A Theory of Baroclinic Turbulence

Farrell, Brian F.; Ioannou, Petros J.

doi:10.1175/2009jas2989.1

Cited by 40 publications

(32 citation statements)

References 40 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[6,21,29,30,45]). As already noticed, in the study by Mamatsashvili et al [29] for baroclinic shear flows with Ri 1 and Ro 1, it is found that (SFH) asymmetric perturbations undergo substantial transient amplification much larger than the growth of symmetric instability (see also Ref.…”

Section: A General Considerationsmentioning

confidence: 99%

Wave-vortex mode coupling in neutrally stable baroclinic flows

Salhi¹,

Pieri

2014

Phys. Rev. E

View full text Add to dashboard Cite

Rotating stratified flows in thermal wind balance are at the center of geophysical fluid dynamics. Recently, endeavors were put on studying the linear response of such flows to potential vorticity perturbations. It has been shown that the initial potential vorticity (PV) distribution is fundamental and is responsible for important transient growth of the perturbation and gravity-wave generation. Using Pfeiffer's theorem [J. Differ. Equat. 11, 145 (1972)], we give the mathematical demonstration of the stability of asymmetric perturbations k1≠0 of a uniform, unbounded flow in thermal wind balance. Incidentally, we prove that both the wave mode (that corresponds to a vanishing PV) and the vortex mode (corresponding to a nonzero PV) are stable. The emphasis is put on the nontrivial behavior of inertia-gravity waves (IGWs) when deformed by a background shear. In particular, we show that in the linear limit, sheared inertia-gravity waves asymptotically oscillate at the inertial waves frequency, but their amplitude is sensitive to shear, stratification, and rotation. Last, we study the development of the IGWs dynamics considering isotropic initial conditions. Computations indicate that both the vortex mode and the wave mode generate IGWs, but the energy of the IGWs generated by the vortex mode is more important than the energy of the IGWs generated by the wave mode. It is also found that, at large times, the energy of the IGWs generated by the vortex mode increases as the ratio kv/kh (initial vertical wavenumber over horizontal wavenumber) increases (like kv(2)/kh(2)), while the energy of the IGWs generated by the wave mode oscillates in function of kv/kh.

show abstract

Section: A General Considerationsmentioning

confidence: 99%

Wave-vortex mode coupling in neutrally stable baroclinic flows

Salhi¹,

Pieri

2014

Phys. Rev. E

View full text Add to dashboard Cite

show abstract

“…The spontaneous formation of long-lived coherent nearly zonal jets in the ocean is yet another example of large-scale phenomena induced by mesoscale variability (Hogg and Owens 1999;Maximenko et al 2005;Kamenkovich et al 2009;Berloff et al 2009;2011). Parallel developments in the meteorological context (e.g., Larichev and Held 1995;Frisius 1998;Farrell and Ioannou 2009) underscore the universal nature of the problem and its broad geophysical significance.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Equilibration of Baroclinic Instability: The Growth Rate Balance Model

Radko

Flanagan

2014

Journal of Physical Oceanography

View full text Add to dashboard Cite

A theoretical model is developed, which attempts to predict the lateral transport by mesoscale variability, generated and maintained by baroclinic instability of large-scale flows. The authors are particularly concerned by the role of secondary instabilities of primary baroclinically unstable modes in the saturation of their linear growth. Theory assumes that the fully developed equilibrium state is characterized by the comparable growth rates of primary and secondary instabilities. This assumption makes it possible to formulate an efficient algorithm for evaluating the equilibrium magnitude of mesoscale eddies as a function of the background parameters: vertical shear, stratification, beta effect, and bottom drag. The proposed technique is applied to two classical models of baroclinic instability-the Phillips two-layer model and the linearly stratified Eady model. Theory predicts that the eddy-driven lateral mixing rapidly intensifies with increasing shear and weakens when the beta effect is increased. The eddy transport is also sensitive to the stratification pattern, decreasing as the ratio of upper/lower layer depths in the Phillips model is decreased below unity. Theory is successfully tested by a series of direct numerical simulations that span a wide parameter range relevant for typical large-scale currents in the ocean. The spontaneous emergence of large-scale patterns induced by mesoscale variability, and their role in the cross-flow eddy transport, is examined using a suite of numerical simulations.

show abstract

“…While for extrinsic sources of turbulence this is probably a good assumption, it is a crude assumption when the eddy excitation represents the nonlinear scattering to other scales, because its amplitude depends then on the very presence of the eddies. Progress on this problem has been made (DelSole 2001;Farrell & Ioannou 2009c) and while being an attractive avenue for future study, such a closure is not necessary for understanding the basic dynamics underlying the structural instability of the resulting equilibria.…”

Section: Introductionmentioning

confidence: 99%

Structural stability theory of two-dimensional fluid flow under stochastic forcing

Bakas

Ioannou

2011

J. Fluid Mech.

Self Cite

View full text Add to dashboard Cite

Large-scale mean flows often emerge in turbulent fluids. In this work, we formulate a stability theory, the stochastic structural stability theory (SSST), for the emergence of jets under external random excitation. We analytically investigate the structural stability of a two-dimensional homogeneous fluid enclosed in a channel and subjected to homogeneous random forcing. We show that two generic competing mechanisms control the instability that gives rise to the emergence of an infinitesimal jet: advection of the eddy vorticity by the mean flow that is shown to be jet forming and advection of the vorticity gradient of the jet by the eddies that is shown to hinder the formation of the mean flow. We show that stochastic forcing with small streamwise coherence and an amplitude larger than a certain threshold leads to the emergence of jets in the channel through a bifurcation of the non-linear SSST system.

show abstract

A Theory of Baroclinic Turbulence

Cited by 40 publications

References 40 publications

Wave-vortex mode coupling in neutrally stable baroclinic flows

Wave-vortex mode coupling in neutrally stable baroclinic flows

Nonlinear Equilibration of Baroclinic Instability: The Growth Rate Balance Model

Structural stability theory of two-dimensional fluid flow under stochastic forcing

Contact Info

Product

Resources

About