The Nonlinear Dynamics of Time Dependent Subcritical Baroclinic Currents
➤ Gửi thông báo lỗi ⚠️ Báo cáo tài liệu vi phạmNội dung chi tiết: The Nonlinear Dynamics of Time Dependent Subcritical Baroclinic Currents
The Nonlinear Dynamics of Time Dependent Subcritical Baroclinic Currents
The Nonlinear Dynamics of Time Dependent Subcritical Baroclinic CurrentsbyG. R. Flierl1Department of Earth and Planetary Sciences Massachusetts Instit The Nonlinear Dynamics of Time Dependent Subcritical Baroclinic Currentstute of Technology Cambridge, MA 02139andJ. Pedlosky-Department of Physical Oceanography Woods Hole Oceanographic Institution Woods Hole. MA 02543October 6. 2005e-mail:1 gkiiujdakr.ujlLtduABSTRACTThe nonlinear dynamics of baroclinically unstable waves in a time dependent zonal shear flow is consider The Nonlinear Dynamics of Time Dependent Subcritical Baroclinic Currentsed in the framework of the two-layer Phillips model on the beta plane. In most cases considered in this study the amplitude of the shear is well belowThe Nonlinear Dynamics of Time Dependent Subcritical Baroclinic Currents
the critical value of the steady shear version of the model. Nevertheless, the time dependent problem in which the shear oscillates periodically is uThe Nonlinear Dynamics of Time Dependent Subcritical Baroclinic CurrentsbyG. R. Flierl1Department of Earth and Planetary Sciences Massachusetts Instit The Nonlinear Dynamics of Time Dependent Subcritical Baroclinic Currentslues of the shear amplitude in the presence of dissipation an analytical, asymptotic theory predicts a self-sustained wave whose amplitude undergoes a nonlinear oscillation whose period is amplitude dependent. There is a sensitive amplitude dependence of the wave on the frequency of the oscillating The Nonlinear Dynamics of Time Dependent Subcritical Baroclinic Currentsshear when the shear amplitude is small. This behavior is also found in a truncated model of the dynamics, and that model is used to examine larger shThe Nonlinear Dynamics of Time Dependent Subcritical Baroclinic Currents
ear amplitudes. When there is a mean value of the shear in addition to the oscillating component, but such that the total shear is still subcritical. The Nonlinear Dynamics of Time Dependent Subcritical Baroclinic CurrentsbyG. R. Flierl1Department of Earth and Planetary Sciences Massachusetts Instit The Nonlinear Dynamics of Time Dependent Subcritical Baroclinic Currentsing shear.For higher, still subcritical. values of the shear we have detected a symmetry breaking in which a second cross-stream mode is generated through an instability' of the unstable wave although this second mode would by itself be stable on the basic time dependent current. For shear values th The Nonlinear Dynamics of Time Dependent Subcritical Baroclinic Currentsat are substantially subcritical but of order of the2critical shear, calculations with a full quasi-geoslrophic numerical model reveal a turbulent floThe Nonlinear Dynamics of Time Dependent Subcritical Baroclinic Currents
w generated by the instability.If the beta effect is disregarded the inviscid, linear problem is formally stable. However, our calculations show that The Nonlinear Dynamics of Time Dependent Subcritical Baroclinic CurrentsbyG. R. Flierl1Department of Earth and Planetary Sciences Massachusetts Instit The Nonlinear Dynamics of Time Dependent Subcritical Baroclinic Currentsnot the longest wave in the system we have observed a cascade up scale to longer waves. Indeed, this classically subcritical flow shows most of the qualitative character of a strongly supercritical flow. This supports previous suggestions of the important role of background time dependence in mainta The Nonlinear Dynamics of Time Dependent Subcritical Baroclinic Currentsining the atmospheric and oceanic synoptic eddy field.31. IntroductionAlthough the classical theory of the instability of zonal flows on the beta planThe Nonlinear Dynamics of Time Dependent Subcritical Baroclinic Currents
e gives clear thresholds required for instability, time dependent flows can exhibit instability when their shears are below the classical critical valThe Nonlinear Dynamics of Time Dependent Subcritical Baroclinic CurrentsbyG. R. Flierl1Department of Earth and Planetary Sciences Massachusetts Instit The Nonlinear Dynamics of Time Dependent Subcritical Baroclinic Currents baroclinic instability each demonstrate the possibility for vigorous parametric instability for flows whose steady counterparts are stable. Parametric instability arises when the frequency of the basic flow matches a multiple characteristic frequency of an otherwise stable perturbation.The work of The Nonlinear Dynamics of Time Dependent Subcritical Baroclinic CurrentsFarrell and loannu (1999) shows the deep connection in the linear version of the problem between the parametric instability and the general theory ofThe Nonlinear Dynamics of Time Dependent Subcritical Baroclinic Currents
