scholarly journals Resonance in Optimal Perturbation Evolution. Part I: Two-Layer Eady Model

2007 ◽  
Vol 64 (3) ◽  
pp. 673-694 ◽  
Author(s):  
H. de Vries ◽  
J. D. Opsteegh
Keyword(s):  
Normal Mode ◽  
Potential Vorticity ◽  
Resonance Effect ◽  
Baroclinic Instability ◽  
Building Blocks ◽  
Variable Number ◽  
Optimal Perturbation ◽  
Surface Development ◽  
Time Optimal ◽  
Asymptotic Normal

Abstract A detailed investigation has been performed of the role of the different growth mechanisms (resonance, potential vorticity unshielding, and normal-mode baroclinic instability) in the evolution of optimal perturbations constructed for a two-layer Eady model and a kinetic energy norm. The two-layer Eady model is obtained by replacing the conventional upper rigid lid by a simple but realistic stratosphere. To make an unambiguous discussion possible, generally applicable techniques have been developed. At the heart of these techniques lies a description of the linear dynamics in terms of a variable number of potential vorticity building blocks (PVBs), which are zonally wavelike, vertically localized sheets of potential vorticity. If the optimal perturbation is composed of only one PVB, the rapid surface cyclogenesis can be attributed to the growth of the surface PVB (the edge wave), which is excited by the tropospheric PVB via a linear resonance effect. If the optimal perturbation is constructed using multiple PVBs, this simple picture is modified only in the sense that PV unshielding dominates the surface amplification for a short time after initialization. The unshielding mechanism rapidly creates large streamfunction values at the surface, as a result of which the resonance effect is much stronger. A similar resonance effect between the tropospheric PVBs and the tropopause PVB acts negatively on the surface streamfunction amplification. The influence of the stratosphere to the surface development is negligible. In all cases reported here, the growth due to traditional normal-mode baroclinic instability contributes either negative or only little to the surface development up to the optimization time of two days. It takes at least four days for the flow to become fully dominated by normal-mode growth, thereby confirming that finite-time optimal perturbation growth differs in many aspects fundamentally from asymptotic normal-mode baroclinic instability.

scholarly journals Resonance in Optimal Perturbation Evolution. Part II: Effects of a Nonzero Mean PV Gradient

2007 ◽  
Vol 64 (3) ◽  
pp. 695-710 ◽  
Author(s):  
H. de Vries ◽  
J. D. Opsteegh
Keyword(s):  
Potential Vorticity ◽  
Propagation Speed ◽  
Building Blocks ◽  
Joint Effect ◽  
Optimal Perturbation ◽  
Orr Mechanism ◽  
Nonzero Mean ◽  
Low Levels ◽  
Pv Gradient

Abstract Optimal perturbations are constructed for a two-layer β-plane extension of the Eady model. The surface and interior dynamics is interpreted using the concept of potential vorticity building blocks (PVBs), which are zonally wavelike, vertically confined sheets of quasigeostrophic potential vorticity. The results are compared with the Charney model and with the two-layer Eady model without β. The authors focus particularly on the role of the different growth mechanisms in the optimal perturbation evolution. The optimal perturbations are constructed allowing only one PVB, three PVBs, and finally a discrete equivalent of a continuum of PVBs to be present initially. On the f plane only the PVB at the surface and at the tropopause can be amplified. In the presence of β, however, PVBs influence each other’s growth and propagation at all levels. Compared to the two-layer f-plane model, the inclusion of β slightly reduces the surface growth and propagation speed of all optimal perturbations. Responsible for the reduction are the interior PVBs, which are excited by the initial PVB after initialization. Their joint effect is almost as strong as the effect from the excited tropopause PVB, which is also negative at the surface. If the optimal perturbation is composed of more than one PVB, the Orr mechanism dominates the initial amplification in the entire troposphere. At low levels, the interaction between the surface PVB and the interior tropospheric PVBs (in particular those near the critical level) takes over after about half a day, whereas the interaction between the tropopause PVB and the interior PVBs is responsible for the main amplification in the upper troposphere. In all cases in which more than one PVB is used, the growing normal mode configuration is not reached at optimization time.

