Finite-Amplitude Wave Activity and Diffusive Flux of Potential Vorticity in Eddy–Mean Flow Interaction

A linear response function (LRF) determines the mean-response of a nonlinear climate system to weak imposed forcings, and an eddy flux matrix (EFM) determines the eddy momentum and heat flux responses to mean-flow changes. Neither LRF nor EFM can be calculated from first principles due to the lack of a complete theory for turbulent eddies. Here the LRF and EFM for an idealized dry atmosphere are computed by applying numerous localized weak forcings, one at a time, to a GCM with Held-Suarez physics and calculating the mean-responses. The LRF and EFM for zonally-averaged responses are then constructed using these forcings and responses through matrix inversion. Tests demonstrate that LRF and EFM are fairly accurate. Spectral analysis of the LRF shows that the most excitable dynamical mode, the neutral vector, strongly resembles the model's Annular Mode. The framework described here can be employed to compute the LRF/EFM for zonally-asymmetric responses and more complex GCMs. The potential applications of the LRF/EFM constructed here are i) forcing a specified mean-flow for hypothesis-testing, ii) isolating/quantifying the eddyfeedbacks in complex eddy-mean flow interaction problems, and iii) evaluating/improving more generallyapplicable methods currently used to construct LRFs or diagnose eddy-feedbacks in comprehensive GCMs or observations. As an example for iii, in Part 2, the LRF is also computed using the fluctuation-dissipation theorem (FDT), and the previously-calculated LRF is exploited to investigate why FDT performs poorly in some cases. It is shown that dimension-reduction using leading EOFs, which is commonly used to construct LRFs from the FDT, can significantly degrade the accuracy due to the non-normality of the operator.

Section: Applications Of the Lrf And Efmmentioning

confidence: 99%

The Linear Response Function of an Idealized Atmosphere. Part I: Construction Using Green’s Functions and Applications

Hassanzadeh

Kuang

2016

“…which is based on the hybrid Eulerian-Lagrangian formulation of Nakamura and Zhu (2010), where A is wave activity, K eff is effective diffusivity, Q is potential vorticity, and Y(Q) is equivalent latitude. As noted by these authors, the Eulerian eddy PV flux across latitude Y(Q), [y 1 *q 1 *], includes both advective and diffusive components, while the PV flux across the Q contour (second term on the right-hand side) is purely diffusive.…”

Section: The Short Time Responsementioning

confidence: 99%

The Impact of Baroclinic Eddy Feedback on the Persistence of Jet Variability in the Two-Layer Model

Zurita‐Gotor

Blanco-Fuentes

Gerber

2013

Although it is well known that the persistence of extratropical jet shifts is enhanced by a positive eddy feedback, the dynamics of this feedback is still debated. Two types of mechanisms have been proposed: barotropic mechanisms rely on changes in upper-level propagation and baroclinic mechanisms rely on the coupling between barotropic and baroclinic flow. Recent studies have suggested that barotropic models can capture key aspects of the observed jet variability but the role of baroclinic dynamics has been less explored.This study investigates the temporal relations between barotropic and baroclinic anomalies and their eddy forcings during the internal variability of the simple two-layer quasigeostrophic model. A large correlation is found between barotropic and baroclinic anomalies and between the meridional and vertical components of the Eliassen-Palm divergence, especially at low frequency. The low-frequency variability is consistent with the baroclinic mechanism: persistent upper-level eddy momentum convergence is associated with (and precedes) persistent anomalies in the poleward eddy heat flux. In contrast, at high frequency, poleward heat flux anomalies are associated with eddy momentum divergence aloft and both eddy forcings have same-sign contributions to the upper-level eddy potential vorticity (PV) flux. In this limit the eddy PV flux is associated with wave activity transience as effective diffusivity is too small to dissipate the wave-mean flow interaction term.The large correlation between barotropic and baroclinic anomalies implies that the low-frequency variability of barotropic flow may be affected by thermal damping when this damping is sufficiently strong. For example, zonal index persistence drops drastically in our model when baroclinicity shifts are prevented by strong thermal restoration.

“…Much of our understanding of isentropic mixing has been developed by using a quasi-conservative tracer as the meridional coordinate, which separates irreversible mixing from reversible undulation of tracer contours (e.g., Butchart and Remsberg 1986;Nakamura 1995). More specifically, Nakamura (1996) showed that a passive tracer advected by a 2D nondivergent flow with pure horizontal diffusion can be formulated in a diffusive form and that the ''effective diffusivity'' can be defined by the mass flux across the tracer contours.…”

Section: Introductionmentioning

confidence: 99%

“…More specifically, Nakamura (1996) showed that a passive tracer advected by a 2D nondivergent flow with pure horizontal diffusion can be formulated in a diffusive form and that the ''effective diffusivity'' can be defined by the mass flux across the tracer contours. Using a passive tracer driven by the nondivergent isentropic winds in the stratosphere and in the upper troposphere, the effective diffusivity can characterize enhanced mixing within the surf zone and mixing barriers at the subtropics and at the polar vortex edge (Haynes and Shuckburgh 2000a,b;Allen and Nakamura 2001).…”

Section: Introductionmentioning

confidence: 99%

“…Using a passive tracer driven by the nondivergent isentropic winds in the stratosphere and in the upper troposphere, the effective diffusivity can characterize enhanced mixing within the surf zone and mixing barriers at the subtropics and at the polar vortex edge (Haynes and Shuckburgh 2000a,b;Allen and Nakamura 2001). This diagnostic can be further generalized to the 3D flow, leading to an exact advectiondiffusion equation with mass and entropy as the meridional and vertical coordinates, respectively (Nakamura 1998). More recently, Leibensperger and Plumb (2014) extended Nakamura's formalism of effective diffusivity from pure horizontal diffusion to both isentropic and diabatic diffusions.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Effective Isentropic Diffusivity of Tropospheric Transport

Chen

Plumb

2014

Tropospheric transport can be described qualitatively by the slow mean diabatic circulation and rapid isentropic mixing, yet a quantitative understanding of the transport circulation is complicated, as nearly half of the isentropic surfaces in the troposphere frequently intersect the ground. A theoretical framework for the effective isentropic diffusivity of tropospheric transport is presented. Compared with previous isentropic analysis of effective diffusivity, a new diagnostic is introduced to quantify the eddy diffusivity of the nearsurface isentropic flow. This diagnostic also links the effective eddy diffusivity directly to a diffusive closure of eddy fluxes through a finite-amplitude wave activity equation.The theory is examined in a dry primitive equation model on the sphere. It is found that the upper troposphere is characterized by a diffusivity minimum at the jet's center with enhanced mixing at the jet's flanks and that the lower troposphere is dominated by stronger mixing throughout the baroclinic zone. This structure of isentropic diffusivity is generally consistent with the diffusivity obtained from the geostrophic component of the flow. Furthermore, the isentropic diffusivity agrees broadly with the tracer equivalent length obtained from either a spectral diffusion scheme or a semi-Lagrangian advection scheme, indicating that the effective diffusivity of tropospheric transport is largely dictated by large-scale stirring rather than details of the smallscale diffusion acting on the tracers.