scholarly journals The Structure of Baroclinic Modes in the Presence of Baroclinic Mean Flow

2020 ◽  
Vol 50 (1) ◽  
pp. 239-253
Author(s):  
K. H. Brink ◽  
J. Pedlosky
Keyword(s):  
Rossby Wave ◽  
Potential Vorticity ◽  
Vertical Structure ◽  
Horizontal Gradient ◽  
Mean Flow ◽  
Stable Mode ◽  
Oceanic Current ◽  
Unstable Solutions ◽  
Rossby Wave Propagation ◽  
Baroclinic Modes

AbstractThis contribution seeks to understand the vertical structure of linearized quasigeostrophic baroclinic modes when they are modified by the presence of a baroclinic mean flow and associated potential vorticity gradients. It is found that even modest, O(0.05 m s−1), mean flows can give rise to very substantial changes in modal structures, often in the sense of increased surface intensification. The extent to which stable modes are modified depends strongly on the direction of Rossby wave propagation. Further, baroclinically unstable solutions can appear, and a meaningful inviscid critical-layer solution can occur at the transition to instability when the horizontal gradient of potential vorticity changes sign at some depth within the water column. In addition, the gravest, n = 0, vertical stable mode is no longer strictly barotropic, but rather it can carry density variability at frequencies much higher than those possible for baroclinic (higher) Rossby wave modes. This finding appears to be consistent with oceanic current-meter observations that suggest temperature variability propagation even when the frequency is too high for traditional baroclinic Rossby waves to exist.

scholarly journals Rossby wave propagation on potential vorticity fronts with finite width

2016 ◽  
Vol 794 ◽  
pp. 775-797 ◽  
Author(s):  
B. J. Harvey ◽  
J. Methven ◽  
M. H. P. Ambaum
Keyword(s):  
Wave Propagation ◽  
Rossby Wave ◽  
Potential Vorticity ◽  
Rossby Waves ◽  
Phase Speed ◽  
Single Layer ◽  
Horizontal Gradient ◽  
Finite Width ◽  
Numerical Weather ◽  
Rossby Wave Propagation

The horizontal gradient of potential vorticity (PV) across the tropopause typically declines with lead time in global numerical weather forecasts and tends towards a steady value dependent on model resolution. This paper examines how spreading the tropopause PV contrast over a broader frontal zone affects the propagation of Rossby waves. The approach taken is to analyse Rossby waves on a PV front of finite width in a simple single-layer model. The dispersion relation for linear Rossby waves on a PV front of infinitesimal width is well known; here, an approximate correction is derived for the case of a finite-width front, valid in the limit that the front is narrow compared to the zonal wavelength. Broadening the front causes a decrease in both the jet speed and the ability of waves to propagate upstream. The contribution of these changes to Rossby wave phase speeds cancel at leading order. At second order the decrease in jet speed dominates, meaning phase speeds are slower on broader PV fronts. This asymptotic phase speed result is shown to hold for a wide class of single-layer dynamics with a varying range of PV inversion operators. The phase speed dependence on frontal width is verified by numerical simulations and also shown to be robust at finite wave amplitude, and estimates are made for the error in Rossby wave propagation speeds due to the PV gradient error present in numerical weather forecast models.

scholarly journals The Spontaneous Imbalance of an Atmospheric Vortex at High Rossby Number

2008 ◽  
Vol 65 (8) ◽  
pp. 2498-2521 ◽  
Author(s):  
David A. Schecter
Keyword(s):  
Rossby Wave ◽  
Potential Vorticity ◽  
Formal Theory ◽  
Resonant Absorption ◽  
Critical Layer ◽  
Wave Radiation ◽  
Rossby Number ◽  
Mean Flow ◽  
Surface Drag ◽  
Isentropic Coordinates

Abstract This paper discusses recent progress toward understanding the instability of a monotonic vortex at high Rossby number, due to the radiation of spiral inertia–gravity (IG) waves. The outward-propagating IG waves are excited by inner undulations of potential vorticity that consist of one or more vortex Rossby waves. An individual vortex Rossby wave and its IG wave emission have angular pseudomomenta of opposite sign, positive and negative, respectively. The Rossby wave therefore grows in response to producing radiation. Such growth is potentially suppressed by the resonant absorption of angular pseudomomentum in a critical layer, where the angular phase velocity of the Rossby wave matches the angular velocity of the mean flow. Suppression requires a sufficiently steep radial gradient of potential vorticity in the critical layer. Both linear and nonlinear steepness requirements are reviewed. The formal theory of radiation-driven instability, or “spontaneous imbalance,” is generalized in isentropic coordinates to baroclinic vortices that possess active critical layers. Furthermore, the rate of angular momentum loss by IG wave radiation is reexamined in the hurricane parameter regime. Numerical results suggest that the negative radiation torque on a hurricane has a smaller impact than surface drag, despite recent estimates of its large magnitude.