Optimal Perturbations in the Eady Model: Resonance versus PV Unshielding

2005 ◽  
Vol 62 (2) ◽  
pp. 492-505 ◽  
Author(s):  
H. de Vries ◽  
J. D. Opsteegh
Keyword(s):  
Growth Mechanism ◽  
Dominant Role ◽  
Resonance Effect ◽  
Potential Temperature ◽  
Region Of Interest ◽  
Building Blocks ◽  
Edge Wave ◽  
Initial Surface ◽  
Optimal Perturbation ◽  
Resonant Level

Abstract Using a nonmodal decomposition technique based on the potential vorticity (PV) perspective, the optimal perturbation or singular vector (SV) of the Eady model without upper rigid lid is studied for a kinetic energy norm. Special emphasis is put on the role of the continuum modes (CMs) in the structure of the SV, and on the importance of resonance to the SV evolution. The basis for the SV is formed by a number of nonmodal structures, each consisting of a superposition of one CM and one edge wave, such that the initial surface potential temperature (PT) is zero. These nonmodal structures are used as PV building blocks to construct the SV. The motivation for using a nonmodal approach is that no attempt has been made so far to include the CM residing at the steering level of the surface edge wave in the perturbation, although it is known that this CM is in linear resonance with the surface edge wave. Experiments with one PV building block in the initial disturbance show that the SV growth is dominated by the resonance effect except for small optimization times (less than 1 day), in which case the unshielding of PV and surface PT dominates the growth of the SV. The PV–PT unshielding provides additional growth to the SV and this explains the observation that the PV resides above the resonant level. More PV building blocks are added to include PV unshielding as a third growth mechanism. Which of the three mechanisms dominates during the SV evolution depends on the region of interest (interior or surface), as well as on the optimization time and on the number of building blocks used. At the surface, resonance plays a dominant role even when a large number of building blocks is used and relatively small optimization times are used. For the interior of the domain, PV unshielding becomes the dominant growth mechanism when more than two PV building blocks are used. With increasing optimization times, the PV distribution of the SV becomes increasingly more concentrated near the steering level of the edge wave. This concentration of PV is explained by the enhanced importance of resonance for long optimization times as compared to short optimization times.

scholarly journals Jet Formation and Evolution in Baroclinic Turbulence with Simple Topography

2010 ◽  
Vol 40 (2) ◽  
pp. 257-278 ◽  
Author(s):  
Andrew F. Thompson
Keyword(s):  
Southern Ocean ◽  
Potential Vorticity ◽  
Baroclinic Instability ◽  
Length Scale ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Jet Formation ◽  
Meridional Transport ◽  
Jet Behavior ◽  
Jet Variability

Abstract Satellite altimetry and high-resolution ocean models indicate that the Southern Ocean comprises an intricate web of narrow, meandering jets that undergo spontaneous formation, merger, and splitting events, as well as rapid latitude shifts over periods of weeks to months. The role of topography in controlling jet variability is explored using over 100 simulations from a doubly periodic, forced-dissipative, two-layer quasigeostrophic model. The system is forced by a baroclinically unstable, vertically sheared mean flow in a domain that is large enough to accommodate multiple jets. The dependence of (i) meridional jet spacing, (ii) jet variability, and (iii) domain-averaged meridional transport on changes in the length scale and steepness of simple sinusoidal topographical features is analyzed. The Rhines scale, ℓβ = 2πVe/β, where Ve is an eddy velocity scale and β is the barotropic potential vorticity gradient, measures the meridional extent of eddy mixing by a single jet. The ratio ℓβ /ℓT, where ℓT is the topographic length scale, governs jet behavior. Multiple, steady jets with fixed meridional spacing are observed when ℓβ ≫ ℓT or when ℓβ ≈ ℓT. When ℓβ < ℓT, a pattern of perpetual jet formation and jet merger dominates the time evolution of the system. Zonal ridges systematically reduce the domain-averaged meridional transport, while two-dimensional, sinusoidal bumps can increase transport by an order of magnitude or more. For certain parameters, bumpy topography gives rise to periodic oscillations in the jet structure between purely zonal and topographically steered states. In these cases, transport is dominated by bursts of mixing associated with the transition between the two regimes. Topography modifies local potential vorticity (PV) gradients and mean flows; this can generate asymmetric Reynolds stresses about the jet core and can feed back on the conversion of potential energy to kinetic energy through baroclinic instability. Both processes contribute to unsteady jet behavior. It is likely that these processes play a role in the dynamic nature of Southern Ocean jets.

scholarly journals Potential Vorticity Diagnostics to Quantify Effects of Latent Heating in Extratropical Cyclones. Part I: Methodology

2017 ◽  
Vol 74 (11) ◽  
pp. 3567-3590 ◽  
Author(s):  
Dominik Büeler ◽  
Stephan Pfahl
Keyword(s):  
Potential Vorticity ◽  
Weather Prediction ◽  
Baroclinic Instability ◽  
Numerical Weather Prediction Model ◽  
Cloud Formation ◽  
Extratropical Cyclones ◽  
Latent Heating ◽  
Strongly Coupled ◽  
Cyclone Intensity ◽  
Diabatic Processes

