scholarly journals Nonlinear geostrophic adjustment in the presence of a boundary

2002 ◽  
Vol 471 ◽  
pp. 257-283 ◽  
Author(s):  
G. M. REZNIK ◽  
R. GRIMSHAW
Keyword(s):  
Time Scales ◽  
Potential Vorticity ◽  
Total Mass ◽  
Initial Conditions ◽  
Slow Component ◽  
Slow Motion ◽  
Wave Profile ◽  
Kelvin Waves ◽  
Kelvin Wave ◽  
Geostrophic Adjustment

The process of nonlinear geostrophic adjustment in the presence of a boundary (i.e. in a half-plane bounded by a rigid wall) is examined in the framework of a rotating shallow water model, using an asymptotic multiple-time-scale theory based on the assumed smallness of the Rossby number ε. The spatial scale is of the order of the Rossby scale. Different initial states are considered: periodic, ‘step’-like, and localized. In all cases the initial perturbation is split in a unique way into slow and fast components evolving with characteristic time scales f−1 and (εf)−1, respectively. The slow component is not influenced by the fast one, at least for times t [les ] (fε)−1, and remains close to geostrophic balance. The fast component consists mainly of linear inertia–gravity waves rapidly propagating outward from the initial disturbance and Kelvin waves confined near the boundary.The theory provides simple formulae allowing us to construct the initial profile of the Kelvin wave, given arbitrary initial conditions. With increasing time, the Kelvin wave profile gradually distorts due to nonlinear-wave self-interaction, the distortion being described by the equation of a simple wave. The presence of Kelvin waves does not prevent the fast–slow splitting, in spite of the fact that the frequency gap between the Kelvin waves and slow motion is absent. The possibility of such splitting is explained by the special structure of the Kelvin waves in each case considered.The slow motion on time scales t [les ] (εf)−1 is governed by the well-known quasigeostrophic potential vorticity equation for the elevation. The theory provides an algorithm to determine initial slow and fast fields, and the boundary conditions to any order in ε. For the periodic and step-like initial conditions, the slow component behaves in the usual way, conserving mass, energy and enstrophy. In the case of a localized initial disturbance the total mass of the lowest-order slow component is not conserved, and conservation of the total mass is provided by the first-order slow correction and the Kelvin wave.On longer time scales t [les ] (ε2f)−1 the slow motion obeys the so-called modified quasi-geostrophic potential vorticity (QGPV) equation. The theory provides initial and boundary conditions for this equation. This modified equation coincides exactly with the ‘improved’ QGPV equation, derived by Reznik, Zeitlin & Ben Jelloul (2001), in the step-like and localized cases. In the periodic case this equation contains an additional term due to the Kelvin-wave self-interaction, this term depending on the initial Kelvin wave profile.

scholarly journals Geostrophic adjustment in a closed basin with islands

2013 ◽  
Vol 738 ◽  
pp. 358-377 ◽  
Author(s):  
E. R. Johnson ◽  
R. H. J. Grimshaw
Keyword(s):  
Initial Conditions ◽  
Initial Density ◽  
Circular Domain ◽  
Kelvin Wave ◽  
Geostrophic Adjustment ◽  
Homogeneous Fluid ◽  
Initial State ◽  
Linearized Theory ◽  
Baroclinic Modes ◽  
Initial Density Distribution

AbstractWe consider the geostrophic adjustment of a density-stratified fluid in a basin of constant depth on an $f$-plane in the context of linearized theory. For a single vertical mode, the equations are equivalent to those for a linearized shallow-water theory for a homogeneous fluid. Associated with any initial state there is a unique steady geostrophically adjusted component of the flow compatible with the initial conditions. This steady component gives the time average of the flow and is analogous to the adjusted flow in an unbounded domain without islands. The remainder of the response consists of superinertial Poincaré and subinertial Kelvin wave modes and expressions for the energy partition between the modes in arbitrary basins again follow directly from the initial conditions. The solution for an arbitrary initial density distribution released from rest in a circular domain is found in closed form. When the Rossby radius is much smaller than the basin radius, appropriate for the baroclinic modes, the interior adjusted solution is close to that of the initial state, except for small-amplitude trapped Poincaré waves, while Kelvin waves propagate around the boundaries, carrying, without change of form, the deviation of the initial height field from its average.

