Structural Stability of Turbulent Jets

Farrell, Brian F.; Ioannou, Petros J.

doi:10.1175/1520-0469(2003)060<2101:ssotj>2.0.co;2

Cited by 135 publications

(214 citation statements)

References 56 publications

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“…These rates are quite different from previous estimates that ignored ocean (Fig. 2f), which again are unstable and feedback on the eddies which sustain the jets 24 .…”

contrasting

confidence: 96%

Dynamics of a Snowball Earth ocean

Ashkenazy

Gildor

Lösch

et al. 2013

Nature

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Geological evidence suggests that marine ice extended to the equator at least twice during the Neoproterozoic (∼750-635 Myr ago) 1, 2 , inspiring the Snowball Earth hypothesis that the Earth was globally ice covered 3, 4 . In a possible Snowball Earth climate, ocean circulation and mixing processes would have determined the melting and freezing rates that determine ice thickness 5,6 , influenced the survival of photosynthetic life 4,5,7-9 , and may provide important constraints for the interpretation of geochemical and sedimentological observations 4,10 . Here we show that in a Snowball Earth, the ocean would have been well mixed and characterized by a dynamic circulation 11 , with vigorous equatorial meridional overturning circulation, zonal equatorial jets, a well-developed eddy field, strong coastal upwelling and convective mixing. This is in contrast to the sluggish ocean often expected in a snowball scenario 3 .As a result of vigorous convective mixing, the ocean temperature, salinity and density were either uniform in the vertical or weakly stratified in a few locations. Our results are based on a coupled ice flow-ocean circulation model driven by a weak geothermal heat flux under a global ∼1 km ice cover. Compared to the modern ocean, the snowball ocean had far larger vertical mixing rates, and comparable horizontal mixing by ocean eddies. The strong circulation and coastal upwelling resulted in melting rates near continents as much as ten times larger than previously estimated 6, 7 . While we cannot resolve the ongoing debate on the existence of a global snowball ice cover 10,12,13 , we discuss the implications to nutrient supply for photosynthetic activity and to banded iron formations. The new insights and constraints on ocean dynamics may help resolve the Snowball Earth controversy when combined with future geochemical and geological observations.The flow of thick ice over a Snowball ocean ("sea glaciers", characterized by very different dynamics from thinner sea ice 14 ), has received significant attention over the past few years [5][6][7]9,14,15 . Similarly, the role and dynamics of atmospheric circulation and heat transport, CO2 concentration, cloud feedbacks, and continental configuration have been studied [16][17][18] , as has the role of dust over the Snowball ice cover 17,19 . In contrast, despite its importance, the ocean circulation during Snowball events has received little attention. The few studies that used full ocean General Circulation Models (GCMs) concentrated mostly on the ocean role in Snowball initiation and aftermath 20,21 . None of these studied accounted for the combined effects of thick ice cover flow and driving by geothermal heating 11,13,22,23 , yet 11 simulated an ocean under a 200 m thick ice cover with no geothermal heat flux, and calculated a non steady--state solution with near--uniform temperature and salinity, and vanishing Eulerian circulation together with a strong parameterized eddy--induced high latitude circulation cells.To allow simulating the special circumstan...

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“…These rates are quite different from previous estimates that ignored ocean (Fig. 2f), which again are unstable and feedback on the eddies which sustain the jets 24 .…”

contrasting

confidence: 96%

Dynamics of a Snowball Earth ocean

Ashkenazy

Gildor

Lösch

et al. 2013

Nature

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“…Several models with a coupling between the mean flow and the linear perturbation equation have been proposed. The stochastic structural stability theory (SSST) has been introduced by Farrell and Ioannou [22,23], consisting in a coupled system of equations where the linear response to white noise forcing rewritten as a Lyapunov equation [20] is coupled to the slowly varying ensemble average mean flow by means of the Reynolds stress. This theory is able to describe sustained coherent structures that appear during the transition to turbulence in the 3D Couette flow [23] as well as in turbulent atmospheric flows [22,24].…”

