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Paola Cessi

Abstract

Welander's flip–flop model exhibits oscillations when forced by stochastic white noise (with zero mean) even in the region of parameters where the deterministic system has a globally stable fixed point. Perturbations away from the attracting solutions decay exponentially in time, without any oscillation. Thus, the oscillation that appears when the system is stochastically forced is not related to an eigenfrequency of the linearized system.

The characteristics of this noise-induced oscillation are contrasted with those obtained when the damped harmonic oscillator is forced stochastically. In the case of a stochastically forced damped harmonic oscillator the spectral peak coincides with the frequency of the oscillator, and the amplitude of the oscillations is proportional to the strength of the noise. In the stochastically forced flip-flop model the amplitude of the oscillations is independent of the strength of the noise and the spectral peak moves to lower frequencies as the amplitude of the noise is reduced. Moreover, for noise below a critical threshold, no spectral peak is obtained.

The flip–flop model shares four characteristics with the thermohaline oscillations observed in OGCMs:

  1. The freshwater flux determines whether the system oscillates or settles into a steady state. The period of the oscillations is very sensitive to the freshwater flux and becomes arbitrarily long near the transition from steady to periodic behavior.

  2. The oscillations are of finite amplitude even just past the threshold value of the freshwater flux that separates periodic behavior from a steady equilibrium.

  3. One extremum of the oscillation excursion is close to the value of the steady state that exists below the threshold for transition.

  4. When the deterministic system reaches a steady state, oscillations can be excited by adding a stochastic component to the freshwater flux. The period of the resulting oscillations decreases with increasing noise amplitude, while the amplitude of the oscillations is insensitive to the amplitude of the noise.

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Paola Cessi

Abstract

It is well established that the mean transport through Bering Strait is balanced by a sea level difference between the North Pacific and the Arctic Ocean, but no mechanism has been proposed to explain this sea level difference. It is argued that the sea level difference across Bering Strait, which geostrophically balances the northward throughflow, is associated with the sea level difference between the North Pacific and the North Atlantic/Arctic. In turn, the latter difference is caused by deeper middepth isopycnals in the Indo-Pacific than in the Atlantic, especially in the northern high latitudes because there is deep water formation in the Atlantic, but not in the Pacific. Because the depth of the middepth isopycnals is associated with the dynamics of the upper branch of the meridional overturning circulation (MOC), a model is formulated that quantitatively relates the sea level difference between the North Pacific and the Arctic/North Atlantic with the wind stress in the Antarctic Circumpolar region, since this forcing powers the MOC, and with the outcropping isopycnals shared between the Northern Hemisphere and the Antarctic circumpolar region, since this controls the location of deep water formation. This implies that if the sinking associated with the MOC were to occur in the North Pacific, rather than the North Atlantic, then the Bering Strait flow would reverse. These predictions, formalized in a theoretical box model, are confirmed by a series of numerical experiments in a simplified geometry of the World Ocean, forced by steady surface wind stress, temperature, and freshwater flux.

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Paola Cessi

Abstract

A simple mechanism for the generation of flow in the eastern region of the oceans is presented. It is shown that even a small amount of upwelling-favorable wind stress parallel to the boundary makes the subducted geostrophic contours veer into the eastern boundary. This sweep toward the wall ventilates the top few hundred meters of the eastern subtropical gyre. The latitudinal extent of the eastern ventilation is calculated. Along a meridional boundary the subsurface flow is eastward and appears to provide the mass source for the poleward undercurrents observed at the eastern boundary of the ocean.

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Paola Cessi

Abstract

A modified Stommel two-box model is considered as a minimal representation of the buoyancy-driven ocean circulation. In the limit of fast temperature relaxation only the salinity evolves in time while the temperature is clamped to the prescribed ambient value. The box model has no intrinsic variability: just two linearly stable and one unstable equilibria. A finite perturbation is needed to shift the system from one stable equilibrium to the other. The minimum amplitude and duration in time of the perturbation are calculated.

A stochastic component of the freshwater flux forcing is then added to model the effect of changes in the global hydrological cycle due to the “weather.” The stochastic forcing is a source of extrinsic time dependence. The salinity gradient obeys an equation analogous to the trajectory of a viscous particle in a double-welled potential, subject to Brownian agitation. If the amplitude of the stochastic driving is above a certain threshold, then there is a finite probability of switching from one stable equilibrium to the other. The threshold variance and the average residence time in each equilibrium are calculated. For timescales on the order of the average residence time or longer, the box model behaves like a random telegraph process.

The stochastic driving also induces a “rattling” around each steady equilibrium whose frequency is proportional to the curvature of the potential well at each equilibrium. The probability of being in each well can be calculated and, within each equilibrium, the box model behaves like an Ornstein-Uhlenbeck process.

Finally the spectrum of the salinity gradient is calculated analytically using standard approximations in stochastic processes. The approximate analytical results are in excellent agreement with those obtained by direct computation.

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Paola Cessi

Abstract

A parameterization for eddy buoyancy fluxes for use in coarse-grid models is developed and tested against eddy-resolving simulations. The development is based on the assumption that the eddies are adiabatic (except near the surface) and the observation that the flux of buoyancy is affected by barotropic, depth-independent eddies. Like the previous parameterizations of Gent and McWilliams (GM) and Visbeck et al. (VMHS), the horizontal flux of a tracer is proportional to the local large-scale horizontal gradient of the tracer through a transfer coefficient assumed to be given by the product of a typical eddy velocity scale and a typical mixing length. The proposed parameterization differs from GM and VMHS in the selection of the eddy velocity scale, which is based on the kinetic energy balance of baroclinic eddies. The three parameterizations are compared to eddy-resolving computations in a variety of forcing configurations and for several sets of parameters. The VMHS and the energy balance parameterizations perform best in the tests considered here.

