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Wim Verkley

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Sebahattin Devecioglu

University of Firat

Armando Marques-Guedes

UNL - New University of Lisbon

Gabriel Gutierrez-Alonso

University of Salamanca

Prof. Dr. Raffaele Pisano, HDR (Habil.)

Université des Sciences et Technologies de Lille (Lille-1)

Lossian Miranda

Instituto Federal de Educação, Ciência e Tecnologia do Piauí

Patrick Blessinger

St. John's University

Steven Ross Murray

University of California, Berkeley

Adam Mickiewicz University in Poznań

Stephen W Merkel

Vrije Universiteit Amsterdam

Andrei Martínez-Finkelshtein

Baylor University

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Papers by Wim Verkley

Synoptic Development In A Two-and-a-half Layer Contour Dynamics System

EGS General Assembly Conference Abstracts, 2002

Buys Ballot's Law, Hamilton's Principle and The Atmosphere's Dynamics

EGSGA, 2002

Subgrid modeling in two-dimensional turbulent flow using the principle of maximum entropy

The non-equilibrium statistical mechanics of a simple geophysical fluid dynamics model

A maximum entropy approach to the parametrization of subgrid processes in two‐dimensional flow

Quarterly Journal of the Royal Meteorological Society, 2016

In numerical models of geophysical fluid systems, parametrization schemes are needed to account f... more In numerical models of geophysical fluid systems, parametrization schemes are needed to account for the effect of unresolved processes on processes that are resolved explicitly. Usually, these parametrization schemes require tuning of their parameters to achieve optimal performance. We propose a new type of parametrization that requires no tuning, as it is based on an assumption that is not specific to any particular model. The assumption is that the unresolved processes can be represented by a probability density function that has maximum information entropy under the constraints of zero average time derivatives of key integral quantities of the unresolved processes. In the context of a model of a simple fluid dynamical system, it is shown that this approach leads to definite expressions for the mean effect of unresolved processes on processes that are resolved. The merits of the parametrization, regarding both short‐range forecasting and long‐term statistics, are demonstrated by n...

Manually adjusting a numerical weather analysis in terms of potential vorticity using three-dimensional variational data-assimilation

Quarterly Journal of the Royal Meteorological Society, 2005

A method is presented to manually adjust the analysis of a numerical weather-forecasting model an... more A method is presented to manually adjust the analysis of a numerical weather-forecasting model and study the impact of the adjustment on the ensuing forecast. The adjustment is made in terms of potential vorticity. The prime motivation for using potential vorticity is that within the constraints of hydrostatic and geostrophic balance the pressure, wind and temperature fields are adjusted whenever the potential vorticity field is adjusted. This is a consequence of the invertibility principle of potential vorticity. Another motivation is that potential vorticity usually correlates well with water vapour satellite images at midlatitudes. Obvious mismatches between the two fields are therefore indicative of errors and may, in actual practice, be a reason to adjust the analysis. The method is based on three-dimensional variational data-assimilation and utilizes the special properties of potential vorticity. The potential vorticity of the analysis is manually adjusted by means of a graphical interface. The resulting modified potential vorticity field is treated as information that is to be incorporated into a new modified analysis. For this purpose we use three-dimensional variational data-assimilation, in which the observation term in the cost function is replaced by a potential vorticity term. In analogy with the observation term the potential vorticity term measures the difference between the modified potential vorticity and the potential vorticity of the model state. The extent to which the modified analysis reproduces the modified potential vorticity depends on the relative weights of the potential vorticity term and the background term in the cost function. An example is given of a modified analysis and its effect on a 24-hour forecast, using a limited-area weather-forecasting model.

Application of a potential vorticity modification method to a case of rapid cyclogenesis over the Atlantic Ocean

