Quasi-geostrophic Numerical Model Research Articles

Symmetry, sidewalls, and the transition to chaos in baroclinic systems

A high-resolution, quasi-geostrophic numerical model is utilized to examine two-layer baroclinic flow in a cylinder. Particular attention is given to the role of horizontal shear of the basic state induced by viscosity near the cylinder wall, and to the desymmetrization brought about by the cylindrical geometry, in the transition to baroclinic chaos. Solutions are computed for both f-plane and β-plane situations, and the results are compared to previous laboratory experiments. Agreement in the former case is found to be good, although the onset of chaos occurs at slightly lower forcing in the laboratory when its basic flow is prograde, and at higher forcing amplitude when the experimental basic azimuthal currents are retrograde. This suggests that the modest discrepancies may be attributable to computationally neglected ageostrophic effects in the interior fluid and Ekman boundary layers. When β ≠ 0, the numerical and laboratory results are in excellent agreement. The computational simulations indicate that the viscous sidewall boundary layer plays a pivotal role in the dynamics. Moreover, in contrast to previous studies performed in a periodic, rectilinear channel, the route to chaos is largely temporal and involves relatively few spatial modes. The reduction in symmetries upon going from f-plane channel to either f-plane or β-plane cylinder models leads to fewer secondary instabilities and fewer spatial modes that are active in the dynamics.

The Effect of Continental Rises on the Wind-Driven Ocean Circulation

The effect of continental rises on the wind-driven circulation is investigated by developing a modification to the Rhines and Young theory and by running a three-layer eddy-resolving quasigeostrophic numerical model. Large-scale bottom topography has an important influence on the mean ocean circulation, particularly when eddies are present. Bottom topography breaks the symmetry between the subpolar and subtropical gyres in a standard double gyre ocean. In the numerical model, the mean midlatitude jet has eddy-scale meanders in it and is deflected to the north of the zero wind-stress curl line. Without topography, there are four zonal eddy-driven gyres in the bottom layer beneath the midlatitude jet. With a continental rise present at the western boundary, these gyres become eddy-scale features except for the southernmost cyclonic gyre, which remains coherent over a large scale and extends southward along the western boundary. A rise at the southern boundary forms closed geostrophic contours and an additional strong bottom layer gyre appears. This cyclonic gyre is driven by pseudowestward stress of the eddies, and the strength of its circulation can be predicted by a modification to the Rhines and Young theory. The amplitude of the circulation depends on the location of the closed geostrophic contours relative to the eddy-rich regions in the middle layer. The topography also changes the character of the spinup of the flow. Initially, the ocean responds barotropically so that the circulation within the closed geostrophic contour region is anticyclonic. Once the upper-layer western boundary current becomes unstable, the flow in this region changes direction to cyclonic.

Practical subjective application of the omega equation and Sutcliffe development theory

AbstractSutcliffe development theory and the similar omega equation provide an objective framework for the understanding of synoptic‐scale development in the extra‐tropics. Both are widely applied by forecasters in the UK Met. Office, with the omega equation also being used by forecasters working in other meteorological services. Using results from experiments with a quasi‐geostrophic numerical model, this paper examines the pitfalls associated with each, and suggests ways in which these can be avoided. The partitioning between so‐called steering and development terms in the Sutcliffe equation is shown to be misleading, and an alternative form is suggested which is more accurate and circumvents significant cancellation problems associated with the existing form. It is shown that oversimplifiction of the omega equation can lead to it being applied in unsuitable ways. In particular, it is argued that the conversion from omega forcing to vertical velocity is best made at the mid‐tropospheric level, say at 500 hPa, and that therefore diagnostics such as Q‐vectors or their divergence are better applied at this level than, say, at 700 hPa. The so‐called Sutcliffe, or Trenberth, form of the omega equation is recommended as being suitable for subjective application.