Potential Vorticity Accumulation Following Atmospheric Kelvin Waves in the Active Convective Region of the MJO

2012 ◽  
Vol 69 (3) ◽  
pp. 908-914 ◽  
Author(s):  
Kyle MacRitchie ◽  
Paul E. Roundy
Keyword(s):  
Potential Vorticity ◽  
Rain Rate ◽  
Diabatic Heating ◽  
Tropical Rainfall Measuring Mission ◽  
Kelvin Waves ◽  
Kelvin Wave ◽  
Total Rainfall ◽  
Cloud Clusters ◽  
Wave Passage ◽  
Active Convection

Abstract Previous works have shown that most of the rainfall embedded within the Madden–Julian oscillation (MJO) occurs in large eastward-moving envelopes of enhanced convection known as super cloud clusters. Many of these superclusters have been identified as convectively coupled Kelvin waves. In this work, a simple composite-averaging technique diagnoses the linear and nonlinear contributions to MJO potential vorticity (PV) structure by convection collocated with Kelvin waves. Results demonstrate that PV is generated coincident with active convection in Kelvin waves, but that this PV remains in the environment after Kelvin wave passage and becomes part of the structure of the MJO. Analysis of the Tropical Rainfall Measuring Mission (TRMM) rainfall suggests that 62% of the total rainfall within the MJO occurs within the active convective phases of the Kelvin waves (88% higher than the rain rate that occurs outside of the Kelvin waves), supporting the hypothesis that diabatic heating in cloud clusters embedded within the Kelvin waves generates this PV.

A generalized mathematical model of geostrophic adjustment and frontogenesis: uniform potential vorticity

2013 ◽  
Vol 736 ◽  
pp. 366-413 ◽  
Author(s):  
Callum J. Shakespeare ◽  
J. R. Taylor
Keyword(s):  
General Solution ◽  
Potential Vorticity ◽  
Large Scale ◽  
Initial Conditions ◽  
Small Strain ◽  
Deformation Field ◽  
Initial Mass ◽  
Mathematical Framework ◽  
Geostrophic Adjustment ◽  
Mass Imbalance

AbstractFronts, or regions with strong horizontal density gradients, are ubiquitous and dynamically important features in the ocean and atmosphere. In the atmosphere, fronts are associated with some of the most severe weather events, while in the ocean, fronts are associated with enhanced turbulence, water mass transformation and biological activity. Here, we examine the dynamics involved in the formation of fronts, or frontogenesis, in detail using a generalized mathematical framework. This extends previous work which has generally revolved around two limiting cases: fronts generated through forcing due to a convergent large-scale flow, and fronts generated spontaneously during the geostrophic adjustment of an initially unbalanced flow. Here, we introduce a new generalized momentum coordinate to simultaneously describe forced and spontaneous frontogenesis. The nonlinear, inviscid, Boussinesq, hydrostatic governing equations for uniform PV flow are solved for arbitrary Rossby and Froude number. The solution is then examined in three distinct cases. Firstly, for a zero potential vorticity (PV) flow bounded by rigid lids, a general solution is derived for the transient response of the fluid to an arbitrary initial mass imbalance and deformation field. The deformation frontogenesis solution of Hoskins & Bretherton (J. Atmos. Sci., vol. 29, 1972, pp. 11–37) and the mass imbalance solution of Blumen (J. Phys. Oceanogr., vol. 30, 2000, pp. 31–39) emerge as two limits of this general solution. Secondly, the problem of geostrophic adjustment of an initial mass imbalance (no deformation field) is considered for uniform PV flow bounded by rigid lids. The general solution is derived, composed of an adjusted state and a transient component describing the propagation of inertia–gravity waves. The criteria for the occurrence of a frontal discontinuity is determined in terms of the Rossby and Froude numbers. The uniform PV solution reduces identically to the zero PV solution of Blumen in the limit of vanishing background stratification. Thirdly, we examine the more general case of uniform PV flow with a deformation field and either balanced or unbalanced initial conditions. In this case the solution is composed of a time-varying mean state – matching the Hoskins & Bretherton solution in the limit of small strain – and an inertia gravity wave field, the dynamics of which are examined in detail. Our analysis provides a unifying framework capable of describing frontal formation and geostrophic adjustment in a wide variety of settings.