Quarterly Journal of the Royal Meteorological Society, 2007

A method to modify the potential vorticity of a numerical weather analysis is applied to a case o... more A method to modify the potential vorticity of a numerical weather analysis is applied to a case of rapid cyclogenesis over the Atlantic Ocean. The development of the cyclone's intensity in terms of mean sea level pressure is underestimated by the Dutch version of the limited-area weather prediction model HIRLAM. The analysis shows a rather clear mismatch between the potential vorticity of the analysis and the corresponding water vapour satellite image. A barotropic displacement of potential vorticity, based on a subjective comparison with the water vapour satellite image, improves the forecast in terms of the cyclone's mean sea level pressure eighteen hours after the analysis. Similar but different modifications are investigated to assess the sensitivity of the development to the modification applied. The numerical analysis of the global ECMWF model displays a similar mismatch between potential vorticity and water vapour image, although the mismatch is somewhat less dramatic than for the HIRLAM model. Notwithstanding, the ECMWF model describes the development of the mean sea level pressure of the cyclone very well. Investigation of targeted singular vectors and a regular ensemble for this case shows, however, that the forecast is sensitive to perturbations of the initial state, in particular in the region of the potential vorticity/water vapour mismatch. The operational forecast lies in the middle of the ECMWF ensemble, the ensemble containing members with both stronger and weaker development of the cyclone. Our study confirms that a mismatch between an analysed potential vorticity field and a water vapour satellite image might indicate an error in the analysis. However, the error is not necessarily confined to the upper atmosphere and may involve the lower atmosphere as well. Pairs of ECMWF ensemble members, differing according to the sign of the initial perturbation and leading to either shallow or deep cyclones, are studied to shed some light on the effect of different initial conditions. The modification that improves the HIRLAM forecast resembles one of the more strongly developing ensemble members, indicating that the modification lies within the range of acceptable possibilities.

Salmon's Hamiltonian approach to balanced flow applied to a one‐layer isentropic model of the atmosphere

Quarterly Journal of the Royal Meteorological Society, 2001

Salmon's Hamiltonian approach is applied to formulate a balanced approximation to a hydrostat... more Salmon's Hamiltonian approach is applied to formulate a balanced approximation to a hydrostatic one‐layer isentropic model of the atmosphere. The model, referred to as the parent model, describes an idealized atmosphere of which the dynamics is closely analogous to a one‐layer shallow‐water model on the sphere. The balance used as input in Salmon's approach is a simplified form of linear balance, in which the balanced velocity vb is given by vb = k×δf−1(M–M). Here k is a vertical unit vector, f is the Coriolis parameter, M is the Montgomery potential and M is the value of the Montgomery potential at the state of rest. This form of balance is used in preference to standard geostrophic balance, vb = k × f−1δM, which forces the meridional wind velocity to be zero at the equator. Salmon's Hamiltonian technique is applied to obtain an equation for the time rate of change of the balanced velocity that guarantees both the material conservation of potential vorticity as well as ...

Evolution of stratosphere-troposphere singular vectors

Quarterly Journal of the Royal Meteorological Society, 2011

ABSTRACT Stratospheric conditions affect the tropospheric circulation on a variety of time-scales... more ABSTRACT Stratospheric conditions affect the tropospheric circulation on a variety of time-scales. This article addresses two issues in stratosphere–troposphere interaction that are relevant for time-scales up to a week: the basic growth mechanisms involved and the role of the stratospheric shear. Idealized simulations are conducted of initially stratospheric perturbations that maximize tropospheric total disturbance energy with a lead time of 5 days, assuming linear quasi-geostrophic dynamics and simplified zonal flow. The evolution is analysed in terms of the basic interactions between three Rossby-wave components. On the f-plane (constant Coriolis parameter), the three-component analysis is very accurate (the error stays within 1% of vertically integrated total energy) because all available growth mechanisms are captured. Energy growth occurs initially through the Orr mechanism, subsequently through resonance and finally through (normal-mode) shear instability. On the β-plane (Coriolis parameter varying linearly with latitude), errors increase because westward retrogression of the untilting potential vorticity structure is neglected by the three-component model. Further study reveals that the tropospheric energy growth strongly depends on the value of the stratospheric shear. Copyright © 2011 Royal Meteorological Society

On the vertical velocity in an isentropic layer

Quarterly Journal of the Royal Meteorological Society, 2000

We investigate the dynamics of an isentropic layer of air, governed by the hydrostatic primitive ... more We investigate the dynamics of an isentropic layer of air, governed by the hydrostatic primitive equations. In such a layer the horizontal velocity is independent of height if this is assumed to be the case at some initial time. From the mass-conservation equation in pressure coordinates it follows that w, the material derivative of the pressure, varies linearly with pressure. From the mass-conservation equation in height coordinates the vertical velocity w is obtained. The resulting expression is shown to be in accordance with Richardson's equation for the vertical velocity in a general hydrostatic atmosphere, when particularized to an isentropic layer.