Updraft/Downdraft Constraints for Moist Baroclinic Modes and Their Implications for the Short-Wave Cutoff and Maximum Growth Rate

2005 ◽  
Vol 62 (12) ◽  
pp. 4450-4458 ◽  
Author(s):  
Pablo Zurita-Gotor
Keyword(s):  
Growth Rate ◽  
Vertical Structure ◽  
Baroclinic Instability ◽  
Maximum Growth ◽  
Static Stability ◽  
Short Wave ◽  
Maximum Growth Rate ◽  
Unstable Solutions ◽  
Baroclinic Modes

Abstract This paper examines the dynamics of moist baroclinic modes, based on the idealized model of moist baroclinic instability devised by Emanuel et al. These authors found that the finite static stability along the downdraft prevents the explosive short-wave cyclogenesis of the zero stratification limit in the moist problem, and allows only moderate (order 2) changes in the growth rate and short-wave cutoff, even when the moist static stability vanishes. To understand the limiting role of the dry static stability, a constraint is derived in this paper that relates the updraft and downdraft structures. This constraint is based on continuity and implies that a bulk wavenumber (defined in the paper) scales as the relevant deformation radius in each region. Because neutral solutions are separable, the vertical structure can be encapsulated in terms of a single, equivalent wavenumber based on the downdraft width. This allows an interpretation of the results in terms of the equivalent dry mode. As the ratio between moist and dry static stability decreases, the downdraft width takes an increasingly larger fraction of the total wavelength. In the limit of moist neutrality all the wavelength is occupied by the downdraft, so that the short-wave cutoff is halved. The vertical phase tilt makes unstable solutions nonseparable, and prevents defining an equivalent wavenumber in that case. However, the constraint between the bulk wavenumbers still applies. As the moist stability is reduced, the updraft solution becomes more suboptimal; in the limit of moist neutrality, the updraft wavenumber equals the short-wave cutoff. This provides a bound to the maximum growth rate in the moist problem, which is in agreement with the results of Emanuel et al.

scholarly journals On the Generalized Eigenvalue Problem for the Rossby Wave Vertical Velocity in the Presence of Mean Flow and Topography

2012 ◽  
Vol 42 (6) ◽  
pp. 1045-1050 ◽  
Author(s):  
Rémi Tailleux
Keyword(s):  
Eigenvalue Problem ◽  
Rossby Wave ◽  
Vertical Velocity ◽  
Vertical Structure ◽  
Nonlinear Term ◽  
Eigenvalue Problems ◽  
Equations Of Motion ◽  
Generalized Eigenvalue Problem ◽  
Mean Flow ◽  
Generalized Eigenvalue

Abstract In a series of papers, Killworth and Blundell have proposed to study the effects of a background mean flow and topography on Rossby wave propagation by means of a generalized eigenvalue problem formulated in terms of the vertical velocity, obtained from a linearization of the primitive equations of motion. However, it has been known for a number of years that this eigenvalue problem contains an error, which Killworth was prevented from correcting himself by his unfortunate passing and whose correction is therefore taken up in this note. Here, the author shows in the context of quasigeostrophic (QG) theory that the error can ultimately be traced to the fact that the eigenvalue problem for the vertical velocity is fundamentally a nonlinear one (the eigenvalue appears both in the numerator and denominator), unlike that for the pressure. The reason that this nonlinear term is lacking in the Killworth and Blundell theory comes from neglecting the depth dependence of a depth-dependent term. This nonlinear term is shown on idealized examples to alter significantly the Rossby wave dispersion relation in the high-wavenumber regime but is otherwise irrelevant in the long-wave limit, in which case the eigenvalue problems for the vertical velocity and pressure are both linear. In the general dispersive case, however, one should first solve the generalized eigenvalue problem for the pressure vertical structure and, if needed, diagnose the vertical velocity vertical structure from the latter.

Does Topographic Form Stress Impede Prograde Ocean Currents?

