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  • 1
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    Modal and nonmodal growths of inviscid planar perturbations in shear flows with a free surface (2009)
    American Institute of Physics
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    Publication Date: 2009-02-01
    Print ISSN: 1070-6631
    Electronic ISSN: 1089-7666
    Topics: Physics
    Published by American Institute of Physics
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  • 2
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    Emergence of Large Scale Structure in Barotropicβ-Plane Turbulence (2013)
    American Physical Society
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    Publication Date: 2013-05-29
    Print ISSN: 0031-9007
    Electronic ISSN: 1079-7114
    Topics: Physics
    Published by American Physical Society
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  • 3
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    A Geometric Interpretation of Zonostrophic Instability (2020)
    American Meteorological Society
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    Publication Date: 2020-09-01
    Description: The zonostrophic instability that leads to the emergence of zonal jets in barotropic beta-plane turbulence is analyzed through a geometric decomposition of the eddy stress tensor. The stress tensor is visualized by an eddy variance ellipse whose characteristics are related to eddy properties. The tilt of the ellipse principal axis is the tilt of the eddies with respect to the shear, and the eccentricity of the ellipse is related to the eddy anisotropy, and its size is related to the eddy kinetic energy. Changes of these characteristics are directly related to the vorticity fluxes forcing the mean flow. The statistical state dynamics of the turbulent flow closed at second order is employed as it provides an analytic expression for both the zonostrophic instability and the stress tensor. For the linear phase of the instability, the stress tensor is analytically calculated at the stability boundary. For the nonlinear equilibration of the instability the tensor is calculated in the limit of small supercriticality in which the amplitude of the jet velocity follows Ginzburg–Landau dynamics. It is found that, dependent on the characteristics of the forcing, the jet is accelerated either because the jet primarily anisotropizes the eddies so as to produce upgradient fluxes, or because the jet changes the eddy tilt. The instability equilibrates as these changes are partially reversed by the nonlinear jet–eddy dynamics.
    Print ISSN: 0022-3670
    Electronic ISSN: 1520-0485
    Topics: Geosciences , Physics
    Published by American Meteorological Society
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  • 4
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    Statistical State Dynamics of Weak Jets in Barotropic Beta-Plane Turbulence (2019)
    American Meteorological Society
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    Publication Date: 2019-03-01
    Description: Zonal jets in a barotropic setup emerge out of homogeneous turbulence through a flow-forming instability of the homogeneous turbulent state (zonostrophic instability), which occurs as the turbulence intensity increases. This has been demonstrated using the statistical state dynamics (SSD) framework with a closure at second order. Furthermore, it was shown that for small supercriticality the flow-forming instability follows Ginzburg–Landau (G–L) dynamics. Here, the SSD framework is used to study the equilibration of this flow-forming instability for small supercriticality. First, we compare the predictions of the weakly nonlinear G–L dynamics to the fully nonlinear SSD dynamics closed at second order for a wide range of parameters. A new branch of jet equilibria is revealed that is not contiguously connected with the G–L branch. This new branch at weak supercriticalities involves jets with larger amplitude compared to the ones of the G–L branch. Furthermore, this new branch continues even for subcritical values with respect to the linear flow-forming instability. Thus, a new nonlinear flow-forming instability out of homogeneous turbulence is revealed. Second, we investigate how both the linear flow-forming instability and the novel nonlinear flow-forming instability are equilibrated. We identify the physical processes underlying the jet equilibration as well as the types of eddies that contribute in each process. Third, we propose a modification of the diffusion coefficient of the G–L dynamics that is able to capture the evolution of weak jets at scales other than the marginal scale (side-band instabilities) for the linear flow-forming instability.
    Print ISSN: 0022-4928
    Electronic ISSN: 1520-0469
    Topics: Geography , Geosciences , Physics
    Published by American Meteorological Society
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  • 5
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    Climatology of the Boundary Layer Height and of the Wind Field over Greece (2020)
    Molecular Diversity Preservation International
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    Publication Date: 2020-08-27
    Description: In this study, a climatology of two key boundary layer features, the Planetary Boundary Layer Height (PBLH) and the wind field over Greece is derived. The climatology is based on daily soundings collected in Athens, Thessaloniki and Heraklion and spanning a 32-year period. The PBLH is estimated using a method based on the gradient of potential temperature and a method based on the bulk Richardson number. The wind field is analyzed by calculating the wind shear and the turning angle of the wind vector between the surface and the top of the boundary layer. The PBLH of the daytime boundary layer over Athens and Thessaloniki is found to exhibit seasonal variability with summer maxima and winter minima and has annual median values in the range of 1.4–1.7 km estimated using the gradient method. The PBLH over Heraklion is found to exhibit weak seasonal variability with a lower median value of 1.2 km. The nighttime boundary layer over all three sites is found to be much shallower with PBLH values in the range of 150–200 m with no seasonal variations. In addition, the bulk Richardson number method is found to systematically underestimate the PBLH compared to the gradient method. The wind field in the daytime boundary layer at all three sites is found to have small shear of the order of 1 ms−1 and wind turning angles that are lower than 15 degrees, while in the nocturnal boundary layer it has larger shear of the order of 5–10 ms−1 with turning angles lower than 20 degrees. In addition, for both the daytime and the nighttime boundary layer there is no general preference for veering or backing.
