Balance in non-hydrostatic rotating stratified turbulence

McKiver, William J.; Dritschel, David G.

doi:10.1017/s0022112007009421

Cited by 28 publications

(45 citation statements)

References 31 publications

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“…Our results suggest that this decoupling remains a good approximation up to Ro = O(1), at least for flows which are nearly balanced initially. Similar conclusions were reached in a recent work on fully turbulent flows (McKiver & Dritschel 2006). We conjecture that the persistence of balance is limited only by inertial and static stability.…”

Section: Discussionsupporting

confidence: 90%

The persistence of balance in geophysical flows

Dritschel

Viúdez

2007

J. Fluid Mech.

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Rotating stably stratified geophysical flows can exhibit a near 'balanced' evolution controlled by the conservative advection of a single scalar quantity, the potential vorticity (PV). This occurs frequently in the Earth's atmosphere and oceans where motions tend to be weak compared with the background planetary rotation and where stratification greatly inhibits vertical motion. Under these circumstances, both high-frequency acoustic waves and lower-frequency inertia-gravity waves (IGWs) contribute little to the flow evolution compared with the even-lower-frequency advection of PV. Moreover, this 'slow' PV-controlled balanced evolution appears unable to excite these higher-frequency waves in any significant way -i.e. balance persists.The present work pushes the limits of balance by systematically exploring the evolution of a range of highly nonlinear flows in which motions are comparable with the background rotation. These flows do not possess a frequency separation between PV advection and IGWs. Nonetheless, the flows exhibit a remarkable persistence of balance. Even when flows are not initialized to minimize the amount of IGWs initially present, and indeed even when flows are deliberately seeded with significant IGW amplitudes, the flow evolution -over many inertial periods (days) -remains strongly controlled by PV advection.

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Section: Discussionsupporting

confidence: 90%

The persistence of balance in geophysical flows

Dritschel

Viúdez

2007

J. Fluid Mech.

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“…While the imbalance is particularly visible here, it nonetheless plays an insignificant role in the flow evolution. This echoes previous findings when care is taken to carefully balance the initial conditions (Dritschel & Viúdez 2007;McKiver & Dritschel 2008). …”

Section: Oblate Weakly-eccentric Vorticessupporting

confidence: 88%

“…In the regime f /N 1, the concept of 'balance', whereby the potential vorticity alone determines all dynamical and thermodynamical fields, has proven immensely useful in understanding geophysical fluid behaviour (Hoskins et al 1985;Ford et al 2000;Mohebalhojeh & Dritschel 2001;McKiver & Dritschel 2008). Balance arises from filtering, in some way, the inertia-gravity waves from the dynamics.…”

Section: Discussionmentioning

confidence: 99%

“…A compromise must be made. Following previous studies (Dritschel & Viúdez 2007;McKiver & Dritschel 2008) and after conducting further tests here, we took τ to be 4 inertial periods. This is sufficiently long not to excite significant IGW activity, though not long enough to avoid all of it.…”

Section: Definitions and Methods Of Analysismentioning

confidence: 99%

“…In both cases, ζ AGb is negative inside the vortex, and weakly positive just outside of it. This is because ζ AGb depends quadratically, to leading order, on the QG balanced fields (see Appendix C or, explicitly, (2.23) of McKiver & Dritschel (2008)). …”

Section: Oblate Weakly-eccentric Vorticesmentioning

confidence: 99%

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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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On the momentum equation for the quasi‐geostrophic model

Mohebalhojeh

2009

Quart J Royal Meteoro Soc

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ABSTRACT:The momentum equation for the quasi-geostrophic (QG) model derived based on the conventional Rossbynumber expansions does not uniquely determine the QG motion up to first order in the Rossby number. There are infinitely many ways of closing the equations. The momentum equation for QG derived by Holm and Zeitlin in 1998 based on a variational formulation for QG is compared with that for the conventional Rossby-number expansions. The underlying assumption in the construction of the variational formulation is geostrophic velocity for the particles. It is shown that the variational momentum equation corresponds to a particular way of closing the conventional momentum equation for QG. The numerical results for potential vorticity (PV) inversion on a circular vortex indicate a smaller range of applicability and loss of accuracy for the variational momentum equation for QG when compared with the QG one that sets the first-order linearized potential vorticity to zero.

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Balance in non-hydrostatic rotating stratified turbulence

Cited by 28 publications

References 31 publications

The persistence of balance in geophysical flows

The persistence of balance in geophysical flows

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

On the momentum equation for the quasi‐geostrophic model

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