Mesoscale data assimilation studies in the Middle Adriatic Sea

In this paper we describe a mesoscale data assimilation experiment in the Middle Adriatic Sea. In order to perform dynamical forecasts we provide a quasigeostrophic numerical model with a set of initial fields regularly gridded via an objective analysis technique. Maps of this initial condition show a surface intensified jet meandering around a cyclonic eddy at the thermocline and deep levels. We dynamically forecasted the flow evolution for 30 days after initialization. The time scale of the variability is of the order of a few weeks and the cyclonic vortex seems to be locked to the topography. A set of numerical experiments with different initial bottom boundary conditions, with and without topography, are made to explore the influence of the topographic constraint on the mesoscale flow evolution. As expected the influence of the topography on the dynamical evolution of the flow is very strong and it confines the jet-cyclone along the bathymetric contours, strengthening the flow. On the other hand the flow is not sensitive to changes in the density bottom initial condition. Finally we analyze the energy and vorticity fields of the 1-month dynamical forecast experiment. It is concluded that a local frontogenetic process consisting of jet strengthening and cyclone development occurs and that available gravitational energy is converted into kinetic energy during the process.

Observations and Modeling of Wind-driven Currents in the Northeast Pacific

Velocity measurements from the interior of the Alaskan gyre are presented from a current meter mooring deployed in 4000 m of water at 49°33′N, 138°38′W, in the vicinity of Ocean Weather Station P. The mooring held five current meters, which spanned the depth of the water column. The data reveal surface-intensified motions with flow fluctuations in the upper layers of the water column characterized by long-period, O(100 d) time scales of variability. At abyssal depths, the flow displays shorter, O(20 d) time scales of variability. The data are compared with observations from one of the NEPAC moorings in the northeast Pacific (42°N, 152°W). Similar characteristics in kinetic energy levels, in the vertical structure of the flow, and in the vertical variation of eddy time scales are found at this location. The current measurements are considered in terms of the linear theory of directly wind-driven variability of Müller and Frankignoul. A comparison with simulated currents from a quasigeostrophic numerical model demonstrates that stochastic atmospheric forcing of the ocean can account for the observed variability. The numerical experiments and a simple extension of the linear theory suggest that the presence of bottom topography is important for the partition of energy between vertical modes and for the vertical variation of the time scales of the flow.

A quasi-geostrophic numerical model of a rotating internally heated fluid

Abstract A quasi-geostrophic numerical model of flow in a rotating channel is integrated under conditions typical of laboratory experiments with an internally heated annulus system. Compared to a laboratory experiment, or a full Navier-Stokes simulation, the quasi geostrophic numerical model is a simple system. It includes nonlinear interactions, dissipation via conventional parameterizations of Ekman layers and internal diffusion, and a steady forcing term which represents heating near the centre of the channel and cooling near both sides. Explicit boundary layers, cylindrical geometry effects, horizontal variations in static stability and variations in conductivity and diffusivity with temperature are all absent, and ageostrophic advection is incompletely represented. Nevertheless, over a range of parameters, flows are produced which strongly resemble those seen in the laboratory thus suggesting that the most important physical processes are represented. The numerical model is used to map out a regime d...

Circulation and Energetics of a Model of the California Current System

Abstract Data from an eight-layer FNOC wind-driven eddy-resolving limited-area quasi-geostrophic numerical model have been used to study the dynamics of the California Current System (CCS). with particular emphasis on the energetics. The model includes quasi-realistic bottom topography and the true coastline, and is embedded in a coarser resolution model occupying almost all of the North Pacific Ocean. The model simulates the main components of the CCS, such as the California Current (CC), the Davidson Current, the California Undercurrent, and the Southern California Eddy. The simulated CC is both an active eddy-mean flow interaction area and an effective wave source for the North Pacific Ocean. Making use of the mean potential vorticity field of the different layers, four different regimes are described for the mean circulation: “inertial”, “intermediate”, “beta”, and “bottom topographic”. Overall, the new-surface circulation is energetically dominated by the mean flow whereas the deep simulation is ener...