scholarly journals A Comparison of Compressible and Anelastic Models of Deep Dry Convection

2008 ◽  
Vol 136 (12) ◽  
pp. 4555-4571 ◽  
Author(s):  
Jonathan W. Smith ◽  
Peter R. Bannon
Keyword(s):  
Potential Vorticity ◽  
Acoustic Waves ◽  
Initial Conditions ◽  
Lamb Waves ◽  
Geostrophic Adjustment ◽  
Buoyancy Flow ◽  
Upper Level ◽  
Sponge Layer ◽  
Vertically Propagating ◽  
Dry Convection

Abstract The response to an instantaneous diabatic warming and the resulting hydrostatic and geostrophic adjustment in compressible and anelastic models is examined. The comparison of the models includes examining the initial conditions, time evolution, potential vorticity, and both the traditional and available energetics. Between the two models, the buoyancy flow fields and potential vorticity perturbations are qualitatively and quantitatively similar. Traditional and available energetics can both be accurately conserved within the models. There are some short-lived (e.g., several minutes) differences in the model solutions as the compressible model undergoes an acoustic adjustment that contains vertically propagating acoustic waves and horizontally propagating Lamb waves. The acoustic waves are effectively eliminated in an upper-level numerical sponge layer using Rayleigh damping. Moreover, the relative computational efficiency and accuracy of the two models are assessed.

scholarly journals The Roles of Intraseasonal Kelvin Waves and Tropical Instability Waves in SST Variability along the Equatorial Pacific in an Isopycnal Ocean Model

2009 ◽  
Vol 22 (12) ◽  
pp. 3470-3487 ◽  
Author(s):  
Chuan Li Jiang ◽  
Lu Anne Thompson ◽  
Kathryn A. Kelly ◽  
Meghan F. Cronin
Keyword(s):  
Time Scales ◽  
Ocean Model ◽  
Kelvin Waves ◽  
Eastern Pacific ◽  
Kelvin Wave ◽  
Central Pacific ◽  
Instability Waves ◽  
Tropical Instability Waves ◽  
Zonal Advection ◽  
Sst Anomalies

Abstract The roles of intraseasonal Kelvin waves and tropical instability waves (TIWs) in the intraseasonal and low-frequency mixed-layer temperature budget were examined in an isopycnal ocean model forced by QuikSCAT winds from 2000 to 2004. Correlations between temperature tendency and other terms of the intraseasonal budget compare well with previous results using Tropical Atmosphere Ocean (TAO) observations: the net heat flux has the largest correlation in the western Pacific and zonal advection has the largest correlation in the central Pacific. In the central Pacific, the intraseasonal variations in zonal advection were due to both the zonal background velocity acting on the Kelvin wave temperature anomaly and the Kelvin wave’s anomalous velocity acting on the background temperature. In the eastern Pacific, three of the four temperature budget terms have comparable correlations. In particular, the vertical processes acting on the shallow thermocline cause large SST anomalies in phase with the intraseasonal thermocline anomalies. On intraseasonal time scales, the influence of individual composite upwelling and downwelling Kelvin waves cancel each other. However, because the intraseasonal SST anomalies increase to the east, a zonal gradient of SST is generated that is in phase with intraseasonal zonal velocity. Consequently, heat advection by the Kelvin waves rectifies into lower frequencies in the eastern Pacific. Rectification resulting from TIWs was also seen. The prevalence of intraseasonal Kelvin waves and the zonal structure of intraseasonal SST from 2002 to early 2004 suggested that they might be important in setting the eastern Pacific SST on interannual time scales.

scholarly journals Kelvin wave hydraulic control induced by interactions between vortices and topography

