Maximum downward propagation of the baroclinic wind-driven circulation into the ocean interior

In the framework of the Young and Rhines theory of the baroclinic, wind-driven circulation, we consider the problem of the determination of the maximum penetration depth, Dmax, of the motion into the ocean. On the basis of general results concerning the interface of no-motion D(x, y), we investigate the dependence of Dmax on a couple of parameters that select each buoyancy profile within a given class, having fixed a special family of vertical Ekman velocity fields. We also show some circulation patterns forced by a typical sinusoidal wind-stress and corresponding to different buoyancy profiles within the same class

Maximum downward propagation of the baroclinic wind-driven circulation into the ocean interior

In the framework of the Young and Rhines theory of the baroclinic, wind-driven circulation, we consider the problem of the determination of the maximum penetration depth, Dmax, of the motion into the ocean. On the basis of general results concerning the interface of no-motion D(x, y), we investigate the dependence of Dmax on a couple of parameters that select each buoyancy profile within a given class, having fixed a special family of vertical Ekman velocity fields. We also show some circulation patterns forced by a typical sinusoidal wind-stress and corresponding to different buoyancy profiles within the same class

The no-slip condition at the western boundary of a homogeneous ocean minimizes energy

It is not obvious, a priori, that the no-slip boundary condition is suitable for ocean circulation models based on quasi-geostrophic equations. But the no-slip condition is the one that minimizes the kinetic energy of the western boundary layer of a wind-driven ocean governed by fourth-order quasi-geostrophic equations. Moreover, the case of a very thin boundary layer is correctly described by the asymptotic solution when the no-slip condition is chosen. Then, it is physically sound to use the no-slip condition even in the western boundary of analytical or numerical ocean circulation models, be they linear or nonlinear

New technique to measure the cavity defects of Fabry-Perot interferometers

(Abridged): We define and test a new technique to accurately measure the cavity defects of air-spaced FPIs, including distortions due to the spectral tuning process typical of astronomical observations. We further develop a correction technique to maintain the shape of the cavity as constant as possible during the spectral scan. These are necessary steps to optimize the spectral transmission profile of a two-dimensional spectrograph using one or more FPIs. We devise a generalization of the techniques developed for the so-called phase-shifting interferometry to the case of FPIs. The technique is applicable to any FPI that can be tuned via changing the cavity spacing ($z$-axis), and can be used for any etalon regardless of the coating' reflectivity. The major strength of our method is the ability to fully characterize the cavity during a spectral scan, allowing for the determination of scan-dependent modifications of the plates. As a test, we have applied this technique to three 50 mm diameter interferometers, with cavity gaps ranging between 600 micron and 3 mm, coated for use in the visible range. We obtain accurate and reliable measures of the cavity defects of air-spaced FPIs, and of their evolution during the entire spectral scan. Our main, and unexpected, result is that the relative tilt between the two FPI plates varies significantly during the spectral scan, and can dominate the cavity defects; in particular, we observe that the tilt component at the extremes of the scan is sensibly larger than at the center of the scan. Exploiting the capability of the electronic controllers to set the reference plane at any given spectral step, we develop a correction technique that allows the minimization of the tilt during a complete spectral scan. The correction remains highly stable over long periods, well beyond the typical duration of astronomical observations.Comment: 15 pages, 20+ figures, accepted for publication in A&A. Two additional movies are available in the online version of the pape

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

On the additional boundary condition of wind-driven ocean models on the eastern coast

In the homogeneous model of the wind-driven ocean circulation, the dynamics of the basin interior is basically governed by the Sverdrup balance and the related no mass-flux condition on the eastern boundary of the basin, which we assume to be square for conceptual simplicity. In the presence of lateral diffusion of relative vorticity, the additional condition on the eastern boundary (like the conditions on the other boundaries) is not demanded on physical grounds but it is arbitrary to a large extent. Hence, certain choices of such boundary condition can produce overall solutions which are “far” from that of Sverdrup in the eastern part of the domain, without any physical reason. In the present note we show that this discrepancy can be strongly reduced if the adopted additional boundary condition has the same form as that implicitly satisfied by the Sverdrup solution. Unlike the common approach, a criterion is thus derived which selects a suitable partial slip boundary condition according to the specific wind-stress field which is taken into account

Elastic moduli approximation of higher symmetry for the acoustical properties of an anisotropic material

The issue of how to define and determine an optimal acoustical fit to a set of anisotropic elastic constants is addressed. The optimal moduli are defined as those which minimize the mean squared difference in the acoustical tensors between the given moduli and all possible moduli of a chosen higher material symmetry. The solution is shown to be identical to minimizing a Euclidean distance function, or equivalently, projecting the tensor of elastic stiffness onto the appropriate symmetry. This has implications for how to best select anisotropic constants to acoustically model complex materials.Comment: 20 page

IBIS (Interferometric BIdimensional spectrometer)

IBIS is a new instrument for solar bidimensional spectroscopy, now under construction at the Arcetri Astrophysical Observatory. It essentially consists of two Fabry-Perot interferometers, piezo-scanned and capacity servo-controlled, which are used in classic mount and in axial-mode, in series with a narrow-band interference filter. This instrument will operate on a large field of view (80����) and on a large wavelength range (5800–8600 ˚A), with high spectral (λ/Δλ � 250000), spatial (�0.2) and temporal (� 5 frames s−1) resolution. When completed in 2002, it will be one of the leading instruments for solar research, well suited for a new generation telescopes such as THEMIS

3D photospheric velocity field of a Supergranular cell

We investigate the plasma flow properties inside a Supergranular (SG) cell, in particular its interaction with small scale magnetic field structures. The SG cell has been identified using the magnetic network (CaII wing brightness) as proxy, applying the Two-Level Structure Tracking (TST) to high spatial, spectral and temporal resolution observations obtained by IBIS. The full 3D velocity vector field for the SG has been reconstructed at two different photospheric heights. In order to strengthen our findings, we also computed the mean radial flow of the SG by means of cork tracing. We also studied the behaviour of the horizontal and Line of Sight plasma flow cospatial with cluster of bright CaII structures of magnetic origin to better understand the interaction between photospheric convection and small scale magnetic features. The SG cell we investigated seems to be organized with an almost radial flow from its centre to the border. The large scale divergence structure is probably created by a compact region of constant up-flow close to the cell centre. On the edge of the SG, isolated regions of strong convergent flow are nearby or cospatial with extended clusters of bright CaII wing features forming the knots of the magnetic network.Comment: 7 pages, submitted to A&A, referee's comments include