The Wind-driven Circulation: Quasi-geostrophic Simulations and Theory for Nonsymmetric Winds

Abstract Simulations of the wind-driven Ocean circulation, carded out with an eddy-resolving quasi-geostrophic numerical model, and symmetric, idealized wind forcing have a large-scale structure that is predicted wen by the steady nonlinear theory of Rhines and Young. The sharp jet and inertial recirculation am often confined weft inside the region of closed hyperbolic characteristics, defined by that theory, and hence do not affect the Sverdrup-dynamics part of the gyre. The characteristics make possible simple predictions about the development of the circulation, including time dependence and eddy stirring. By tilting the line of vanishing Ekman pumping away from the east-west orientation (as it is tilted in the North Atlantic, and less so the North Pacific), we explore a family of circulations. As the tilt of the wind held is increased, characteristics originating at the eastern boundary begin to thread through the energetic region occupied by the free jet. Then, extensive new branches of eddy-driven f...

Response of eddy-resolved general circulation numerical models to asymmetrical wind forcing

The classical double-gyre wind-driven mid-latitude ocean circulation simulated by means of eddy-resolving quasi-geostrophic numerical models is reconsidered by introducing some asymmetry into the wind forcing configuration. The main objective is to explore the changes in the basin-scale dynamics which result from the wind asymmetry: jet profile and penetration, eddy energy radiation, downward energy propagation, homogenization, ring formation and gyre exchange, etc. Some rationalization of the dynamical control of the jet detachment from the coast, in relation to the wind forcing, is attempted from a survey of asymmetrical quasi-geostrophic experiments: multilayer unsteady configurations as well as simpler steady ocean models. It is found that this dynamical control in complex unsteady stratified experiments has strong similarities to inertially dominated steady barotropic situations.

A consistent algorithm for quasigeostrophic energy and energy flux analysis

The energy flux vector is familiar to geophysical fluid dynamics, but only in the abstract. Equations for computing the energy balance and the energy flux vector (S) for a quasigeostrophic numerical ocean model are provided in both analytic and finite difference form. The multilayer model includes wind, lateral and bottom friction, and bathymetry. The finite difference approximation to the analytic energy balance is consistent with the finite difference approximation to the quasigeostrophic potential vorticity equation. An application of the algorithms to a simple steady ocean gyre illustrates their use. This choice of the flux vector (from an infinity of possibilities) has several advantages: it is computationally convenient; it is capable of field measurement; it has nice mathematical properties in the limit of small amplitude motion; and it facilitates intuition about the dynamics.

南北両半球における準地衡風渦位輸送と簡単な経度平均気候モデル

The meridional transport of quasi-geostrophic potential vorticity is calculated for the Northern and Southern Hemispheres. The results show that the transport of potential vorticity is negative over most of the atmosphere except over a thin layer near surface where it is positive. Exchange coefficients for the transport of potential vorticity are computed for both the hemispheres using the evaluations of the transport of quasi-geostrophic potential vorticity and calculating the meridional gradient of potential vorticity. The values of the exchange coefficients are used in a simple, two-level quasi-geostrophic numerical model for tonally averaged conditions. The model is applied to the Northern and Southern Hemispheres and the general characteristics of mean annual temperature and zonal wind variation are reproduced reasonably well.

A note on consistent quasi-geostrophic boundary conditions in partially open, simply and multiply connected domains

Mass conservation is used to elucidate differences between initial boundary value problems for the quasi-geostrophic vorticity equation in regions that are fully enclosed versus regions that are partially open. In fully closed domains, mass conservation is explicitly imposed as a consistency constraint on the dynamical evolution of the flow. Partially or fully open domains do not require an explicit mass conservation constraint. In these cases, the mass conservation balance is used as a diagnostic to describe the interaction between open boundary conditions and the inflow/outflow vorticity implied by the quasi-geostrophic equation. The new formalism is carried over the multiply connected, partially open domains, where explicit circulation integral constraints are required around island boundaries. Implications concerning coastal applications of quasi-geostrophic numerical models are outlined.

