In order to discuss the one-dimensional bottom motion of a vein of dense water over a mild slope and underlying upper water at rest, we obtain an integrodifferential partial nonlinear equation in the ...vein thickness. Some elementary solutions and their physical meaning are discussed.
In this paper an analytical method to study the hydrodynamic stability of simple barotropic, non-divergent flows is discussed. The method is based on the variational approach introduced by Arnold and ...derived from the Lyapunov stability criteria. In this context, the sufficient condition for the stability of a steady barotropic flow ψ(x,y) is obtained when dP(ψ)/dP
ψ = ψ
, the derivative of the absolute vorticity P(ψ), is positive definite. In this case, we discuss the effect of higher derivatives d
n
P(ψ)/dψ
n
ψ
ψ = ψ
on the non-linear stability. Then we show that some classical examples of oceanic non-divergent flows (i.e. lee waves downstream an Island, steady flows through a Strait, the Fofonoff gyre) are stable to finite-amplitude perturbations.
This synthesis summarizes 5 chapters: 1- Introduction, 2- Uptodate on the Eastern Mediterraean Transient, 3- The new situation of the Deep Western Maditerranean, 4- Processes of deep water formation, ...5- General recommendation and future work.
In this note we make a theoretical analysis of how a mild fluid viscosity can affect the potential vorticity for stratified fluids in a rotating system. The classical Ertel (1942) Theorem is applied ...to slightly viscous fluids to obtain the law of conservation corresponding to novel invariants. These invariants do not have a classical form: indeed one example is a simple classical potential vorticity multiplied by a function of time. It has to be stressed that similar relations hold for a large class of conserved quantities, such as tracers, entropy, etc. Our results are compared with the recent Impermeability Theorem by Haynes and McIntyre (1987). Among other results this comparison provides an effective way of estimating the importance of frictional effects on the potential vorticity evolution along streamlines, also using a generalization of the classical Margules equation. In general these ideas can be fruitfully applied to various cases of oceanic interest, in an analysis of superficial phenomena as observed in satellite imagery or systematic analysis of deep currents. So here we analyse some interesting aspects of equatorial currents, small space-scale motions, as well as steady or quasi-steady fronts and cold filaments, namely the long patches that are often observed in thermal satellite images.
Generalizing an idea of Arnold, we discuss the hydrodynamic stability à la Lyapunov of solitary water-waves which are rotational solutions of the Euler equation, travelling with constant phase speed ...ctildeT. In the reference frame moving with the wave profile, the solitary wave is described by a solution of
We show that if
as in other applications of Arnold's idea, and if
at the air sea surface, a rather realistic request, the system is stable for (a) small vertical or horizontal space scale perturbations; (b) perturbations with a very long vertical space scale and very small horizontal space scale or with a very long horizontal space scale and very small vertical space scale. Finally we show that the system is also stable for irrotational perturbations.
We discuss the motion and spreading of a bottom vein of very marine water, which originates ( sigma less than or equal to 29.4) in winter through cooling and evaporation processes resulting from the ...violent Bora wind blowing over the shallow North Adriatic Sea into the deepest layers of the southern Adriatic and Ionian seas (eastern Mediterranean basin). Analysis is focused on the peculiar physical processes that control this bottom flow. First describe the vein motion in the southern Adriatic Sea in which this current follows approximately the isobaths (in partial accordance with the conservation of potential vorticity) and the main mixing process of dense water with Levantine Intermediate Water occurring in an offshore-oriented canyon near Bari. This canyon causes a deepening and flattening of the original vein of dense water, such that downstream the water can be observed only on the Otranto Sill (at depths of similar to 800 m with sigma similar to 29.25). The subsequent flow in the Ionian Sea follows approximately the 900-m isobath in the Gulf of Taranto and along the Calabrian and east Sicilian coasts, in agreement with the results of Smith's and Killworth's theoretical models of steady motion of density driven currents over a regular slope, in a rotating system, for stratified fluids.
Thermo-poro-elastic equations describing fluid migration through fluid-saturated porous media at depth in the crust are analyzed theoretically following recent formulations of Rice and Cleary (1976), ...McTigue (1986) and Bonafede (1991). In this study these ideas are applied to a rather general model, namely to a deep hot and pressurized reservoir of fluid, which suddenly enters into contact with an overlaying large colder fluid-saturated layer. In a one-dimensional idealization this system can be described by two nonlinear differential heat-like equations on the matrix-fluid temperature and on the fluid overpressure over the hydrostatic value. The nonlinear couplings are due to Darcy thermal advection and to the mechanical work rate. Here we first sketch nonlinear solutions corresponding to Burgers' "solitary shock waves", which have recently been found valid for rocks with very low fluid diffusivity. Subsequently other nonlinear transient waves are discussed, such as "thermal" and "compensated" waves, which are found to exist for every value of the parameters present in the equations involved. One interesting aspect of these mechanisms is that the resulting time-scales are particularly small. Moreover, in order to figure out the system time-evolution and the role played by the fluid diffusivity/thermal diffusivity ratio, a mechanical similitude is proposed, which we treat both analytically and numerically. Although for realistic systems these solutions are somewhat idealized, they allow one to gain fundamental insight into fluid migration mechanisms in volcanic areas and in fault regions under strong frictional heating. As already discussed by McTigue, the theory is also of interest in studying areas of nuclear waste disposal. Furthermore such a theoretical study allows one to investigate the site at depth at which such nonlinear waves are generated.
We study some explicit cases of marine thermocline. We focus our attention on the strongly vertically trapped internal waves, which in our cases allow an explicit dispersion relation and a ...simple behaviour in terms of elementary functions. The explicit form of the Vaisala-Brunt frequency N2{z) is proportional to 1 / z—20| in one case and to A2—B2(z—zD)2 in the other. A comparison with some experimental data concerning the Ligurian Sea is actually in course.
A nonlinear model of temperature and pressure waves in one-dimensional fluid-saturated porous-permeable rocks is discussed in order to investigate hydrogeological problems affecting hyperthermal ...areas. Nonlinear solutions, consisting in waves moving with constant velocity
V, are analyzed. They behave as perturbations that increase with time till a critical value for vertical pressure gradient is reached, a gradient that is related to the time-asymptotic Darcy velocity. From the geological point of view, the effect of rock fracturing phenomena can be schematized by using some of the solutions of our model, if one postulates that our coefficients depend on the waves vertical pressure gradients. This allows to interpret measurement of the time-evolution of the Darcy velocity, as measured in a superficial position, as a way to reconstruct the porous rock reaction to the temperature-pressure jump carried by these nonlinear waves.