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Paola Cessi

Abstract

The axisymmetric model of the Hadley circulation can be systematically reduced in the limit of small Rossby number to a simpler one-dimensional system. The reduced system governs the nonlinear evolution of the surface angular momentum and the vertically averaged potential temperature. The meridional transports of heat and angular momentum take the form of downgradient nonlinear diffusion, which acts to homogenize laterally the angular momentum and the potential temperature within the meridional Hadley cells. The diffusivities for both quantities are proportional to the square of the latitudinal gradient of potential temperature. The reduced system is amenable to analytic exploration and allows the explicit determination of the extent and strength of the meridional circulation in terms of the parameters of the problem, such as the Rossby number, the stratification imposed by the radiative–convective equilibrium, and the surface drag. The reduced system also shows that surface easterlies at the equator are possible even when the heating distribution is latitudinally symmetric, as long as the surface drag or the imposed stratification are small.

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Paola Cessi

Abstract

In an earlier paper it was shown that the presence of bottom topography can substantially alter the Sverdrup prediction for the large-scale wind driven flow. In their model the abyssal water is set in motion by the eddy field, parameterized as lateral diffusion of potential vorticity. If the topography has a structure in the east-west direction, then the solution found in the inviscid limit by Cessi and Pedlosky predicts the occurrence of strong jets in the interior of the model ocean. In this note I used a numerical model to test whether the jets predicted by the analytic solutions survive when inertia and diffusion are included explicitly.

In the inviscid limit, according to the structure of the topography these internal jets can occur in both vertically homogeneous and stratified models. Specifically, if the topographic slope changes sign, then one kind of jets is observed both in baroclinic and barotropic models. In the present work it is shown that this phenomenon is observed with moderate amounts of diffusion and is not disturbed by the occurrence of recirculating inertial gyres within the basin.

If the topographic slope is constant, then another kind of internal jets is theoretically predicted in the inviscid limit, and it occurs in stratified models only. Numerical calculations did not exhibit this kind of internal jets in the presence of inertia and weak diffusion, and the reasons for this failure are rationalized.

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Paola Cessi

Abstract

A model that isolates the interaction between midlatitude ocean gyres and the wind stress due to atmospheric baroclinic eddies is formulated. The ocean and atmosphere are coupled through their respective heat balances and global heat and momentum conservations are enforced. The ocean flow creates a steep oceanic thermal front at the midlatitude intergyre boundary. This frontogenesis sharpens the atmospheric temperature gradients and locally increases the atmospheric eddy heat transport. The result is a well-defined storm track that, because of the delayed adjustment of the gyres to the wind stress, oscillates in time with a period of about 18 yr.

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Paola Cessi

Abstract

The role of the relative geometry of mechanical forcing (wind stress) and buoyancy forcing (prescribed surface temperature) in the maintenance of the main thermocline is explored. In particular, the role of the wind stress curl in enhancing or suppressing the generation of baroclinic eddies is studied in simplified domains. The dependence of key quantities, such as the depth of the thermocline and the maximum heat transport, on the external parameters such as diapycnal mixing and dissipation rate is examined. Qualitatively different regimes are found depending on the relative phase of the wind stress and surface buoyancy distribution. The most efficient arrangement for eddy generation has Ekman pumping (suction) in conjunction with high (low) surface buoyancy. This corresponds to the situation found in the midlatitudes, where the surface Ekman flow carries heat toward the warmer region (i.e., upgradient of the surface temperature). In this case, strong eddy fluxes are generated in order to counteract the upgradient heat transport by the Ekman cell. The result is a thermocline whose depth is independent of the diapycnal diffusivity. However, the competition between these opposing heat fluxes leads to a weak net heat transport, proportional to the diffusivity responsible for the diabatic forcing. This arrangement of wind stress provides a large source of available potential energy on which eddies can grow, so the mechanical energy balance for the eddies is consistent with a substantial eddy heat flux. When the same surface temperature distribution is paired with the opposite wind stress curl, the mean flow produces a sink, rather than a source, of available potential energy and eddies are suppressed. With this arrangement, typical of low latitudes and the subpolar regions, the Ekman overturning cell carries heat downgradient of the surface temperature. Thus, the net heat transport is almost entirely due to the Ekman flow and is independent of the diapycnal diffusivity. At the same time the thermocline is a thin, diffusive boundary layer. Quantitative scalings for the thermocline depth and the poleward heat transport in these two limiting cases are contrasted and successfully compared with eddy-resolving computations.

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Paola Cessi

Abstract

An inertial gyre with characteristics very similar to the recirculation observed in eddy-resolving general circulation models is obtained with a simple, analytically tractable, two-layer model. The recirculating gyre is contained in a box of simple geometry, which isolates it from the sverdrup interior. The gyre is forced by prescribing anomalous values of potential vorticity northward in the subtropical gyre or can be though of as a rough parametrization of diabatic forcing. In both cases the forcing is confined to the water above the thermocline, which is represented by the upper layer and is transmitted to the abyssal ocean through interfacial friction.

The condition for the abyssal water to be set in motion, is derived and for oceanic values the recirculation goes all the way to the bottom. When this occurs the center of the gyre is dominated by a barotropic flow, while the baroclinic flow is confined to the edges of the gyre. The width and strength of the gyre can be easily calculated in the limit of long, narrow gyres. The meridional scale of the gyre is directly proportional to the vorticity anomaly injected at the northern boundary, and the barotropic part of the transport is proportional to the cube of the abyssal gyre width, in close analogy with the results found by Cessi, Ierley and Young in a one layer model.

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