A note on consistent quasi-geostrophic boundary conditions in partially open, simply and multiply connected domains

Mass conservation is used to elucidate differences between initial boundary value problems for the quasi-geostrophic vorticity equation in regions that are fully enclosed versus regions that are partially open. In fully closed domains, mass conservation is explicitly imposed as a consistency constraint on the dynamical evolution of the flow. Partially or fully open domains do not require an explicit mass conservation constraint. In these cases, the mass conservation balance is used as a diagnostic to describe the interaction between open boundary conditions and the inflow/outflow vorticity implied by the quasi-geostrophic equation. The new formalism is carried over the multiply connected, partially open domains, where explicit circulation integral constraints are required around island boundaries. Implications concerning coastal applications of quasi-geostrophic numerical models are outlined.

A numerical study of the nonlinear stability of the eastern ocean circulation

Nonlinear unstable waves in the eastern ocean basin are analyzed using a three‐layer quasi‐geostrophic numerical model. The upper two layers are forced to maintain a mean circulation in the absence of mesoscale motion. The waves are produced by initial small perturbations added to the mean flow. Two experiments, focused on the eastern ocean basin and differing only by mean flow strength, are performed. A region of high eddy kinetic energy is formed in the southern region, but the eastern and northern regions are vacant of eddies because of the energy efflux by westward and southwestward propagating unstable waves. Regional energetics are calculated to highlight the differences between the eastern and southern regions. Two dominant waves are found in the southern region. Waves with a period of 120 days propagate to the west and form several wave trains parallel to the southern boundary. Longer‐period waves with a period of 200 days propagate to the southwest. Comparisons with observed eddies in the northeast Pacific are discussed. Besides baroclinic instability, it is found that the energy flux by propagating waves is very important in the finite amplitude stability of the eastern ocean general circulation.

A Quasi-Geostrophic Circulation Model of the Northeast Pacific. Part I: A Preliminary Numerical Experiment

Abstract A limited-area quasi-geostrophic numerical model with mesoscale resolution is developed to study the circulation in the northeast (NE) Pacific Ocean. The model domain extends from the British Columbia-Alaska coast out to 170°W and down to 45°N, and incorporates the coastline geometry and bottom topography of the region. A long-term integration was conducted using a steady climatological wind stress curl field to drive the circulation. Several statistical properties of the solution are determined and compared with observations. A cyclonic circulation develops in the model basin with a meandering Alaska Current feeding, at the head of the Gulf of Alaska, into an intense boundary current corresponding to the Alaskan Stream. The head of the Gulf is a region where anticyclonic closed streamline features are occasionally generated with characteristics resembling those of the Sitka Eddy. In the downstream region, the boundary current separates and is subject to lateral meandering due to topographic wave...

The Distortion of a Baroclinic Fofonoff Gyre by Wind Forcing

Abstract The subtropical recirculation regions are considered as examples of nonlinear free flow—“baroclinic Fofonoff gyres.” In the interior, where relative vorticity may be neglected, the quad-geostrophic assumption may be relaxed, and the layered treatment extended to a continuously stratified model. The implied density field is compared with observations. The deformation of the inertial gyre caused by the presence of an anticyclonic wind stress curl is then considered. In addition to the recirculating “free” component of the flow along latitude circles, there is a meridional component whose depth-integrated transport is set by the magnitude of the imposed wind stress curl. It is found that the “bowl” within which the recirculation is contained deepens towards the north and west, and exhibits the “champagne glass“ structure found in the quasi-geostrophic eddy-resolving numerical models.

