Temperature statistics in two-dimensional stably stratified turbulence

2002 ◽  
Vol 66 (1) ◽  
Author(s):  
Scott Wunsch ◽  
Yuan-Nan Young
Keyword(s):  
Two Dimensional ◽  
Stratified Turbulence

scholarly journals Phenomenology of two-dimensional stably stratified turbulence under large-scale forcing

2017 ◽  
Vol 18 (3) ◽  
pp. 219-239 ◽  
Author(s):  
Abhishek Kumar ◽  
Mahendra K. Verma ◽  
Jai Sukhatme
Keyword(s):  
Large Scale ◽  
Two Dimensional ◽  
Stratified Turbulence

scholarly journals Two-dimensional moist stratified turbulence and the emergence of vertically sheared horizontal flows

2012 ◽  
Vol 24 (3) ◽  
pp. 036602 ◽  
Author(s):  
Jai Sukhatme ◽  
Andrew J. Majda ◽  
Leslie M. Smith
Keyword(s):  
Two Dimensional ◽  
Stratified Turbulence ◽  
Horizontal Flows

scholarly journals Theoretical analysis of the zigzag instability of a vertical columnar vortex pair in a strongly stratified fluid

2000 ◽  
Vol 419 ◽  
pp. 29-63 ◽  
Author(s):  
PAUL BILLANT ◽  
JEAN-MARC CHOMAZ
Keyword(s):  
Froude Number ◽  
Evolution Equations ◽  
Vortex Pair ◽  
Horizontal Velocity ◽  
Phase Variable ◽  
Two Dimensional ◽  
Stratified Turbulence ◽  
Periodic Patterns ◽  
Phase Dynamics ◽  
Columnar Vortex

A general theoretical account is proposed for the zigzag instability of a vertical columnar vortex pair recently discovered in a strongly stratified experiment.The linear inviscid stability of the Lamb–Chaplygin vortex pair is analysed by a multiple-scale expansion analysis for small horizontal Froude number (Fh = U/LhN, where U is the magnitude of the horizontal velocity, Lh the horizontal lengthscale and N the Brunt–Väisälä frequency) and small vertical Froude number (Fv = U/LvN, where Lv is the vertical lengthscale) using the scaling of the equations of motion introduced by Riley, Metcalfe & Weissman (1981). In the limit Fv = 0, these equations reduce to two-dimensional Euler equations for the horizontal velocity with undetermined vertical dependence. Thus, at leading order, neutral modes of the flow are associated, among others, to translational and rotational invariances in each horizontal plane. To each broken invariance is related a phase variable that may vary freely along the vertical. Conservation of mass and potential vorticity impose at higher order the evolution equations governing the phase variables that we derive for Fh [Lt ] 1 and Fv [Lt ] 1 in the spirit of phase dynamics techniques established for periodic patterns. In agreement with the experimental observations, this asymptotic analysis shows the existence of an instability consisting of a vertically modulated rotation and a translation of the columnar vortex pair perpendicular to the travelling direction. The dispersion relation as well as the spatial eigenmode of the zigzag instability are determined. The analysis predicts that the most amplified vertical wavelength should scale as U/N and the maximum growth rate as U/Lh.Our main finding is thus that the typical thickness of the ensuing layers will be such that Fv = O(1) and not Fv [Lt ] 1 as assumed by Riley et al. (1981) and Lilly (1983). This implies that such strongly stratified flows are not described by two- dimensional horizontal equations. These results may help to understand the layering commonly observed in stratified turbulence and the fundamental differences with strictly two-dimensional turbulence.

scholarly journals A Case Study of Two-Dimensional Stratified Turbulence

1999 ◽  
Vol 56 (7) ◽  
pp. 959-976 ◽  
Author(s):  
Ulf Högström ◽  
Ann-Sofi Smedman ◽  
Hans Bergström
Keyword(s):  
Two Dimensional ◽  
Stratified Turbulence

scholarly journals Vertically Sheared Horizontal Flow-Forming Instability in Stratified Turbulence: Analytical Linear Stability Analysis of Statistical State Dynamics Equilibria

