Stratified Kolmogorov flow. Part 2

Balmforth, N. J.; Young, Yuan-Nan

doi:10.1017/s002211200400271x

Cited by 32 publications

(23 citation statements)

References 22 publications

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“…Moreover, a number of measurements have also been made in terms of assessing the characteristics of turbulence while using different forms of the natural media including the atmosphere, large wind tunnels, the ocean, etc. [1] [2]. These measurements have been effective in confirming the different predictions of the multidimensional theory that was proposed by Kolmogorov [3].…”

Section: Introductionsupporting

confidence: 60%

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Kolmogorov Flow: Seven Decades of History

Fylladitakis¹

2018

JAMP

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The Kolmogorov flow (k-flow) is generated by a stationary sinusoidal force that varies in space. This flow is rather academic since generating such a periodic forcing in an unbounded flow is difficult to appear in nature. Nevertheless, it allows for simple experimental measurements and for a fairly detailed analytical treatment. Although simple, the k-flow makes a good test case for investigating simultaneously inhomogeneous, sheared, and anisotropic features in a flow, and several studies concerning the stability, transition, and turbulence of the k-flow have been published. The present article reviews the most important published works incorporating the k-flow as a test-bed for studying fluid mechanics, testing numerical or experimental methods, or even studying the properties of the k-flow itself.

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Section: Introductionsupporting

confidence: 60%

“…Comprehending the fully matured or developed turbulence is important for a number of applications of geophysical flows. The k-flow has long been studied in the domains of geophysical fluid dynamics in relevance to the finite amplitude Rossby waves with the atmosphere as the setting [1] [2].…”

Section: Kolmogorov's Studies On Turbulencementioning

confidence: 99%

Kolmogorov Flow: Seven Decades of History

Fylladitakis¹

2018

JAMP

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“…Balmforth & Young (2005), for instance, show that layering may also develop as a result of the nonlinear evolution of laminar mixing flows. The resulting system of gentle layers frequently exhibit coarsening, not unlike that discussed in our study.…”

Section: Discussionmentioning

confidence: 99%

Mechanics of merging events for a series of layers in a stratified turbulent fluid

Radko¹

2007

J. Fluid Mech.

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This study attempts to explain the evolutionary pattern of a series of well-mixed layers separated by thin high-gradient interfaces frequently observed in stratified fluids. Such layered structures form as a result of the instability of the equilibrium with uniform stratification, and their subsequent evolution is characterized by a sequence of merging events which systematically increase the average layer thickness. The coarsening of layers can take one of two forms, depending on the realized vertical buoyancy flux law. Layers merge either when the high-gradient interfaces drift and collide, or when some interfaces gradually erode without moving vertically. The selection of a preferred pattern of coarsening is rationalized by the analytical theory -the merging theorem -which is based on linear stability analysis for a series of identical layers and strongly stratified interfaces. The merging theorem suggests that the merger by erosion of weak interfaces occurs when the vertical buoyancy flux decreases with the buoyancy variation across the step. If the buoyancy flux increases with step height, then coarsening of a staircase may result from drift and collision of the adjacent interfaces. Our model also quantifies the time scale of merging events and makes it possible to predict whether the layer merging continues indefinitely or whether the coarsening is ultimately arrested. The merging theorem is applied to extant one-dimensional models of turbulent mixing and successfully tested against the corresponding fully nonlinear numerical simulations. It is hypothesized that the upscale cascade of buoyancy variance associated with merging events may be one of the significant sources of the fine-scale (∼10 m) variability in the ocean.

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“…This problem is not uncommon and not insurmountable. Notable examples of analyzing the stability of timedependent flows come from studies based on the Kolmogorov model-the sinusoidal parallel flow in viscous fluid (Sivashinsky 1985;Manfroi andYoung 1999, 2002;Balmforth andYoung 2002, 2005). Since the unforced viscous parallel flow would inevitably decay, the Kolmogorov model circumvents this problem by introducing artificial forcing in the momentum equation that maintains the steady state.…”

Section: Theoretical Modelmentioning

confidence: 99%

Nonlinear Equilibration of Baroclinic Instability: The Growth Rate Balance Model

Radko

Flanagan

2014

Journal of Physical Oceanography

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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.

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Stratified Kolmogorov flow. Part 2

Cited by 32 publications

References 22 publications

Kolmogorov Flow: Seven Decades of History

Kolmogorov Flow: Seven Decades of History

Mechanics of merging events for a series of layers in a stratified turbulent fluid

Nonlinear Equilibration of Baroclinic Instability: The Growth Rate Balance Model

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