Pion-4He scattering length

Nuclear Physics A, 1981

We present relativistic three-body calculations for the real part of the π-4He scattering length ... more We present relativistic three-body calculations for the real part of the π-4He scattering length Re a. Nucleon binding, exclusion principle and Fermi motion are all included in a very careful manner. Because of our careful evaluation of the single-scattering process the remaining discrepancies with the experimental data can be attributed to higher-order mechanisms involving more than one nucleon. In particular for the πA S-wave interaction at threshold, one expects that these higher-order contributions arise largely from the absorption effect. We have performed our calculations for four current models of the input πN t-matrix. Using a πN t-matrix which reproduces the low energy πN phase shifts correctly leads to Re aabs ⋍-Im aabs, if we attribute the discrepancy of the calculated value with the accurately determined empirical value of Re a to pion absorption. We determine the strength parameter B0 in a p2 optical potential term from an adjustment to the π-4He scattering length. Finally some cross sections are calculated for Tlabπ = 10 MeV and Tlabπ = 15 MeV.

The Construction of Barotropic Modons on a Sphere

Journal of the Atmospheric Sciences, 1984

Abstract It is shown that exact modon solutions of the barotropic vorticity equation on a sphere ... more Abstract It is shown that exact modon solutions of the barotropic vorticity equation on a sphere can be constructed. By using Legendre functions of real and complex degree and superimposing dipole and monopole streamfunctions, the zeroth, first and second derivatives of the total streamfunction can be made continuous on the boundary circle. As a necessary condition, a nonlinear constraint similar to that in the beta plane case must be satisfied. This constraint is analyzed by graphical methods, concentrating on the smallest and simplest modons it allows. A few examples of these modons are discussed in more detail. It is shown that the beta plane modons are recovered by taking the small-modon limit.

Stationary Barotropic Modons in Westerly Background Flows

Journal of the Atmospheric Sciences, 1987

On the Beta Plane Approximation

Journal of the Atmospheric Sciences, 1990

A Numerical Method for Finding Form-preserving Free Solutions of the Barotropic Vorticity Equation on a Sphere

Journal of the Atmospheric Sciences, 1993

Abstract A numerical method is presented that allows one to obtain steady or zonally moving (i.e.... more Abstract A numerical method is presented that allows one to obtain steady or zonally moving (i.e., form-preserving) solutions of the barotropic vorticity equation on a sphere. The solutions are characterized by nonlinear functional relationships between the streakfunction (the streamfunction in a steady or zonally moving frame of reference) and the absolute vorticity. Three new examples of steady solutions are obtained that resemble atmospheric blocking. The examples have approximately the same global structure but differ in the degree of uniformity of the streamfunction and the absolute vorticity in the blocking region. From a numerical linear stability analysis it is concluded that the example in which the absolute vorticity in this region is the most uniform is to be preferred as a description of atmospheric blocking. This conclusion is consistent with recent observational evidence.

Modons with Uniform Absolute Vorticity

Journal of the Atmospheric Sciences, 1990

A Balanced Approximation of the One-Layer Shallow-Water Equations on a Sphere

Journal of the Atmospheric Sciences, 2009

A global version of the equivalent barotropic vorticity equation is derived for the one-layer sha... more A global version of the equivalent barotropic vorticity equation is derived for the one-layer shallow-water equations on a sphere. The equation has the same form as the corresponding beta plane version, but with one important difference: the stretching (Cressman) term in the expression of the potential vorticity retains its full dependence on f 2, where f is the Coriolis parameter. As a check of the resulting system, the dynamics of linear Rossby waves are considered. It is shown that these waves are rather accurate approximations of the westward-propagating waves of the second class of the original shallow-water equations. It is also concluded that for Rossby waves with short meridional wavelengths the factor f 2 in the stretching term can be replaced by the constant value f02, where f0 is the Coriolis parameter at ±45° latitude.

Orography in a Contour Dynamics Model of Large-Scale Atmospheric Flow

Journal of the Atmospheric Sciences, 1995

Tropopause Dynamics and Planetary Waves

Journal of the Atmospheric Sciences, 1994

A series solution of the nonlinear wind-driven ocean circulation and its inertial limit

Journal of Fluid Mechanics, 1995

A series solution approach to the forced and damped quasi-geostrophic barotropic vorticity equati... more A series solution approach to the forced and damped quasi-geostrophic barotropic vorticity equation is considered in order to examine the strongly forced and inertial limits of ocean gyre dynamics. The strongly forced limit is the limit investigated numerically by Veronis (1966b). It is shown that this limit, although superficially having the same symmetry properties as the inertial limit, is distinguishably different from the latter. After isolating the inertial limit in an appropriate way it is shown that our series solution method is able to find the 'free mode' and its 'almost free correction', that the 'free mode' obeys the integral criteria of Niiler (1966) and Pierrehumbert & and that the relationship between the streamfunction and the absolute vorticity is in general a nonlinear one.

