scholarly journals Comparison of the Effect of Parameterized Eddy Fluxes of Thickness and Potential Vorticity

2014 ◽  
Vol 44 (9) ◽  
pp. 2470-2484 ◽  
Author(s):  
V. O. Ivchenko ◽  
S. Danilov ◽  
J. Schröter
Keyword(s):  
Potential Vorticity ◽  
Velocity Profiles ◽  
Momentum Conservation ◽  
Ocean Dynamics ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Alternative Scheme ◽  
Zonal Velocity ◽  
Eddy Fluxes ◽  
The Impact

Abstract Parameterization of mesoscale eddies is an important problem of modern ocean dynamics and modeling. The most widely used scheme is the so-called Gent–McWilliams parameterization, which describes the eddy-induced transport of tracers, including temperature, density, and isopycnal thickness (TH). An alternative scheme, proposed by Green and Welander, deals with parameterizing eddy fluxes of potential vorticity (PV). Many recent studies propose using it, for it includes the effect of eddy Reynolds stresses that may influence mean flows. These two schemes are compared in the simplest configuration of two-layer quasigeostrophic channel flow, which enables analytical solutions for zonal-mean fields. It is shown how the parameterizations shape the zonally averaged zonal velocity profiles, with special attention paid to the role of the Reynolds stresses and momentum conservation. The zonally averaged zonal velocity profiles are sensitive to the amplitude and profiles of TH and PV diffusivities. For small enough diffusivities the TH parameterization may lead to solutions resembling those for the PV parameterization if it uses the diffusivity of the latter; that is, it may mimic the impact of the Reynolds stresses on the mean flow.

scholarly journals Influence of Bottom Topography on Integral Constraints in Zonal Flows with Parameterized Potential Vorticity Fluxes

2013 ◽  
Vol 43 (2) ◽  
pp. 311-323 ◽  
Author(s):  
V. O. Ivchenko ◽  
B. Sinha ◽  
V. B. Zalesny ◽  
R. Marsh ◽  
A. T. Blaker
Keyword(s):  
Potential Vorticity ◽  
Bottom Topography ◽  
Momentum Conservation ◽  
Integral Constraint ◽  
Mean Flow ◽  
Transfer Coefficients ◽  
Flat Bottom ◽  
Zonal Flows ◽  
Eddy Fluxes ◽  
The Mean

Abstract An integral constraint for eddy fluxes of potential vorticity (PV), corresponding to global momentum conservation, is applied to two-layer zonal quasigeostrophic channel flow. This constraint must be satisfied for any type of parameterization of eddy PV fluxes. Bottom topography strongly influences the integral constraint compared to a flat bottom channel. An analytical solution for the mean flow solution has been found by using asymptotic expansion in a small parameter, which is the ratio of the Rossby radius to the meridional extent of the channel. Applying the integral constraint to this solution, one can find restrictions for eddy PV transfer coefficients that relate the eddy fluxes of PV to the mean flow. These restrictions strongly deviate from restrictions for the channel with flat bottom topography.

scholarly journals Jet Formation and Evolution in Baroclinic Turbulence with Simple Topography

2010 ◽  
Vol 40 (2) ◽  
pp. 257-278 ◽  
Author(s):  
Andrew F. Thompson
Keyword(s):  
Southern Ocean ◽  
Potential Vorticity ◽  
Baroclinic Instability ◽  
Length Scale ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Jet Formation ◽  
Meridional Transport ◽  
Jet Behavior ◽  
Jet Variability

Abstract Satellite altimetry and high-resolution ocean models indicate that the Southern Ocean comprises an intricate web of narrow, meandering jets that undergo spontaneous formation, merger, and splitting events, as well as rapid latitude shifts over periods of weeks to months. The role of topography in controlling jet variability is explored using over 100 simulations from a doubly periodic, forced-dissipative, two-layer quasigeostrophic model. The system is forced by a baroclinically unstable, vertically sheared mean flow in a domain that is large enough to accommodate multiple jets. The dependence of (i) meridional jet spacing, (ii) jet variability, and (iii) domain-averaged meridional transport on changes in the length scale and steepness of simple sinusoidal topographical features is analyzed. The Rhines scale, ℓβ = 2πVe/β, where Ve is an eddy velocity scale and β is the barotropic potential vorticity gradient, measures the meridional extent of eddy mixing by a single jet. The ratio ℓβ /ℓT, where ℓT is the topographic length scale, governs jet behavior. Multiple, steady jets with fixed meridional spacing are observed when ℓβ ≫ ℓT or when ℓβ ≈ ℓT. When ℓβ < ℓT, a pattern of perpetual jet formation and jet merger dominates the time evolution of the system. Zonal ridges systematically reduce the domain-averaged meridional transport, while two-dimensional, sinusoidal bumps can increase transport by an order of magnitude or more. For certain parameters, bumpy topography gives rise to periodic oscillations in the jet structure between purely zonal and topographically steered states. In these cases, transport is dominated by bursts of mixing associated with the transition between the two regimes. Topography modifies local potential vorticity (PV) gradients and mean flows; this can generate asymmetric Reynolds stresses about the jet core and can feed back on the conversion of potential energy to kinetic energy through baroclinic instability. Both processes contribute to unsteady jet behavior. It is likely that these processes play a role in the dynamic nature of Southern Ocean jets.