Stratified rotating flow over and around isolated three-dimensional topography

Laboratory and numerical experiments have been conducted on the flow of a linearly stratified rotating fluid past isolated obstacles of revolution (conical and cosinesquared profiles). Laboratory experiments are considered for a range of Rossby, Ekman and Burger numbers, the pertinent dynamical parameters of the system. In these experiments, inertial, Coriolis, pressure, viscous and buoyancy forces all play a significant role. Emphasis is given to examining the nature of the time development of the flow fields as well as its long-time behaviour, including eddy shedding. It is shown, for example, that increased stratification tends to diminish the steering effect of the obstacle, other parameters being fixed, at elevation levels above the topography. At levels below the top of the obstacle, increased stratification tends to force the fluid around rather than over the body and this, in turn, tends to develop vortex shedding at smaller Reynolds numbers than would occur in corresponding lower stratification cases. Data for the cone reveal that the Strouhal number for the eddy-shedding regime is relatively insensitive to the values of Ro , Ek and S for the range of parameters investigated. Stratification tends to induce lee waves in the topography wake, and the nature of this lee-wave pattern is modified by the presence of rotation. For example, it is demonstrated that for vertically upward rotation, the lee waves on the right, facing downstream, have a larger amplitude than their counterparts at the same location on the left. The steering effects, as predicted by a three-level quasigeostrophic numerical model, are shown to be in good agreement with the laboratory results for a narrow range of parameter space. The numerical model is used to examine the effects of rotation, friction and stratification in modifying the flow. The quasigeostrophic numerical simulations do not produce eddy shedding, and it is concluded that a full, primitive equation numerical model would be needed to explore this phenomenon.

Steady, Free Circulation in a Stratified Quasi-Geostrophic Ocean

Abstract Steady solutions in which quasi-geostrophic potential vorticity is constant along a streamline of the flow are derived for a baroclinic ocean. Friction, transfer by geostrophic eddies, and wind forcing are treated as high-order effects that serve only to remove the indeterminacy of completely free flow. Solutions are obtained that are a generalization to a baroclinic ocean of Fofonoff's baratropic calculations. The vortex stretching permitted by stratification is found to allow gyres in which, in an integral sense, lateral down-gradient eddy transfer of potential vorticity, q, balances the wind-stress curl. Beneath the surface layer, the effect of eddies is then to make q uniform if q contours close on themselves Our simple solutions have many features in common with observations of the subtropical recirculation and with the cream flows obtained from eddy-resolving, quasi-geostrophic numerical models. In particular, the southern margin of the recirculation is found to recede progressively toward ...

Use of linearised quasi-geostrophic numerical model for evaluation of truncation errors

A linear, quasi-geostrophic, multilayer, numerical model which has been developed in an earlier study (Mishra & Salvekar 1980) for investigating baroclinlc instability mechanism of mean monsoon zonal flow, is used here to obtain vertical and time truncation errors in gowth rate and phase velocity of a baroclinic unstable wave that arise due to finite difference approximations.

Role of Baroclinic Instability in the Development of Monsoon Disturbances

A linear baroclinic stability analysis of the zonal wind representing the mean monsoon situation over India is performed by the use of a multi-level quasi-geostrophic numerical model. An initial value approach is chosen to determine the instability characteristics of the wind. The dependency of the growth rate spectrum on the number of levels in the vertical and on the presence of vertical walls is studied. It is shown that 20 levels in the vertical are sufficient to realize the baroclinic instability of the monsoon mean wind. A shorter unstable wave of wavelength 1500 km and a longer unstable wave of wavelength 4750 km are found to be the most preferred growing waves from the growth rate spectrum. The shorter unstable wave is essentially confined below 500 mb, whereas the longer unstable wave is above 500 mb. It is also shown that the removal of wind shear below (above) the level of the westerly (easterly) jet from the wind profile, shifts the shorter (longer) unstable wave toward higher wavelengths by ∼ 1000 km, with a significant decrease in the growth rates. The horizontal scale (1500 km), level of nondivergence (900 mb), and level of maximum intensity (825 mb) associated with the shorter unstable wave are in close agreement with the observed values, obtained from a composite monsoon depression. The computed phase velocity of the unstable wave is opposite to the observed westward motion. The computed levels of cold core, warm core and top of the wave are at 900, 800 and 500 mb, respectively, which are ∼100 mb lower than the observed levels. The computed phase velocity of the longer unstable wave (−23 m s−1) is found to be very close to the observed value for disturbances along the easterly jet level. The longer unstable wave has a level of nondivergence at 200 mb which is supported from the results of barotropic studies obtained by others.