nonnormal generation of perturbations and point out, as did PT, how the presence of time dependence of the basic state weakens the necessary' conditioThe Nonlinear Dynamics of Time Dependent Subcritical Baroclinic CurrentsbyG. R. Flierl1Department of Earth and Planetary Sciences Massachusetts Instit The Nonlinear Dynamics of Time Dependent Subcritical Baroclinic Currentsear behavior of the perturbations which arise from the parametric instability. We study the dynamics of baroclinic instabilities in the Phillips (1954) two-layer model on the beta plane and consider parameter values such that the basic state would be well below the threshold for instability in that The Nonlinear Dynamics of Time Dependent Subcritical Baroclinic Currentsmodel were it steady. We demonstrate a wide range of finite amplitude and turbulent behavior all present in flows which by any classical criterion wouThe Nonlinear Dynamics of Time Dependent Subcritical Baroclinic Currents
ld be considered stable. This has obvious implications for parameterizations of eddy development in large scale circulation models that use a criticalThe Nonlinear Dynamics of Time Dependent Subcritical Baroclinic CurrentsbyG. R. Flierl1Department of Earth and Planetary Sciences Massachusetts Instit The Nonlinear Dynamics of Time Dependent Subcritical Baroclinic Currentsrd section we discuss an analytical theory for tillite amplitude perturbations on weak but oscillating shears that clearly illustrates the possibility for instability for shears well below the classical critical value. In section 4 we introduce a truncated modal version of the two-layer problem that The Nonlinear Dynamics of Time Dependent Subcritical Baroclinic Currents we use to go beyond the formal asymptotics of section 3 to describe the role of mean shear on the fluxes generated by the disturbances. Section 5 desThe Nonlinear Dynamics of Time Dependent Subcritical Baroclinic Currents
cribes a truncation allowing several modes with which we demonstrate the symmetry breaking for larger, but still subcritical shears, in which a meridiThe Nonlinear Dynamics of Time Dependent Subcritical Baroclinic CurrentsbyG. R. Flierl1Department of Earth and Planetary Sciences Massachusetts Instit The Nonlinear Dynamics of Time Dependent Subcritical Baroclinic Currentsne with a full numerical version of the quasi-geostrophic model in section 6. Strongly turbulent end states can appear, again for classically stable values of the shear. Section 6 also describes the nonlinear cascade to longer wavelengths when the most destabilized wave is not the largest wave possi The Nonlinear Dynamics of Time Dependent Subcritical Baroclinic Currentsble in the periodic channel.In section 7 we describe the behavior of the instability for p=o. The linear inviscid problem for a purely oscillating sheThe Nonlinear Dynamics of Time Dependent Subcritical Baroclinic Currents
ar is formally always stable in this case, but we demonstrate that the addition of nonlinearity destabilizes the flow although it still provides a finThe Nonlinear Dynamics of Time Dependent Subcritical Baroclinic CurrentsbyG. R. Flierl1Department of Earth and Planetary Sciences Massachusetts Instit The Nonlinear Dynamics of Time Dependent Subcritical Baroclinic Currents) two-layer model on the beta plane in which a zonal flow with vertical but no horizontal shear is confined in a channel of width L. The layer thicknesses in the absence of motion are assumed each to be equal to D for the sake of simplicity. If ụj... is the geostrophic streamfunction in each layer w The Nonlinear Dynamics of Time Dependent Subcritical Baroclinic Currentshere n=l refers to the5https://khothuvien.cori!upper layer and n=2 to the lower layer, the nondimensional governing equations are.Pedlosky(1987).<•1,2The Nonlinear Dynamics of Time Dependent Subcritical Baroclinic Currents
where:1. - ’X +(-lJ f[vẠ - .(2.1 a,b,c.d)The Nonlinear Dynamics of Time Dependent Subcritical Baroclinic CurrentsbyG. R. Flierl1Department of Earth and Planetary Sciences Massachusetts InstitThe Nonlinear Dynamics of Time Dependent Subcritical Baroclinic CurrentsbyG. R. Flierl1Department of Earth and Planetary Sciences Massachusetts InstitGọi ngay
Chat zalo
Facebook