scholarly journals Integral Constraints for Momentum and Energy in Zonal Flows with Parameterized Potential Vorticity Fluxes: Governing Parameters

2014 ◽  
Vol 44 (3) ◽  
pp. 922-943 ◽  
Author(s):  
V. O. Ivchenko ◽  
S. Danilov ◽  
B. Sinha ◽  
J. Schröter
Keyword(s):  
Ocean Circulation ◽  
Potential Vorticity ◽  
Channel Model ◽  
Bottom Topography ◽  
Flat Bottom ◽  
Zonal Flows ◽  
Integral Constraints ◽  
Variable Bottom ◽  
Eddy Fluxes ◽  
The Impact

Abstract Integral constraints for momentum and energy impose restrictions on parameterizations of eddy potential vorticity (PV) fluxes. The impact of these constraints is studied for a wind-forced quasigeostrophic two-layer zonal channel model with variable bottom topography. The presence of a small parameter, given by the ratio of Rossby radius to the width of the channel, makes it possible to find an analytical/asymptotic solution for the zonally and time-averaged flow, given diffusive parameterizations for the eddy PV fluxes. This solution, when substituted in the constraints, leads to nontrivial explicit restrictions on diffusivities. The system is characterized by four dimensionless governing parameters with a clear physical interpretation. The bottom form stress, the major term balancing the external force of wind stress, depends on the governing parameters and fundamentally modifies the restrictions compared to the flat bottom case. While the analytical solution bears an illustrative character, it helps to see certain nontrivial connections in the system that will be useful in the analysis of more complicated models of ocean circulation. A numerical solution supports the analytical study and confirms that the presence of topography strongly modifies the eddy fluxes.

scholarly journals Impact of SLA assimilation in the Sicily Channel Regional Model: model skills and mesoscale features

Ocean Science ◽  
2012 ◽  
Vol 8 (4) ◽  
pp. 485-496 ◽  
Author(s):  
A. Olita ◽  
S. Dobricic ◽  
A. Ribotti ◽  
L. Fazioli ◽  
A. Cucco ◽  
...  
Keyword(s):  
Sea Level ◽  
Qualitative Evaluation ◽  
Regional Model ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Qualitative Comparison ◽  
Mesoscale Structures ◽  
Sicily Channel ◽  
Along Track ◽  
The Impact

Abstract. The impact of the assimilation of MyOcean sea level anomalies along-track data on the analyses of the Sicily Channel Regional Model was studied. The numerical model has a resolution of 1/32° degrees and is capable to reproduce mesoscale and sub-mesoscale features. The impact of the SLA assimilation is studied by comparing a simulation (SIM, which does not assimilate data) with an analysis (AN) assimilating SLA along-track multi-mission data produced in the framework of MyOcean project. The quality of the analysis was evaluated by computing RMSE of the misfits between analysis background and observations (sea level) before assimilation. A qualitative evaluation of the ability of the analyses to reproduce mesoscale structures is accomplished by comparing model results with ocean colour and SST satellite data, able to detect such features on the ocean surface. CTD profiles allowed to evaluate the impact of the SLA assimilation along the water column. We found a significant improvement for AN solution in terms of SLA RMSE with respect to SIM (the averaged RMSE of AN SLA misfits over 2 years is about 0.5 cm smaller than SIM). Comparison with CTD data shows a questionable improvement produced by the assimilation process in terms of vertical features: AN is better in temperature while for salinity it gets worse than SIM at the surface. This suggests that a better a-priori description of the vertical error covariances would be desirable. The qualitative comparison of simulation and analyses with synoptic satellite independent data proves that SLA assimilation allows to correctly reproduce some dynamical features (above all the circulation in the Ionian portion of the domain) and mesoscale structures otherwise misplaced or neglected by SIM. Such mesoscale changes also infer that the eddy momentum fluxes (i.e. Reynolds stresses) show major changes in the Ionian area. Changes in Reynolds stresses reflect a different pumping of eastward momentum from the eddy to the mean flow, in turn influencing transports through the channel.