Section: Introductionmentioning

confidence: 99%

“…The stochastic structural stability theory (SSST) has been introduced by Farrell and Ioannou [22,23], consisting in a coupled system of equations where the linear response to white noise forcing rewritten as a Lyapunov equation [20] is coupled to the slowly varying ensemble average mean flow by means of the Reynolds stress. This theory is able to describe sustained coherent structures that appear during the transition to turbulence in the 3D Couette flow [23] as well as in turbulent atmospheric flows [22,24]. As an alternative, the reduced nonlinear model (RNL) approach has been proposed [25] coupling the mean flow to a single realization of the stochastic linear response, avoiding the computation of the Lyapunov equation [23].…”

Section: Introductionmentioning

confidence: 99%

“…Motivated by the SSST [22,23] and the low order modeling based on harmonic optima [17], we propose a model to describe the nonlinear dynamics of the response to white noise forcing in a strongly amplifying flow, with the objective to capture its saturation with an increasing forcing amplitude. The model is applied to a canonical amplifier flow, the incompressible backward-facing step flow, which is archetypical in fundamental studies of flow separation induced by abrupt changes of geometry.…”

Section: Introductionmentioning

confidence: 99%

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Saturation of the response to stochastic forcing in two-dimensional backward-facing step flow: A self-consistent approximation

Mantič-Lugo

Gallaire

2016

Phys. Rev. Fluids

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Selective noise amplifiers are characterized by large linear amplification to external perturbations in a particular frequency range despite their global linear stability. Applying a stochastic forcing with increasing amplitude, the response undergoes a strong nonlinear saturation when compared to the linear estimation. Building upon our previous work, we introduce a predictive model that describes this nonlinear dynamics, and we apply it to a canonical example of selective noise amplifiers: the backward-facing step flow. Rewriting conveniently the stochastic forcing and response in the frequency domain, the model consists in a mean flow equation coupled to the linear response to forcing at each frequency. This coupling is attained by the Reynolds stress, which is constructed by the integral in frequency of the independent responses. We generalize the model for a response to a white noise forcing δ-correlated in space and time restricting the flow dynamics to its most energetic patterns calculated from the optimal harmonic forcing and response of the flow. The model estimates accurately the response saturation when compared to direct numerical simulations, and it correctly approximates the structure of the response and the mean flow modification. It also shows that the response undergoes a selective process governed by the nonlinear gain, which promotes a response structure with an approximately single frequency and wavelength in the whole domain. These results suggest that the mean flow modification by the Reynolds stress is the key nonlinearity in the saturation process of the response to white noise.

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“…A multiple-jet structure may be obtained in a forced barotropic flow (Farrell and Ioannou 2003) or in a weakly unstable baroclinic flow driven by thermal relaxation (Charney 1973). A common feature of both flows is a finite meridional scale of the eddy field.…”

Section: Introductionmentioning

confidence: 99%

Zonal Flow Regime Changes in a GCM and in a Simple Quasigeostrophic Model: The Role of Stratospheric Dynamics

Bordi

Fraedrich

Ghil

et al. 2009

Journal of the Atmospheric Sciences

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The atmospheric general circulation is characterized by both single-and double-jet patterns. The doublejet structure of the zonal mean zonal wind is analyzed in Southern Hemisphere observations for the two calendar months of November and April. The observed features are studied further in an idealized quasigeostrophic and a simplified general circulation model (GCM). Results suggest that capturing the bimodality of the zonal mean flow requires the parameterization of momentum and heat fluxes associated with baroclinic instability of the three-dimensional fields.The role of eddy heat fluxes in generating the observed double-jet pattern is ascertained by using an analytical Eady model with stratospheric easterlies, in which a single wave disturbance interacts with the mean flow. In this model, the dual jets are generated by the zonal mean flow correction. Sensitivity of the results to the tropospheric vertical wind shear (or, equivalently, the meridional temperature gradient in the basic state's troposphere) is also studied in the Eady model and compared to related experiments using the simplified GCM.

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Structural Stability of Turbulent Jets

Cited by 135 publications

References 56 publications

Dynamics of a Snowball Earth ocean

Dynamics of a Snowball Earth ocean

Saturation of the response to stochastic forcing in two-dimensional backward-facing step flow: A self-consistent approximation

Zonal Flow Regime Changes in a GCM and in a Simple Quasigeostrophic Model: The Role of Stratospheric Dynamics

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