (precision ? 0.003) and the results expressed on "total scale" at 25?C (pHT@25?C). AT was measured by potentiometric titration at 25?C (precision ? 3 Qmol/kg) and the results were checked against sea water certified as reference material. The other parameters of the carbonate system (pCO2, DIC, CO3 =, lAr, lCa) were computed from pH, AT, salinity, temperature, SiO2, PO4. To our knowledge this is the first time series of these parameters collected in the North Adriatic Sea. These data allowed an initial identification of roles played by biological ad physical factors in controlling the carbonate system dynamics and the pH annual cycle. During the stratified period (April to September), CO2 uptake by primary producers in the upper layer (DO sat > 100 %, Fig 1) determined the highest annual values of pHT@25?C in both years (Fig 1). By contrast, remineralization processes generally prevailed in the deeper waters undersaturated of oxygen (DO down to 48%, Fig 1) and the minima annual values of pHT@25?C were reached. From January to March of both years the water column was homogeneous and cold, reaching the lowest annual temperatures (down to 8.8 ?C). The pHT@25?C values were generally low and constant and the oxygen saturation was around 100 %. These characteristics indicated that biological processes were playing a minor role in determining the observed values of pHT@25?C while physical factors as temperature induced CO2 solubilization were more important. AT concentrations (median value 2633 Qmol/kg) were higher than in open Mediterranean sea (~ 2600 Qmol/Kg ) due to the inflow of rivers with a carbonatic drainage basin. AT variability was mainly modulated by riverine inputs with variable AT concentrations and by the occurrence of strong remineralization processes in the bottom layer (Aug.- Nov. 2008, up to 2658 Qmol/kg, S=37.5) as shown by the relationship with AOU. The seasonal evolution of in situ pCO2 was deeply influenced by the variations of temperature that modulated not only CO2 solubility but also the chemical equilibria between carbonate species. Despite the production processes in the upper water column during summer, pCO2 values were higher than 400 Qatm on the whole water column, from July to December 2008 and from August to October 2009. During these months the Gulf of Trieste was thus acting as a potential CO2 source. In contrast, from January to June of both years, pCO2 values were always lower than 400 Qatm and the Gulf was a CO2 sink (up to -19.0 mmol C m-2 d-1, on 14 Jan 2009) especially during high wind events. An exception to this trend were the high pCO2 value (up to 606 Qatm) observed in April 2009 and May 2008, in surface low salinity waters (S down to 27.6 psu), which were ascribed to the ventilation of CO2 from supersaturated riverine waters

A generalized 2-D Poincaré inequality

<p/> <p>Two 1-D Poincar&#233;-like inequalities are proved under the mild assumption that the integrand function is zero at just one point. These results are used to derive a 2-D generalized Poincare inequality in which the integrand function is zero on a suitable arc contained in the domain (instead of the whole boundary). As an application, it is shown that a set of boundary conditions for the quasi geostrophic equation of order four are compatible with general physical constraints dictated by the dissipation of kinetic energy.</p