scholarly journals The Emergence of Shallow Easterly Jets within QBO Westerlies

2018 ◽  
Vol 75 (1) ◽  
pp. 21-40 ◽  
Author(s):  
Peter Hitchcock ◽  
Peter H. Haynes ◽  
William J. Randel ◽  
Thomas Birner
Keyword(s):  
Potential Vorticity ◽  
General Circulation ◽  
Circulation Model ◽  
Shear Zones ◽  
Wave Activity ◽  
Mean Flow ◽  
Quasi Biennial Oscillation ◽  
Westerly Jet ◽  
Eddy Fluxes ◽  
Biennial Oscillation

A configuration of an idealized general circulation model has been obtained in which a deep, stratospheric, equatorial, westerly jet is established that is spontaneously and quasi-periodically disrupted by shallow easterly jets. Similar to the disruption of the quasi-biennial oscillation (QBO) observed in early 2016, meridional fluxes of wave activity are found to play a central role. The possible relevance of two feedback mechanisms to these disruptions is considered. The first involves the secondary circulation produced in the shear zones on the upper and lower flanks of the easterly jet. This is found to play a role in maintaining the aspect ratio of the emerging easterly jet. The second involves the organization of the eddy fluxes by the mean flow: the presence of a weak easterly anomaly within a tall, tropical, westerly jet is demonstrated to produce enhanced and highly focused wave activity fluxes that reinforce and strengthen the easterly anomalies. The eddies appear to be organized by the formation of strong potential vorticity gradients on the subtropical flanks of the easterly anomaly. Similar wave activity and potential vorticity structures are found in the ERA-Interim for the observed QBO disruption, indicating this second feedback was active then.

Rotor Boundary Layer Response to an Impinging Wake

Volume 1 ◽  
2004 ◽  
Author(s):  
Francesco Soranna ◽  
Yi-Chih Chow ◽  
Oguz Uzol ◽  
Joseph Katz
Keyword(s):  
Boundary Layer ◽  
Guide Vane ◽  
Suction Side ◽  
Velocity Profiles ◽  
Inlet Guide Vane ◽  
Pressure Gradients ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Image Velocimetry ◽  
Entire Flow

This paper presents results of an experimental investigation on the response of a rotor boundary layer to an impinging Inlet Guide Vane (IGV) wake. High resolution two-dimensional Particle Image Velocimetry (PIV) measurements are conducted in a refractive index matched facility that provides an unobstructed view of the entire flow field. Data obtained at four different rotor phases, as the wake is chopped and passes by the rotor blade, allows us to examine the response of the rotor boundary layer to the mean flow and turbulence associated with the impinging wake. We focus on the suction side boundary layer in regions with adverse pressure gradients, from mid chord to the trailing edge. The phase-averaged velocity profiles are used for calculating the momentum and displacement thicknesses of the boundary layer, and for estimating the pressure gradients along the wall. Distributions of Reynolds stresses are also provided. The phase-averaged velocity profiles in the rotor boundary layer vary significantly with phase. During wake impingement the boundary layer becomes significantly thinner and more stable compared to other phases at the same location. Analysis of the possible causes for this trend suggests that the dominant contributors are unsteady, phase-dependent variation in pressure gradients along the wall.

scholarly journals A Framework for Parameterizing Eddy Potential Vorticity Fluxes

2012 ◽  
Vol 42 (4) ◽  
pp. 539-557 ◽  
Author(s):  
David P. Marshall ◽  
James R. Maddison ◽  
Pavel S. Berloff
Keyword(s):  
Stress Tensor ◽  
Potential Vorticity ◽  
Large Scale ◽  
Eddy Diffusivity ◽  
Linear Instability ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Conservation Of Energy ◽  
The Mean ◽  
Energy And Momentum

Abstract A framework for parameterizing eddy potential vorticity fluxes is developed that is consistent with conservation of energy and momentum while retaining the symmetries of the original eddy flux. The framework involves rewriting the residual-mean eddy force, or equivalently the eddy potential vorticity flux, as the divergence of an eddy stress tensor. A norm of this tensor is bounded by the eddy energy, allowing the components of the stress tensor to be rewritten in terms of the eddy energy and nondimensional parameters describing the mean shape and orientation of the eddies. If a prognostic equation is solved for the eddy energy, the remaining unknowns are nondimensional and bounded in magnitude by unity. Moreover, these nondimensional geometric parameters have strong connections with classical stability theory. When applied to the Eady problem, it is shown that the new framework preserves the functional form of the Eady growth rate for linear instability. Moreover, in the limit in which Reynolds stresses are neglected, the framework reduces to a Gent and McWilliams type of eddy closure where the eddy diffusivity can be interpreted as the form proposed by Visbeck et al. Simulations of three-layer wind-driven gyres are used to diagnose the eddy shape and orientations in fully developed geostrophic turbulence. These fields are found to have large-scale structure that appears related to the structure of the mean flow. The eddy energy sets the magnitude of the eddy stress tensor and hence the eddy potential vorticity fluxes. Possible extensions of the framework to ensure potential vorticity is mixed on average are discussed.

