The Next-Order Corrections to Quasigeostrophic Theory

Muraki, David J.; Snyder, Chris; Rotunno, Richard

doi:10.1175/1520-0469(1999)056<1547:tnoctq>2.0.co;2

Cited by 67 publications

(69 citation statements)

References 22 publications

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“…This was recognized by Muraki et al (1999) and Hakim et al (2002) for the special case of the surface temperature in QG ϩ1 and surface QG ϩ1 theory (where, for the latter, PV is assumed to be uniform in the interior of the fluid). The superscript ϩ1 stands for the next-order correction in the Rossby number included in the QG ϩ1 model as compared with the standard QG model.…”

Section: ͑7͒mentioning

confidence: 88%

“…Equation (7) is the central point of our paper. Muraki et al (1999) obtained a corollary by integrating the PV conservation equation over the threedimensional space, by which they found that f 0 ͗͘ ϩ ͗ ͘ at the surface (z ϭ 0) should not depend on time.…”

Section: ͑7͒mentioning

confidence: 99%

“…Expanding each variable in a Rossby number expansion, density can be written such that, as ϭ 0 ϩ 0 ϩ Ro 1 ϩ · · · , where Ro is the Rossby number and ‫ץ‬ z 0 ϭ Ϫ 0 N 2 /g is related to the mean stratification (independent of time and x and y). Also, we have ϭ Ro 1 ϩ · · · and w ϭ Ro 2 w 2 ϩ · · · using the density equation [see Muraki et al (1999) …”

Section: ͑7͒mentioning

confidence: 99%

See 2 more Smart Citations

Oceanic Restratification Forced by Surface Frontogenesis

Lapeyre

Klein

Hua

2006

Journal of Physical Oceanography

121

103

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Potential vorticity (PV) conservation implies a strong constraint on the time evolution of the mean density at a given depth. The authors show that, on an f plane and in the absence of sources and sinks of PV, it only depends on two terms, namely, the time evolution of the product between density anomaly and relative vorticity and the vertical PV flux. This primitive equation result, which applies at any depth, suggests that the ageostrophic dynamics induced by baroclinic eddies strongly affect the mean oceanic stratification profile. This result is illustrated for two simple initial-value simulations of a baroclinic, balanced jet. For initial situations propitious to surface frontogenesis, the simulations show a restratification over the whole water column characterized by the amplification in time of the Brunt-Väisälä frequency in the upper oceanic layers. In the absence of surface frontogenesis, such as when the jet is initialized at the middepth of the water column, the restratification is much weaker and slower. Because both simulations have similar kinetic energy and growth rate of baroclinic instability, the results clearly reveal that the restratification is driven by surface frontogenesis in the first case and by vertical PV flux in the interior in the second case. The authors also point out that the dynamics of the interior PV is tightly related to the surface dynamics because of total mass conservation.

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Section: ͑7͒mentioning

confidence: 88%

Section: ͑7͒mentioning

confidence: 99%

Section: ͑7͒mentioning

confidence: 99%

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Oceanic Restratification Forced by Surface Frontogenesis

Lapeyre

Klein

Hua

2006

Journal of Physical Oceanography

121

103

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“…Warn et al (1995), Muraki et al (1999) In figure 6(b), we plot | Ω | versus q 0 for several cases having similar aspect ratios λ and µ . Corresponding to each of these cases, we construct the velocity field from an ellipsoid of uniform PV with the same λ , µ and q 0 by NQG PV inversion.…”

Section: Vortex Rotation Rate Estimated By a Higher-order Balanced Modelmentioning

confidence: 99%

Ellipsoidal vortices in rotating stratified fluids: beyond the quasi-geostrophic approximation

Tsang

Dritschel

2014

J. Fluid Mech.

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We examine the basic properties and stability of isolated vortices having uniform potential vorticity in a non-hydrostatic rotating stratified fluid, under the Boussinesq approximation. For simplicity, we consider a uniform background rotation and a linear basic-state stratification for which both the Coriolis and buoyancy frequencies, f and N , are constant. Moreover, we take f /N ≪ 1, as typically observed in the Earth's atmosphere and oceans. In the small Rossby number 'quasigeostrophic' limit, when the flow is weak compared to the background rotation, there exists exact solutions for steadily-rotating ellipsoidal volumes of uniform potential vorticity in an unbounded flow (Zhmur & Shchepetkin 1991;Meacham 1992). Furthermore, a wide range of these solutions are stable so long as the horizontal and vertical aspect ratios λ and µ do not depart greatly from unity (Dritschel et al. 2005). In the present study, we examine the behaviour of ellipsoidal vortices at Rossby numbers up to near unity in magnitude. We find that there is a monotonic increase in stability as one varies the Rossby number from nearly −1 (anticyclone) to nearly +1 (cyclone). That is, quasi-geostrophic vortices are more stable than anticyclones at finite (negative) Rossby number, and generally less stable than cyclones at finite (positive) Rossby number. Ageostrophic effects strengthen both the rotation and the stratification within a cyclone, enhancing its stability. The converse is true for an anticyclone. For all Rossby numbers, stability is reinforced by increasing λ towards unity or decreasing µ. An unstable vortex often restabilises by developing a near-circular cross section, typically resulting in a roughly ellipsoidal vortex, but occasionally a binary system is formed. Throughout the nonlinear evolution of a vortex, the emission of inertiagravity waves is negligible across the entire parameter space investigated. Thus, vortices at small to moderate Rossby numbers, and any associated instabilities are (ageostrophically) balanced. A manifestation of this balance is that, at finite Rossby number, an anticyclone rotates faster than a cyclone.

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“…At the surface of the fluid, potential temperature is related to streamfunction in dimensionless form, via θ(x, y, t) = ∂ z ψ(x, y, z = 0, t) (the normalization of all variables is given in Muraki et al, 1999). Potential temperature is advected by the horizontal velocity at the surface according to…”

Section: Model and Parametersmentioning

confidence: 99%

Vortex merger in surface quasi-geostrophy

Carton

Ciani

Verron

et al. 2015

Geophysical & Astrophysical Fluid Dynamics

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The merger of two identical surface temperature vortices is studied in the surface quasigeostrophic model. The motivation for this study is the observation of the merger of submesoscale vortices in the ocean. Firstly, the interaction between two point vortices, in the absence or in the presence of an external deformation field, is investigated. The rotation rate of the vortices, their stationary positions and the stability of these positions are determined. Then, a numerical model provides the steady states of two finite-area, constant-temperature, vortices. Such states are less deformed than their counterparts in two-dimensional incompressible flows. Finally, numerical simulations of the nonlinear surface quasi-geostrophic equations are used to investigate the finite-time evolution of initially identical and symmetric, constant temperature vortices. The critical merger distance is obtained and the deformation of the vortices before or after merger is determined. The addition of external deformation is shown to favor or to oppose merger depending on the orientation of the vortex pair with respect to the strain axes. An explanation for this observation is proposed. Conclusions are drawn towards an application of this study to oceanic vortices.2

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The Next-Order Corrections to Quasigeostrophic Theory

Cited by 67 publications

References 22 publications

Oceanic Restratification Forced by Surface Frontogenesis

Oceanic Restratification Forced by Surface Frontogenesis

Ellipsoidal vortices in rotating stratified fluids: beyond the quasi-geostrophic approximation

Vortex merger in surface quasi-geostrophy

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