Abstract Extratropical cyclones develop because of baroclinic instability, but their intensification is often substantially amplified by diabatic processes, most importantly, latent heating (LH) through cloud formation. Although this amplification is well understood for individual cyclones, there is still need for a systematic and quantitative investigation of how LH affects cyclone intensification in different, particularly warmer and moister, climates. For this purpose, the authors introduce a simple diagnostic to quantify the contribution of LH to cyclone intensification within the potential vorticity (PV) framework. The two leading terms in the PV tendency equation, diabatic PV modification and vertical advection, are used to derive a diagnostic equation to explicitly calculate the fraction of a cyclone’s positive lower-tropospheric PV anomaly caused by LH. The strength of this anomaly is strongly coupled to cyclone intensity and the associated impacts in terms of surface weather. To evaluate the performance of the diagnostic, sensitivity simulations of 12 Northern Hemisphere cyclones with artificially modified LH are carried out with a numerical weather prediction model. Based on these simulations, it is demonstrated that the PV diagnostic captures the mean sensitivity of the cyclones’ PV structure to LH as well as parts of the strong case-to-case variability. The simple and versatile PV diagnostic will be the basis for future climatological studies of LH effects on cyclone intensification.

scholarly journals Marginal Sea Overflows and the Upper Ocean Interaction

2009 ◽  
Vol 39 (2) ◽  
pp. 387-403 ◽  
Author(s):  
Shinichiro Kida ◽  
Jiayan Yang ◽  
James F. Price
Keyword(s):  
Ocean Circulation ◽  
Potential Vorticity ◽  
Baroclinic Instability ◽  
Upper Ocean ◽  
Marginal Sea ◽  
The Mediterranean ◽  
The Difference ◽  
Set Up ◽  
Numerical Model Experiments ◽  
Gyre Circulation

Abstract Marginal sea overflows and the overlying upper ocean are coupled in the vertical by two distinct mechanisms—by an interfacial mass flux from the upper ocean to the overflow layer that accompanies entrainment and by a divergent eddy flux associated with baroclinic instability. Because both mechanisms tend to be localized in space, the resulting upper ocean circulation can be characterized as a β plume for which the relevant background potential vorticity is set by the slope of the topography, that is, a topographic β plume. The entrainment-driven topographic β plume consists of a single gyre that is aligned along isobaths. The circulation is cyclonic within the upper ocean (water columns are stretched). The transport within one branch of the topographic β plume may exceed the entrainment flux by a factor of 2 or more. Overflows are likely to be baroclinically unstable, especially near the strait. This creates eddy variability in both the upper ocean and overflow layers and a flux of momentum and energy in the vertical. In the time mean, the eddies accompanying baroclinic instability set up a double-gyre circulation in the upper ocean, an eddy-driven topographic β plume. In regions where baroclinic instability is growing, the momentum flux from the overflow into the upper ocean acts as a drag on the overflow and causes the overflow to descend the slope at a steeper angle than what would arise from bottom friction alone. Numerical model experiments suggest that the Faroe Bank Channel overflow should be the most prominent example of an eddy-driven topographic β plume and that the resulting upper-layer transport should be comparable to that of the overflow. The overflow-layer eddies that accompany baroclinic instability are analogous to those observed in moored array data. In contrast, the upper layer of the Mediterranean overflow is likely to be dominated more by an entrainment-driven topographic β plume. The difference arises because entrainment occurs at a much shallower location for the Mediterranean case and the background potential vorticity gradient of the upper ocean is much larger.

Interactions between Water Vapor and Potential Vorticity in Synoptic-Scale Monsoonal Disturbances: Moisture Vortex Instability

2018 ◽  
Vol 75 (6) ◽  
pp. 2083-2106 ◽  
Author(s):  
Ángel F. Adames ◽  
Yi Ming
Keyword(s):  
Potential Vorticity ◽  
Baroclinic Instability ◽  
Relative Role ◽  
Synoptic Scale ◽  
Vortex Instability ◽  
Tropical Variability ◽  
Moisture Advection ◽  
Energy Gradient ◽  
Gross Moist Stability ◽  
Static Energy

