667 research outputs found

### The nonlinear dynamics of time-dependent subcritical baroclinic currents

Author Posting. Â© American Meteorological Society, 2007. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 37 (2007): 1001-1021, doi:10.1175/jpo3034.1.The nonlinear dynamics of baroclinically unstable waves in a time-dependent zonal shear flow is considered 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 below the critical value of the steady shear version of the model. Nevertheless, the time-dependent problem in which the shear oscillates periodically is unstable, and the unstable waves grow to substantial amplitudes, in some cases with strongly nonlinear and turbulent characteristics. For very small values 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 shear 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 shear 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 resulting nonlinear states exhibit a rectified horizontal buoyancy flux with a nonzero time average as a result of the instability of the oscillating shear. For higher, still subcritical, values of the shear, a symmetry breaking is detected 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 that are substantially subcritical but of order of the critical shear, calculations with a full quasigeostrophic numerical model reveal a turbulent flow generated by the instability. If the beta effect is disregarded, the inviscid, linear problem is formally stable. However, calculations show that a small degree of nonlinearity is enough to destabilize the flow, leading to large amplitude vacillations and turbulence. When the most unstable wave is not the longest wave in the system, a cascade up scale to longer waves is observed. Indeed, this classically subcritical flow shows most of the qualitative character of a strongly supercritical flow. This result supports previous suggestions of the important role of background time dependence in maintaining the atmospheric and oceanic synoptic eddy field.GRF was supported by NSF
Grant OCE-0137023, and JP was supported by NSF
Grant OCE- 9901654

### Evolution of the bursting-layer wave during a Type 1 X-ray burst

In a popular scenario due to Heyl, quasi periodic oscillations (QPOs) which
are seen during type 1 X-ray bursts are produced by giant travelling waves in
neutron-star oceans. Piro and Bildsten have proposed that during the burst
cooling the wave in the bursting layer may convert into a deep crustal
interface wave, which would cut off the visible QPOs. This cut-off would help
explain the magnitude of the QPO frequency drift, which is otherwise
overpredicted by a factor of several in Heyl's scenario. In this paper, we
study the coupling between the bursting layer and the deep ocean. The coupling
turns out to be weak and only a small fraction of the surface-wave energy gets
transferred to that of the crustal-interface wave during the burst. Thus the
crustal-interface wave plays no dynamical role during the burst, and no early
QPO cut-off should occur.Comment: 8 pages, submitted to MNRA

### The baroclinic adjustment of time-dependent shear flows

Author Posting. Â© American Meteorological Society, 2010. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 40 (2010): 1851-1865, doi:10.1175/2010JPO4217.1.Motivated by the fact that time-dependent currents are ubiquitous in the ocean, this work studies the two-layer Phillips model on the beta plane with baroclinic shear flows that are steady, periodic, or aperiodic in time to understand their nonlinear evolution better. When a linearly unstable basic state is slightly perturbed, the primary wave grows exponentially until nonlinear advection adjusts the growth. Even though for long time scales these nearly two-dimensional motions predominantly cascade energy to large scales, for relatively short times the waveâ€“mean flow and waveâ€“wave interactions cascade energy to smaller horizontal length scales. The authors demonstrate that the manner through which these mechanisms excite the harmonics depends significantly on the characteristics of the basic state. Time-dependent basic states can excite harmonics very rapidly in comparison to steady basic states. Moreover, in all the simulations of aperiodic baroclinic shear flows, the barotropic component of the primary wave continues to grow after the adjustment by the nonlinearities. Furthermore, the authors find that the correction to the zonal mean flow can be much larger when the basic state is aperiodic compared to the periodic or steady limits. Finally, even though time-dependent baroclinic shear on an f plane is linearly stable, the authors show that perturbations can grow algebraically in the linear regime because of the erratic variations in the aperiodic flow. Subsequently, baroclinicity adjusts the growing wave and creates a final state that is more energetic than the nonlinear adjustment of any of the unstable steady baroclinic shears that are considered.FJP was supported by NSERC
and JP was supported by NSF OCE 0925061 during the
research and writing of this manuscript

### Ensemble inequivalence, bicritical points and azeotropy for generalized Fofonoff flows

We present a theoretical description for the equilibrium states of a large
class of models of two-dimensional and geophysical flows, in arbitrary domains.
We account for the existence of ensemble inequivalence and negative specific
heat in those models, for the first time using explicit computations. We give
exact theoretical computation of a criteria to determine phase transition
location and type. Strikingly, this criteria does not depend on the model, but
only on the domain geometry. We report the first example of bicritical points
and second order azeotropy in the context of systems with long range
interactions.Comment: 4 pages, submitted to Phys. Rev. Let

### Rossby waves in rapidly rotating Bose-Einstein condensates

We predict and describe a new collective mode in rotating Bose-Einstein
condensates, which is very similar to the Rossby waves in geophysics. In the
regime of fast rotation, the Coriolis force dominates the dynamics and acts as
a restoring force for acoustic-drift waves along the condensate. We derive a
nonlinear equation that includes the effects of both the zero-point pressure
and the anharmonicity of the trap. It is shown that such waves have negative
phase speed, propagating in the opposite sense of the rotation. We discuss
different equilibrium configurations and compare with those resulting from the
Thomas-Fermi approximation.Comment: 4 pages, 2 figures (submitted to PRL

