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 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.

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 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.

Simple explicit model of liquid mean flow in region above axial impeller

1985 ◽  
Vol 50 (11) ◽  
pp. 2396-2410
Author(s):  
Miloslav Hošťálek ◽  
Ivan Fořt
Keyword(s):  
Vortex Flow ◽  
Flow Model ◽  
Quantitative Agreement ◽  
Mean Flow ◽  
Flat Bottom ◽  
Proposed Model ◽  
Minimum Number ◽  
The Mean ◽  
Model Equations ◽  
Radial Circulation

The study describes a method of modelling axial-radial circulation in a tank with an axial impeller and radial baffles. The proposed model is based on the analytical solution of the equation for vortex transport in the mean flow of turbulent liquid. The obtained vortex flow model is tested by the results of experiments carried out in a tank of diameter 1 m and with the bottom in the shape of truncated cone as well as by the data published for the vessel of diameter 0.29 m with flat bottom. Though the model equations are expressed in a simple form, good qualitative and even quantitative agreement of the model with reality is stated. Apart from its simplicity, the model has other advantages: minimum number of experimental data necessary for the completion of boundary conditions and integral nature of these data.

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.

Wave-induced mean flows in rotating shallow water with uniform potential vorticity

2018 ◽  
Vol 839 ◽  
pp. 408-429 ◽  
Author(s):  
Jim Thomas ◽  
Oliver Bühler ◽  
K. Shafer Smith
Keyword(s):  
Shallow Water ◽  
Potential Vorticity ◽  
Rotation Rate ◽  
Standing Waves ◽  
Leading Order ◽  
Mean Flow ◽  
Wave Fields ◽  
The Mean ◽  
Rotating Shallow Water ◽  
Wave Induced

Theoretical and numerical computations of the wave-induced mean flow in rotating shallow water with uniform potential vorticity are presented, with an eye towards applications in small-scale oceanography where potential-vorticity anomalies are often weak compared to the waves. The asymptotic computations are based on small-amplitude expansions and time averaging over the fast wave scale to define the mean flow. Importantly, we do not assume that the mean flow is balanced, i.e. we compute the full mean-flow response at leading order. Particular attention is paid to the concept of modified diagnostic relations, which link the leading-order Lagrangian-mean velocity field to certain wave properties known from the linear solution. Both steady and unsteady wave fields are considered, with specific examples that include propagating wavepackets and monochromatic standing waves. Very good agreement between the theoretical predictions and direct numerical simulations of the nonlinear system is demonstrated. In particular, we extend previous studies by considering the impact of unsteady wave fields on the mean flow, and by considering the total kinetic energy of the mean flow as a function of the rotation rate. Notably, monochromatic standing waves provide an explicit counterexample to the often observed tendency of the mean flow to decrease monotonically with the background rotation rate.

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.

scholarly journals Is the Coefficient of Eddy Potential Vorticity Diffusion Positive? Part I: Barotropic Zonal Channel

2018 ◽  
Vol 48 (7) ◽  
pp. 1589-1607 ◽  
Author(s):  
V. O. Ivchenko ◽  
V. B. Zalesny ◽  
B. Sinha
Keyword(s):  
Potential Vorticity ◽  
Independent Solution ◽  
Zonal Flow ◽  
Momentum Balance ◽  
Eddy Fluxes ◽  
The Mean ◽  
Zonal Momentum Balance ◽  
Circumpolar Current ◽  
The Antarctic ◽  
Zonal Momentum

AbstractThe question of whether the coefficient of diffusivity of potential vorticity by mesoscale eddies is positive is studied for a zonally reentrant barotropic channel using the quasigeostrophic approach. The topography is limited to the first mode in the meridional direction but is unlimited in the zonal direction. We derive an analytic solution for the stationary (time independent) solution. New terms associated with parameterized eddy fluxes of potential vorticity appear both in the equations for the mean zonal momentum balance and in the kinetic energy balance. These terms are linked with the topographic form stress exerted by parameterized eddies. It is demonstrated that in regimes with zonal flow (analogous to the Antarctic Circumpolar Current), the coefficient of eddy potential vorticity diffusivity must be positive.