AbstractSouth Asian monsoon low pressure systems, referred to as synoptic-scale monsoonal disturbances (SMDs), are convectively coupled cyclonic disturbances that are responsible for up to half of the total monsoon rainfall. In spite of their importance, the mechanisms that lead to the growth of these systems have remained elusive. It has long been thought that SMDs grow because of a variant of baroclinic instability that includes the effects of convection. Recent work, however, has shown that this framework is inconsistent with the observed structure and dynamics of SMDs. Here, we present an alternative framework that may explain the growth of SMDs and may also be applicable to other modes of tropical variability. Moisture is prognostic and is coupled to precipitation through a simplified Betts–Miller scheme. Interactions between moisture and potential vorticity (PV) in the presence of a moist static energy gradient can be understood in terms of a “gross” PV (qG) equation. The qG summarizes the dynamics of SMDs and reveals the relative role that moist and dry dynamics play in these disturbances, which is largely determined by the gross moist stability. Linear solutions to the coupled PV and moisture equations reveal Rossby-like modes that grow because of a moisture vortex instability. Meridional temperature and moisture advection to the west of the PV maximum moisten and destabilize the column, which results in enhanced convection and SMD intensification through vortex stretching. This instability occurs only if the moistening is in the direction of propagation of the SMD and is strongest at the synoptic scale.

Transient growth in strongly stratified shear layers

2014 ◽  
Vol 758 ◽  
Author(s):  
A. K. Kaminski ◽  
C. P. Caulfield ◽  
J. R. Taylor
Keyword(s):  
Shear Layer ◽  
Normal Mode ◽  
Richardson Number ◽  
Mixing Layer ◽  
Three Dimensional ◽  
Buoyancy Frequency ◽  
Transient Growth ◽  
Time Intervals ◽  
Optimal Perturbation ◽  
Target Time

AbstractWe investigate numerically transient linear growth of three-dimensional perturbations in a stratified shear layer to determine which perturbations optimize the growth of the total kinetic and potential energy over a range of finite target time intervals. The stratified shear layer has an initial parallel hyperbolic tangent velocity distribution with Reynolds number $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\mathit{Re}=U_0 h/\nu =1000$ and Prandtl number $\nu /\kappa =1$, where $\nu $ is the kinematic viscosity of the fluid and $\kappa $ is the diffusivity of the density. The initial stable buoyancy distribution has constant buoyancy frequency $N_0$, and we consider a range of flows with different bulk Richardson number ${\mathit{Ri}}_b=N_0^2h^2/U_0^2$, which also corresponds to the minimum gradient Richardson number ${\mathit{Ri}}_g(z)=N_0^2/(\mathrm{d}U/\mathrm{d} z)^2$ at the midpoint of the shear layer. For short target times, the optimal perturbations are inherently three-dimensional, while for sufficiently long target times and small ${\mathit{Ri}}_b$ the optimal perturbations are closely related to the normal-mode ‘Kelvin–Helmholtz’ (KH) instability, consistent with analogous calculations in an unstratified mixing layer recently reported by Arratia et al. (J. Fluid Mech., vol. 717, 2013, pp. 90–133). However, we demonstrate that non-trivial transient growth occurs even when the Richardson number is sufficiently high to stabilize all normal-mode instabilities, with the optimal perturbation exciting internal waves at some distance from the midpoint of the shear layer.

scholarly journals The Poleward Motion of Extratropical Cyclones from a Potential Vorticity Tendency Analysis

2016 ◽  
Vol 73 (4) ◽  
pp. 1687-1707 ◽  
Author(s):  
Talia Tamarin ◽  
Yohai Kaspi
Keyword(s):  
Heat Release ◽  
Latent Heat ◽  
Potential Vorticity ◽  
Growth Stage ◽  
Baroclinic Instability ◽  
Propagation Time ◽  
Latent Heat Release ◽  
Low Level ◽  
Upper Level ◽  
Tendency Analysis

Abstract The poleward propagation of midlatitude storms is studied using a potential vorticity (PV) tendency analysis of cyclone-tracking composites, in an idealized zonally symmetric moist GCM. A detailed PV budget reveals the important role of the upper-level PV and diabatic heating associated with latent heat release. During the growth stage, the classic picture of baroclinic instability emerges, with an upper-level PV to the west of a low-level PV associated with the cyclone. This configuration not only promotes intensification, but also a poleward tendency that results from the nonlinear advection of the low-level anomaly by the upper-level PV. The separate contributions of the upper- and lower-level PV as well as the surface temperature anomaly are analyzed using a piecewise PV inversion, which shows the importance of the upper-level PV anomaly in advecting the cyclone poleward. The PV analysis also emphasizes the crucial role played by latent heat release in the poleward motion of the cyclone. The latent heat release tends to maximize on the northeastern side of cyclones, where the warm and moist air ascends. A positive PV tendency results at lower levels, propagating the anomaly eastward and poleward. It is also shown here that stronger cyclones have stronger latent heat release and poleward advection, hence, larger poleward propagation. Time development of the cyclone composites shows that the poleward propagation increases during the growth stage of the cyclone, as both processes intensify. However, during the decay stage, the vertical alignment of the upper and lower PV anomalies implies that these processes no longer contribute to a poleward tendency.

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