Synoptic Development In A Two-and-a-half Layer Contour Dynamics System

EGS General Assembly Conference Abstracts, 2002

Buys Ballot's Law, Hamilton's Principle and The Atmosphere's Dynamics

EGSGA, 2002

Subgrid modeling in two-dimensional turbulent flow using the principle of maximum entropy

The non-equilibrium statistical mechanics of a simple geophysical fluid dynamics model

A maximum entropy approach to the parametrization of subgrid processes in two‐dimensional flow

Quarterly Journal of the Royal Meteorological Society, 2016

In numerical models of geophysical fluid systems, parametrization schemes are needed to account f... more In numerical models of geophysical fluid systems, parametrization schemes are needed to account for the effect of unresolved processes on processes that are resolved explicitly. Usually, these parametrization schemes require tuning of their parameters to achieve optimal performance. We propose a new type of parametrization that requires no tuning, as it is based on an assumption that is not specific to any particular model. The assumption is that the unresolved processes can be represented by a probability density function that has maximum information entropy under the constraints of zero average time derivatives of key integral quantities of the unresolved processes. In the context of a model of a simple fluid dynamical system, it is shown that this approach leads to definite expressions for the mean effect of unresolved processes on processes that are resolved. The merits of the parametrization, regarding both short‐range forecasting and long‐term statistics, are demonstrated by n...

Manually adjusting a numerical weather analysis in terms of potential vorticity using three-dimensional variational data-assimilation

Quarterly Journal of the Royal Meteorological Society, 2005

A method is presented to manually adjust the analysis of a numerical weather-forecasting model an... more A method is presented to manually adjust the analysis of a numerical weather-forecasting model and study the impact of the adjustment on the ensuing forecast. The adjustment is made in terms of potential vorticity. The prime motivation for using potential vorticity is that within the constraints of hydrostatic and geostrophic balance the pressure, wind and temperature fields are adjusted whenever the potential vorticity field is adjusted. This is a consequence of the invertibility principle of potential vorticity. Another motivation is that potential vorticity usually correlates well with water vapour satellite images at midlatitudes. Obvious mismatches between the two fields are therefore indicative of errors and may, in actual practice, be a reason to adjust the analysis. The method is based on three-dimensional variational data-assimilation and utilizes the special properties of potential vorticity. The potential vorticity of the analysis is manually adjusted by means of a graphical interface. The resulting modified potential vorticity field is treated as information that is to be incorporated into a new modified analysis. For this purpose we use three-dimensional variational data-assimilation, in which the observation term in the cost function is replaced by a potential vorticity term. In analogy with the observation term the potential vorticity term measures the difference between the modified potential vorticity and the potential vorticity of the model state. The extent to which the modified analysis reproduces the modified potential vorticity depends on the relative weights of the potential vorticity term and the background term in the cost function. An example is given of a modified analysis and its effect on a 24-hour forecast, using a limited-area weather-forecasting model.

Application of a potential vorticity modification method to a case of rapid cyclogenesis over the Atlantic Ocean

Quarterly Journal of the Royal Meteorological Society, 2007

A method to modify the potential vorticity of a numerical weather analysis is applied to a case o... more A method to modify the potential vorticity of a numerical weather analysis is applied to a case of rapid cyclogenesis over the Atlantic Ocean. The development of the cyclone's intensity in terms of mean sea level pressure is underestimated by the Dutch version of the limited-area weather prediction model HIRLAM. The analysis shows a rather clear mismatch between the potential vorticity of the analysis and the corresponding water vapour satellite image. A barotropic displacement of potential vorticity, based on a subjective comparison with the water vapour satellite image, improves the forecast in terms of the cyclone's mean sea level pressure eighteen hours after the analysis. Similar but different modifications are investigated to assess the sensitivity of the development to the modification applied. The numerical analysis of the global ECMWF model displays a similar mismatch between potential vorticity and water vapour image, although the mismatch is somewhat less dramatic than for the HIRLAM model. Notwithstanding, the ECMWF model describes the development of the mean sea level pressure of the cyclone very well. Investigation of targeted singular vectors and a regular ensemble for this case shows, however, that the forecast is sensitive to perturbations of the initial state, in particular in the region of the potential vorticity/water vapour mismatch. The operational forecast lies in the middle of the ECMWF ensemble, the ensemble containing members with both stronger and weaker development of the cyclone. Our study confirms that a mismatch between an analysed potential vorticity field and a water vapour satellite image might indicate an error in the analysis. However, the error is not necessarily confined to the upper atmosphere and may involve the lower atmosphere as well. Pairs of ECMWF ensemble members, differing according to the sign of the initial perturbation and leading to either shallow or deep cyclones, are studied to shed some light on the effect of different initial conditions. The modification that improves the HIRLAM forecast resembles one of the more strongly developing ensemble members, indicating that the modification lies within the range of acceptable possibilities.