    Electronic ISSN: 2073-4433
    Topics: Geosciences
    Published by Molecular Diversity Preservation International
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  • 6
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    Generalized stability of a shear flow with a free surface with respect to three-dimensional perturbations (2017)
    American Physical Society
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    Publication Date: 2017-02-06
    Electronic ISSN: 2469-990X
    Topics: Physics
    Published by American Physical Society
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  • 7
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    Mechanisms underlying transient growth of planar perturbations in unbounded compressible shear flow (2009)
    Cambridge University Press
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    Publication Date: 2009-10-16
    Description: Non-modal mechanisms underlying transient growth of propagating acoustic waves and non-propagating vorticity perturbations in an unbounded compressible shear flow are investigated, making use of closed form solutions. Propagating acoustic waves amplify mainly due to two mechanisms: growth due to advection of streamwise velocity that is typically termed as the lift-up mechanism leading for large Mach numbers to an almost linear increase in streamwise velocity with time and growth due to the downgradient irrotational component of the Reynolds stress leading to linear growth of acoustic wave energy for large times. Synergy between these mechanisms along with the downgradient solenoidal component of the Reynolds stress produces large and robust energy amplification. On the other hand, non-propagating vorticity perturbations amplify due to kinematic deformation of vorticity by the mean flow. For weakly compressible flows, an initial vorticity perturbation abruptly excites acoustic waves with exponentially small amplitude, and the energy gained by vorticity perturbations is transferred back to the mean flow. For moderate Mach numbers, a strong coupling between vorticity perturbations and acoustic waves is found with the energy gained by vorticity perturbations being transferred to acoustic waves that are abruptly excited by the vortex. Calculation of the optimal perturbations for a viscous flow shows that for low Mach numbers, acoustic wave excitation by vorticity perturbations and the subsequent growth of acoustic waves leads to robust energy growth of the order of Reynolds number, while for large Mach numbers, synergy between the lift-up mechanism and the downgradient solenoidal component of the Reynolds stress dominates the growth and leads to a comparable large amplification of streamwise velocity. © 2009 Cambridge University Press.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Published by Cambridge University Press
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  • 8
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    A theory for the emergence of coherent structures in beta-plane turbulence (2014)
    Cambridge University Press
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    Publication Date: 2014-01-06
    Description: Planetary turbulent flows are observed to self-organize into large-scale structures such as zonal jets and coherent vortices. One of the simplest models of planetary turbulence is obtained by considering a barotropic flow on a beta-plane channel with turbulence sustained by random stirring. Nonlinear integrations of this model show that as the energy input rate of the forcing is increased, the homogeneity of the flow is broken with the emergence of non-zonal, coherent, westward propagating structures and at larger energy input rates by the emergence of zonal jets. We study the emergence of non-zonal coherent structures using a non-equilibrium statistical theory, stochastic structural stability theory (S3T, previously referred to as SSST). S3T directly models a second-order approximation to the statistical mean turbulent state and allows the identification of statistical turbulent equilibria and study of their stability. Using S3T, the bifurcation properties of the homogeneous state in barotropic beta-plane turbulence are determined. Analytic expressions for the zonal and non-zonal large-scale coherent flows that emerge as a result of structural instability are obtained. Through numerical integrations of the S3T dynamical system, it is found that the unstable structures equilibrate at finite amplitude. Numerical simulations of the nonlinear equations confirm the characteristics (scale, amplitude and phase speed) of the structures predicted by S3T. © © 2014 Cambridge University Press.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Published by Cambridge University Press
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  • 9
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    Structural stability theory of two-dimensional fluid flow under stochastic forcing (2011)
    Cambridge University Press
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    Publication Date: 2011-07-15
    Description: 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. © Cambridge University Press 2011.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Published by Cambridge University Press
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  • 10
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    Is spontaneous generation of coherent baroclinic flows possible? (2019)
    Cambridge University Press
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    Publication Date: 2019-01-15
    Description: Geophysical turbulence is observed to self-organize into large-scale flows such as zonal jets and coherent vortices. Previous studies of barotropic-plane turbulence have shown that coherent flows emerge from a background of homogeneous turbulence as a bifurcation when the turbulence intensity increases. The emergence of large-scale flows has been attributed to a new type of collective, symmetry-breaking instability of the statistical state dynamics of the turbulent flow. In this work, we extend the analysis to stratified flows and investigate turbulent self-organization in a two-layer fluid without any imposed mean north-south thermal gradient and with turbulence supported by an external random stirring. We use a second-order closure of the statistical state dynamics, that is termed S3T, with an appropriate averaging ansatz that allows the identification of statistical turbulent equilibria and their structural stability. The bifurcation of the statistically homogeneous equilibrium state to inhomogeneous equilibrium states comprising zonal jets and/or large-scale waves when the energy input rate of the excitation passes a critical threshold is analytically studied. Our theory predicts that there is a large bias towards the emergence of barotropic flows. If the scale of excitation is of the order of (or larger than) the deformation radius, the large-scale structures are barotropic. Mixed barotropic-baroclinic states with jets and/or waves arise when the excitation is at scales shorter than the deformation radius with the baroclinic component of the flow being subdominant for low energy input rates and insignificant for higher energy input rates. The predictions of the S3T theory are compared with nonlinear simulations. The theory is found to accurately predict both the critical transition parameters and the scales of the emergent structures but underestimates their amplitude. © 2019 Cambridge University Press.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Published by Cambridge University Press
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