2018 ◽  
Vol 75 (12) ◽  
pp. 4201-4227 ◽  
Author(s):  
Joseph G. Fitzgerald ◽  
Brian F. Farrell
Keyword(s):  
Stability Analysis ◽  
Large Scale ◽  
Fundamental Problem ◽  
Direct Analysis ◽  
Two Dimensional ◽  
Stratified Turbulence ◽  
Dynamical Equations ◽  
Flow Forming ◽  
Quasi Biennial Oscillation ◽  
Statistical State

Abstract Vertically banded zonal jets are frequently observed in weakly or nonrotating stratified turbulence, with the quasi-biennial oscillation in the equatorial stratosphere and the ocean’s equatorial deep jets being two examples. Explaining the formation of jets in stratified turbulence is a fundamental problem in geophysical fluid dynamics. Statistical state dynamics (SSD) provides powerful methods for analyzing turbulent systems exhibiting emergent organization, such as banded jets. In SSD, dynamical equations are written directly for the evolution of the turbulence statistics, enabling direct analysis of the statistical interactions between the incoherent component of turbulence and the coherent large-scale structure component that underlie jet formation. A second-order closure of SSD, known as S3T, has previously been applied to show that meridionally banded jets emerge in barotropic β-plane turbulence via a statistical instability referred to as the zonostrophic instability. Two-dimensional Boussinesq turbulence provides a simple model of nonrotating stratified turbulence analogous to the β-plane model of planetary turbulence. Jets known as vertically sheared horizontal flows (VSHFs) often emerge in simulations of Boussinesq turbulence, but their dynamics is not yet clearly understood. In this work S3T analysis of the zonostrophic instability is extended to study VSHF emergence in two-dimensional Boussinesq turbulence using an analytical formulation of S3T amenable to perturbation stability analysis. VSHFs are shown to form via an instability that is analogous in stratified turbulence to the zonostrophic instability in β-plane turbulence. This instability is shown to be strikingly similar to the zonostrophic instability, suggesting that jet emergence in both geostrophic and nonrotating stratified turbulence may be understood as instances of the same generic phenomenon.

Statistical state dynamics analysis of buoyancy layer formation via the Phillips mechanism in two-dimensional stratified turbulence

2019 ◽  
Vol 864 ◽  
Author(s):  
Joseph G. Fitzgerald ◽  
Brian F. Farrell
Keyword(s):  
Equations Of Motion ◽  
Two Dimensional ◽  
Stratified Turbulence ◽  
Diffusion Property ◽  
Theoretical Understanding ◽  
Flux Gradient ◽  
Statistical State ◽  
The Operating Mechanism ◽  
Fundamental Equations ◽  
Negative Diffusion

Horizontal density layers are commonly observed in stratified turbulence. Recent work (e.g. Taylor & Zhou, J. Fluid Mech., vol. 823, 2017, R5) has reinvigorated interest in the Phillips instability (PI), by which density layers form via negative diffusion if the turbulent buoyancy flux weakens as stratification increases. Theoretical understanding of PI is incomplete, in part because it remains unclear whether and by what mechanism the flux-gradient relationship for a given example of turbulence has the required negative-diffusion property. Furthermore, the difficulty of analysing the flux-gradient relation in evolving turbulence obscures the operating mechanism when layering is observed. These considerations motivate the search for an example of PI that can be analysed clearly. Here PI is shown to occur in two-dimensional Boussinesq sheared stratified turbulence maintained by stochastic excitation. PI is analysed using the second-order S3T closure of statistical state dynamics, in which the dynamics is written directly for statistical variables of the turbulence. The predictions of S3T are verified using nonlinear simulations. This analysis provides theoretical underpinning of PI based on the fundamental equations of motion that complements previous analyses based on phenomenological models of turbulence.

scholarly journals A flux loop mechanism in two-dimensional stratified turbulence

2011 ◽  
Vol 95 (3) ◽  
pp. 34001 ◽  
Author(s):  
G. Boffetta ◽  
F. De Lillo ◽  
A. Mazzino ◽  
S. Musacchio
Keyword(s):  
Two Dimensional ◽  
Stratified Turbulence
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