Salmon's Hamiltonian approach to balanced flow applied to a one‐layer isentropic model of the atmosphere

Quarterly Journal of the Royal Meteorological Society, 2001

Salmon's Hamiltonian approach is applied to formulate a balanced approximation to a hydrostat... more Salmon's Hamiltonian approach is applied to formulate a balanced approximation to a hydrostatic one‐layer isentropic model of the atmosphere. The model, referred to as the parent model, describes an idealized atmosphere of which the dynamics is closely analogous to a one‐layer shallow‐water model on the sphere. The balance used as input in Salmon's approach is a simplified form of linear balance, in which the balanced velocity vb is given by vb = k×δf−1(M–M). Here k is a vertical unit vector, f is the Coriolis parameter, M is the Montgomery potential and M is the value of the Montgomery potential at the state of rest. This form of balance is used in preference to standard geostrophic balance, vb = k × f−1δM, which forces the meridional wind velocity to be zero at the equator. Salmon's Hamiltonian technique is applied to obtain an equation for the time rate of change of the balanced velocity that guarantees both the material conservation of potential vorticity as well as ...

Evolution of stratosphere-troposphere singular vectors

Quarterly Journal of the Royal Meteorological Society, 2011

ABSTRACT Stratospheric conditions affect the tropospheric circulation on a variety of time-scales... more ABSTRACT Stratospheric conditions affect the tropospheric circulation on a variety of time-scales. This article addresses two issues in stratosphere–troposphere interaction that are relevant for time-scales up to a week: the basic growth mechanisms involved and the role of the stratospheric shear. Idealized simulations are conducted of initially stratospheric perturbations that maximize tropospheric total disturbance energy with a lead time of 5 days, assuming linear quasi-geostrophic dynamics and simplified zonal flow. The evolution is analysed in terms of the basic interactions between three Rossby-wave components. On the f-plane (constant Coriolis parameter), the three-component analysis is very accurate (the error stays within 1% of vertically integrated total energy) because all available growth mechanisms are captured. Energy growth occurs initially through the Orr mechanism, subsequently through resonance and finally through (normal-mode) shear instability. On the β-plane (Coriolis parameter varying linearly with latitude), errors increase because westward retrogression of the untilting potential vorticity structure is neglected by the three-component model. Further study reveals that the tropospheric energy growth strongly depends on the value of the stratospheric shear. Copyright © 2011 Royal Meteorological Society

On the vertical velocity in an isentropic layer

Quarterly Journal of the Royal Meteorological Society, 2000

We investigate the dynamics of an isentropic layer of air, governed by the hydrostatic primitive ... more We investigate the dynamics of an isentropic layer of air, governed by the hydrostatic primitive equations. In such a layer the horizontal velocity is independent of height if this is assumed to be the case at some initial time. From the mass-conservation equation in pressure coordinates it follows that w, the material derivative of the pressure, varies linearly with pressure. From the mass-conservation equation in height coordinates the vertical velocity w is obtained. The resulting expression is shown to be in accordance with Richardson's equation for the vertical velocity in a general hydrostatic atmosphere, when particularized to an isentropic layer.