### Dissipation scales and anomalous sinks in steady two-dimensional turbulence

In previous papers I have argued that the \emph{fusion rules hypothesis},
which was originally introduced by L'vov and Procaccia in the context of the
problem of three-dimensional turbulence, can be used to gain a deeper insight
in understanding the enstrophy cascade and inverse energy cascade of
two-dimensional turbulence. In the present paper we show that the fusion rules
hypothesis, combined with \emph{non-perturbative locality}, itself a
consequence of the fusion rules hypothesis, dictates the location of the
boundary separating the inertial range from the dissipation range. In so doing,
the hypothesis that there may be an anomalous enstrophy sink at small scales
and an anomalous energy sink at large scales emerges as a consequence of the
fusion rules hypothesis. More broadly, we illustrate the significance of
viewing inertial ranges as multi-dimensional regions where the fully unfused
generalized structure functions of the velocity field are self-similar, by
considering, in this paper, the simplified projection of such regions in a
two-dimensional space, involving a small scale $r$ and a large scale $R$, which
we call, in this paper, the $(r, R)$-plane. We see, for example, that the
logarithmic correction in the enstrophy cascade, under standard molecular
dissipation, plays an essential role in inflating the inertial range in the
$(r, R)$ plane to ensure the possibility of local interactions. We have also
seen that increasingly higher orders of hyperdiffusion at large scales or
hypodiffusion at small scales make the predicted sink anomalies more resilient
to possible violations of the fusion rules hypothesis.Comment: 22 pages, resubmitted to Phys. Rev.

### Marangoni shocks in unobstructed soap-film flows

It is widely thought that in steady, gravity-driven, unobstructed soap-film
flows, the velocity increases monotonically downstream. Here we show
experimentally that the velocity increases, peaks, drops abruptly, then lessens
gradually downstream. We argue theoretically and verify experimentally that the
abrupt drop in velocity corresponds to a Marangoni shock, a type of shock
related to the elasticity of the film. Marangoni shocks induce locally intense
turbulent fluctuations and may help elucidate the mechanisms that produce
two-dimensional turbulence away from boundaries.Comment: 4 pages, 5 figures, published in PR

### Parametric instability in oscillatory shear flows

Author Posting. Â© Cambridge University Press, 2003. This article is posted here by permission of Cambridge University Press for personal use, not for redistribution. The definitive version was published in Journal of Fluid Mechanics 481 (2003): 329-353, doi:10.1017/S0022112003004051.In this article we investigate time-periodic shear flows in the context of the two-dimensional vorticity equation, which may be applied to describe certain large-scale atmospheric and oceanic flows. The linear stability analyses of both discrete and continuous profiles demonstrate that parametric instability can arise even in this simple model: the oscillations can stabilize (destabilize) an otherwise unstable (stable) shear flow, as in Mathieu's equation (Stoker 1950). Nonlinear simulations of the continuous oscillatory basic state support the predictions from linear theory and, in addition, illustrate the evolution of the instability process and thereby show the structure of the vortices that emerge. The discovery of parametric instability in this model suggests that this mechanism can occur in geophysical shear flows and provides an additional means through which turbulent mixing can be generated in large-scale flows.F.P.â€™s and G.F.â€™s research was supported by grants from NSF, OPP-
9910052 and OCE-0137023. J.P.â€™s research is supported in part by a grant from NSF,
OCE-9901654

### Rapidly rotating plane layer convection with zonal flow

The onset of convection in a rapidly rotating layer in which a thermal wind
is present is studied. Diffusive effects are included. The main motivation is
from convection in planetary interiors, where thermal winds are expected due to
temperature variations on the core-mantle boundary. The system admits both
convective instability and baroclinic instability. We find a smooth transition
between the two types of modes, and investigate where the transition region
between the two types of instability occurs in parameter space. The thermal
wind helps to destabilise the convective modes. Baroclinic instability can
occur when the applied vertical temperature gradient is stable, and the
critical Rayleigh number is then negative. Long wavelength modes are the first
to become unstable. Asymptotic analysis is possible for the transition region
and also for long wavelength instabilities, and the results agree well with our
numerical solutions. We also investigate how the instabilities in this system
relate to the classical baroclinic instability in the Eady problem. We conclude
by noting that baroclinic instabilities in the Earth's core arising from
heterogeneity in the lower mantle could possibly drive a dynamo even if the
Earth's core were stably stratified and so not convecting.Comment: 20 pages, 7 figure

### Energy Spectrum of Quasi-Geostrophic Turbulence

We consider the energy spectrum of a quasi-geostrophic model of forced,
rotating turbulent flow. We provide a rigorous a priori bound E(k) <= Ck^{-2}
valid for wave numbers that are smaller than a wave number associated to the
forcing injection scale. This upper bound separates this spectrum from the
Kolmogorov-Kraichnan k^{-{5/3}} energy spectrum that is expected in a
two-dimensional Navier-Stokes inverse cascade. Our bound provides theoretical
support for the k^{-2} spectrum observed in recent experiments

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