2021 ◽  
Author(s):  
YUE BAI ◽  
YAN WANG ◽  
ANDREW L. STEWART
Keyword(s):  
Wave Propagation ◽  
Rossby Wave ◽  
Rossby Waves ◽  
Bottom Friction ◽  
Stress Generation ◽  
Momentum Balance ◽  
Mean Flow ◽  
Rossby Wave Propagation ◽  
Circumpolar Current ◽  
Current Systems

AbstractTopographic form stress (TFS) plays a central role in constraining the transport of the Antarctic Circumpolar Current (ACC), and thus the rate of exchange between the major ocean basins. Topographic form stress generation in the ACC has been linked to the formation of standing Rossby waves, which occur because the current is retrograde (opposing the direction of Rossby wave propagation). However, it is unclear whether TFS similarly retards current systems that are prograde (in the direction of Rossby wave propagation), which cannot arrest Rossby waves. An isopycnal model is used to investigate the momentum balance of wind-driven prograde and retrograde flows in a zonal channel, with bathymetry consisting of either a single ridge or a continental shelf and slope with a meridional excursion. Consistent with previous studies, retrograde flows are almost entirely impeded by TFS, except in the limit of flat bathymetry, whereas prograde flows are typically impeded by a combination of TFS and bottom friction. A barotropic theory for standing waves shows that bottom friction serves to shift the phase of the standing wave’s pressure field from that of the bathymetry, which is necessary to produce TFS. The mechanism is the same in prograde and retrograde flows, but is most efficient when the mean flow arrests a Rossby wave with a wavelength comparable to that of the bathymetry. The asymmetry between prograde and retrograde momentum balances implies that prograde current systems may be more sensitive to changes in wind forcing, for example associated with climate shifts.

Coupled Interannual Rossby Waves in a Quasigeostrophic Ocean–Atmosphere Model

2007 ◽  
Vol 37 (5) ◽  
pp. 1192-1214 ◽  
Author(s):  
Riccardo Farneti
Keyword(s):  
Wave Propagation ◽  
Rossby Wave ◽  
Rossby Waves ◽  
Phase Relationship ◽  
Phase Speed ◽  
Middle Latitude ◽  
Mean Flow ◽  
Ocean Atmosphere ◽  
Rossby Wave Propagation ◽  
Atmosphere Model

Abstract Rossby wave propagation is investigated in the framework of an idealized middle-latitude quasigeostrophic coupled ocean–atmosphere model. The Rossby waves are observed to propagate faster than both the classical linear theory (unperturbed solution) and the phase speed estimates when the effect of the zonal mean flow is added (perturbed solution). Moreover, using statistical eigentechniques, a clear coupled Rossby wave mode is identified between a baroclinic oceanic Rossby wave and an equivalent barotropic atmospheric wave. The spatial phase relationship of the coupled wave is similar to the one predicted by Goodman and Marshall, suggesting a positive ocean–atmosphere feedback. It is argued that oceanic Rossby waves can be efficiently coupled to the overlying atmosphere and that the atmospheric coupling is capable of adding an extra speedup to the wave; in fact, when the ocean is simply forced, the Rossby wave propagation speed approaches the perturbed solution.

A Climatology of Rossby Wave Breaking on the Southern Hemisphere Tropopause

2011 ◽  
Vol 68 (4) ◽  
pp. 798-811 ◽  
Author(s):  
Thando Ndarana ◽  
Darryn W. Waugh
Keyword(s):  
Southern Hemisphere ◽  
Rossby Wave ◽  
Potential Vorticity ◽  
Seasonal Variations ◽  
Wave Breaking ◽  
Polar Front ◽  
Rossby Wave Breaking ◽  
South Pacific Ocean ◽  
Ocean Region ◽  
Summer Minimum

Abstract A 30-yr climatology of Rossby wave breaking (RWB) on the Southern Hemisphere (SH) tropopause is formed using 30 yr of reanalyses. Composite analysis of potential vorticity and meridional fluxes of wave activity show that RWB in the SH can be divided into two broad categories: anticyclonic and cyclonic events. While there is only weak asymmetry in the meridional direction and most events cannot be classified as equatorward or poleward in terms of the potential vorticity structure, the position and structure of the fluxes associated with equatorward breaking differs from those of poleward breaking. Anticyclonic breaking is more common than cyclonic breaking, except on the lower isentrope examined (320 K). There are marked differences in the seasonal variations of RWB on the two surfaces, with a winter minimum for RWB around 350 K but a summer minimum for RWB around 330 K. These seasonal variations are due to changes in the location of the tropospheric jets and dynamical tropopause. During winter the subtropical jet and tropopause at 350 K are collocated in the Australian–South Pacific Ocean region, resulting in a seasonal minimum in the 350-K RWB. During summer the polar front jet and 330-K tropopause are collocated over the Southern Atlantic and Indian Oceans, inhibiting RWB in this region.

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