Pion-4He scattering length

Nuclear Physics A, 1981

We present relativistic three-body calculations for the real part of the π-4He scattering length ... more We present relativistic three-body calculations for the real part of the π-4He scattering length Re a. Nucleon binding, exclusion principle and Fermi motion are all included in a very careful manner. Because of our careful evaluation of the single-scattering process the remaining discrepancies with the experimental data can be attributed to higher-order mechanisms involving more than one nucleon. In particular for the πA S-wave interaction at threshold, one expects that these higher-order contributions arise largely from the absorption effect. We have performed our calculations for four current models of the input πN t-matrix. Using a πN t-matrix which reproduces the low energy πN phase shifts correctly leads to Re aabs ⋍-Im aabs, if we attribute the discrepancy of the calculated value with the accurately determined empirical value of Re a to pion absorption. We determine the strength parameter B0 in a p2 optical potential term from an adjustment to the π-4He scattering length. Finally some cross sections are calculated for Tlabπ = 10 MeV and Tlabπ = 15 MeV.

The Construction of Barotropic Modons on a Sphere

Journal of the Atmospheric Sciences, 1984

Abstract It is shown that exact modon solutions of the barotropic vorticity equation on a sphere ... more Abstract It is shown that exact modon solutions of the barotropic vorticity equation on a sphere can be constructed. By using Legendre functions of real and complex degree and superimposing dipole and monopole streamfunctions, the zeroth, first and second derivatives of the total streamfunction can be made continuous on the boundary circle. As a necessary condition, a nonlinear constraint similar to that in the beta plane case must be satisfied. This constraint is analyzed by graphical methods, concentrating on the smallest and simplest modons it allows. A few examples of these modons are discussed in more detail. It is shown that the beta plane modons are recovered by taking the small-modon limit.

Stationary Barotropic Modons in Westerly Background Flows

Journal of the Atmospheric Sciences, 1987

On the Beta Plane Approximation

Journal of the Atmospheric Sciences, 1990

A Numerical Method for Finding Form-preserving Free Solutions of the Barotropic Vorticity Equation on a Sphere

Journal of the Atmospheric Sciences, 1993

Abstract A numerical method is presented that allows one to obtain steady or zonally moving (i.e.... more Abstract A numerical method is presented that allows one to obtain steady or zonally moving (i.e., form-preserving) solutions of the barotropic vorticity equation on a sphere. The solutions are characterized by nonlinear functional relationships between the streakfunction (the streamfunction in a steady or zonally moving frame of reference) and the absolute vorticity. Three new examples of steady solutions are obtained that resemble atmospheric blocking. The examples have approximately the same global structure but differ in the degree of uniformity of the streamfunction and the absolute vorticity in the blocking region. From a numerical linear stability analysis it is concluded that the example in which the absolute vorticity in this region is the most uniform is to be preferred as a description of atmospheric blocking. This conclusion is consistent with recent observational evidence.

Modons with Uniform Absolute Vorticity

Journal of the Atmospheric Sciences, 1990

A Balanced Approximation of the One-Layer Shallow-Water Equations on a Sphere

Journal of the Atmospheric Sciences, 2009

A global version of the equivalent barotropic vorticity equation is derived for the one-layer sha... more A global version of the equivalent barotropic vorticity equation is derived for the one-layer shallow-water equations on a sphere. The equation has the same form as the corresponding beta plane version, but with one important difference: the stretching (Cressman) term in the expression of the potential vorticity retains its full dependence on f 2, where f is the Coriolis parameter. As a check of the resulting system, the dynamics of linear Rossby waves are considered. It is shown that these waves are rather accurate approximations of the westward-propagating waves of the second class of the original shallow-water equations. It is also concluded that for Rossby waves with short meridional wavelengths the factor f 2 in the stretching term can be replaced by the constant value f02, where f0 is the Coriolis parameter at ±45° latitude.

Orography in a Contour Dynamics Model of Large-Scale Atmospheric Flow

Journal of the Atmospheric Sciences, 1995

Tropopause Dynamics and Planetary Waves

Journal of the Atmospheric Sciences, 1994

A series solution of the nonlinear wind-driven ocean circulation and its inertial limit

Journal of Fluid Mechanics, 1995

A series solution approach to the forced and damped quasi-geostrophic barotropic vorticity equati... more A series solution approach to the forced and damped quasi-geostrophic barotropic vorticity equation is considered in order to examine the strongly forced and inertial limits of ocean gyre dynamics. The strongly forced limit is the limit investigated numerically by Veronis (1966b). It is shown that this limit, although superficially having the same symmetry properties as the inertial limit, is distinguishably different from the latter. After isolating the inertial limit in an appropriate way it is shown that our series solution method is able to find the 'free mode' and its 'almost free correction', that the 'free mode' obeys the integral criteria of Niiler (1966) and Pierrehumbert & and that the relationship between the streamfunction and the absolute vorticity is in general a nonlinear one.