scholarly journals Gulf Stream Dynamics along the Southeastern U.S. Seaboard

2015 ◽  
Vol 45 (3) ◽  
pp. 690-715 ◽  
Author(s):  
Jonathan Gula ◽  
M. Jeroen Molemaker ◽  
James C. McWilliams
Keyword(s):  
Gulf Stream ◽  
Ocean Modeling ◽  
Mean Flow ◽  
Regional Ocean Modeling System ◽  
Meridional Transport ◽  
Local Pressure ◽  
Straits Of Florida ◽  
Eddy Fluxes ◽  
The Mean ◽  
Mean Current

AbstractThe Gulf Stream strongly interacts with the topography along the southeastern U.S. seaboard, between the Straits of Florida and Cape Hatteras. The dynamics of the Gulf Stream in this region is investigated with a set of realistic, very high-resolution simulations using the Regional Ocean Modeling System (ROMS). The mean path is strongly influenced by the topography and in particular the Charleston Bump. There are significant local pressure anomalies and topographic form stresses exerted by the bump that retard the mean flow and steer the mean current pathway seaward. The topography provides, through bottom pressure torque, the positive input of barotropic vorticity necessary to balance the meridional transport of fluid and close the gyre-scale vorticity balance. The effect of the topography on the development of meanders and eddies is studied by computing energy budgets of the eddies and the mean flow. The baroclinic instability is stabilized by the slope everywhere except past the bump. The flow is barotropically unstable, and kinetic energy is converted from the mean flow to the eddies following the Straits of Florida and at the bump with regions of eddy-to-mean conversion in between. There is eddy growth by Reynolds stress and downstream development of the eddies. Interaction of the flow with the topography acts as an external forcing process to localize these oceanic storm tracks. Associated time-averaged eddy fluxes are essential to maintain and reshape the mean current. The pattern of eddy fluxes is interpreted in terms of eddy life cycle, eddy fluxes being directed downgradient in eddy growth regions and upgradient in eddy decay regions.

Measurements of turbulent fluctuations and Reynolds stresses in a tidal current

1956 ◽  
Vol 237 (1210) ◽  
pp. 422-438 ◽  
Keyword(s):  
Tidal Current ◽  
Electromagnetic Flowmeter ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Flat Bottom ◽  
Auto Correlation ◽  
Vertical Scale ◽  
Sea Bed ◽  
The Mean ◽  
The Magnetic Field

Observations have been made of u and w , the horizontal and vertical components of turbulent velocity, in a tidal current, at heights of 50 to 175 cm above the bottom. The measuring instrument was an electromagnetic flowmeter, in which the magnetic field was produced by a. c. at 50 c/s and the p. d. induced in the flowing water was measured by two pairs of electrodes. The measuring head of the instrument was 10 cm in diameter, and two such heads were mounted on a tripod which was laid on the sea bed. The observations were made off Red Wharf Bay, Anglesey, in depths of 12 to 22 m, on a fairly flat bottom consisting mainly of firm sand. For mean currents, U , in the range 25 to 50 cm/s, the r. m. s. values of u were of the order of 10% of U , while those of w were about 6% of U . On a number of records, u and w were recorded simultaneously, and from these the Reynolds stress — ρ [ uw ] was evaluated. At 75 cm above the bottom the values of stress were from 2 to 4 dyn/cm 2 , the corresponding coefficient of correlation between u and w averaging —0·4. Auto-correlation curves and spectrum functions computed from these records showed that u contained considerably more energy in the fluctuations of longer period than w did. Other records were of traces of u or of w at two different heights and showed the smaller vertical scale of w compared with that of u . In the case of u the vertical scale appears to be only about one-third of the scale in the direction of the mean flow.

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