Eddy fluxes and topography in stratified quasi-geostrophic models

1999 ◽  
Vol 380 ◽  
pp. 59-80 ◽  
Author(s):  
WILLIAM J. MERRYFIELD ◽  
GREG HOLLOWAY
Keyword(s):  
Layer Thickness ◽  
Stream Function ◽  
Potential Vorticity ◽  
Lower Layer ◽  
Stratified Flow ◽  
Mean Flow ◽  
Random Forcing ◽  
Flow Over Topography ◽  
Eddy Fluxes ◽  
The Mean

Turbulent stratified flow over topography is studied using layered quasi-geostrophic models. Mean flows develop under random forcing, with lower-layer mean stream-function positively correlated with topography. When friction is sufficiently small, upper-layer mean flow is weaker than, but otherwise resembles, lower-layer mean flow. When lower-layer friction is larger, upper-layer mean flow reverses and can exceed lower-layer mean flow in strength. The mean interface between layers is domed over topographic elevations. Eddy fluxes of potential vorticity and layer thickness act in the sense of driving the flow toward higher entropy. Such behaviour contradicts usual eddy parameterizations, to which modifications are suggested.

scholarly journals Evolution and structure of sink-flow turbulent boundary layers

2001 ◽  
Vol 428 ◽  
pp. 1-27 ◽  
Author(s):  
M. B. JONES ◽  
IVAN MARUSIC ◽  
A. E. PERRY
Keyword(s):  
Boundary Layers ◽  
Velocity Profiles ◽  
Turbulent Boundary Layers ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Mean Velocity ◽  
Flow Measurements ◽  
Law Of The Wall ◽  
The Mean ◽  
Logarithmic Law

An experimental and theoretical investigation of turbulent boundary layers developing in a sink-flow pressure gradient was undertaken. Three flow cases were studied, corresponding to different acceleration strengths. Mean-flow measurements were taken for all three cases, while Reynolds stresses and spectra measurements were made for two of the flow cases. In this study attention was focused on the evolution of the layers to an equilibrium turbulent state. All the layers were found to attain a state very close to precise equilibrium. This gave equilibrium sink flow data at higher Reynolds numbers than in previous experiments. The mean velocity profiles were found to collapse onto the conventional logarithmic law of the wall. However, for profiles measured with the Pitot tube, a slight ‘kick-up’ from the logarithmic law was observed near the buffer region, whereas the mean velocity profiles measured with a normal hot wire did not exhibit this deviation from the logarithmic law. As the layers approached equilibrium, the mean velocity profiles were found to approach the pure wall profile and for the highest level of acceleration Π was very close to zero, where Π is the Coles wake factor. This supports the proposition of Coles (1957), that the equilibrium sink flow corresponds to pure wall flow. Particular interest was also given to the evolutionary stages of the boundary layers, in order to test and further develop the closure hypothesis of Perry, Marusic & Li (1994). Improved quantitative agreement with the experimental results was found after slight modification of their original closure equation.

Experimental investigation of turbulent shear flow with quadratic mean-velocity profiles

1976 ◽  
Vol 73 (1) ◽  
pp. 165-188 ◽  
Author(s):  
H. K. Richards ◽  
J. B. Morton
Keyword(s):  
Flow Direction ◽  
Correlation Coefficients ◽  
Velocity Profiles ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Mean Velocity ◽  
Quadratic Mean ◽  
The Mean

Three turbulent shear flows with quadratic mean-velocity profiles are generated by using an appropriately designed honeycomb and parallel-rod grids with adjustable rod spacing. The details of two of the flow fields, with quadratic mean-velocity profiles with constant positive mean-shear gradients ($\partial^2\overline{U}_1/\partial X^2_2 >0$), are obtained, and include, in the mean flow direction, the development and distribution of mean velocities, fluctuating velocities, Reynolds stresses, microscales, integral scales, energy spectra, shear correlation coefficients and two-point spatial velocity correlation coefficients. A third flow field is generated with a quadratic mean velocity profile with constant negative mean-shear gradient ($\partial^2\overline{U}_1/\partial X^2_2 < 0$), to investigate in the mean flow direction the effect of the change in sign on the resulting field. An open-return wind tunnel with a 2 × 2 × 20 ft test-section is used.

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