2011 ◽  
Vol 687 ◽  
pp. 194-208 ◽  
Author(s):  
Andrew McC. Hogg ◽  
William K. Dewar ◽  
Pavel Berloff ◽  
Marshall L. Ward
Keyword(s):  
Shallow Water ◽  
Analytical Solutions ◽  
Critical Condition ◽  
Numerical Models ◽  
Kelvin Waves ◽  
Water Model ◽  
Hydraulic Jumps ◽  
Hydraulic Control ◽  
Kelvin Wave ◽  
Shallow Water Model

AbstractThe interaction of a dipolar vortex with topography is examined using a combination of analytical solutions and idealized numerical models. It is shown that an anticyclonic vortex may generate along-topography flow with sufficient speeds to excite hydraulic control with respect to local Kelvin waves. A critical condition for Kelvin wave hydraulic control is found for the simplest case of a 1.5-layer shallow water model. It is proposed that in the continuously stratified case this mechanism may allow an interaction between low mode vortices and higher mode Kelvin waves, thereby generating rapidly converging isopycnals and hydraulic jumps. Thus, Kelvin wave hydraulic control may contribute to the flux of energy from mesoscale to smaller, unbalanced, scales of motion in the ocean.

scholarly journals PNA Predictability at Various Time Scales

2013 ◽  
Vol 26 (22) ◽  
pp. 9090-9114 ◽  
Author(s):  
Waqar Younas ◽  
Youmin Tang
Keyword(s):  
Time Scales ◽  
Initial Conditions ◽  
Prediction Skill ◽  
Multiple Model ◽  
Coupled Models ◽  
Potential Predictability ◽  
Effective Measure ◽  
Dispersion Component ◽  
Significant Difference ◽  
Better Than

Abstract In this study, the predictability of the Pacific–North American (PNA) pattern is evaluated on time scales from days to months using state-of-the-art dynamical multiple-model ensembles including the Canadian Historical Forecast Project (HFP2) ensemble, the Development of a European Multimodel Ensemble System for Seasonal-to-Interannual Prediction (DEMETER) ensemble, and the Ensemble-Based Predictions of Climate Changes and their Impacts (ENSEMBLES). Some interesting findings in this study include (i) multiple-model ensemble (MME) skill was better than most of the individual models; (ii) both actual prediction skill and potential predictability increased as the averaging time scale increased from days to months; (iii) there is no significant difference in actual skill between coupled and uncoupled models, in contrast with the potential predictability where coupled models performed better than uncoupled models; (iv) relative entropy (REA) is an effective measure in characterizing the potential predictability of individual prediction, whereas the mutual information (MI) is a reliable indicator of overall prediction skill; and (v) compared with conventional potential predictability measures of the signal-to-noise ratio, the MI-based measures characterized more potential predictability when the ensemble spread varied over initial conditions. Further analysis found that the signal component dominated the dispersion component in REA for PNA potential predictability from days to seasons. Also, the PNA predictability is highly related to the signal of the tropical sea surface temperature (SST), and SST–PNA correlation patterns resemble the typical ENSO structure, suggesting that ENSO is the main source of PNA seasonal predictability. The predictable component analysis (PrCA) of atmospheric variability further confirmed the above conclusion; that is, PNA is one of the most predictable patterns in the climate variability over the Northern Hemisphere, which originates mainly from the ENSO forcing.

scholarly journals Convectively Coupled Kelvin Waves: From Linear Theory to Global Models

2015 ◽  
Vol 73 (1) ◽  
pp. 407-428 ◽  
Author(s):  
Michael J. Herman ◽  
Zeljka Fuchs ◽  
David J. Raymond ◽  
Peter Bechtold
Keyword(s):  
Composite Structures ◽  
Large Scale ◽  
Kelvin Waves ◽  
Radiosonde Data ◽  
3D Analysis ◽  
Kelvin Wave ◽  
Scale Characteristics ◽  
Precipitation Anomalies ◽  
Convective Inhibition ◽  
Ecmwf Model

Abstract The authors analyze composite structures of tropical convectively coupled Kelvin waves (CCKWs) in terms of the theory of Raymond and Fuchs using radiosonde data, 3D analysis and reanalysis model output, and annual integrations with the ECMWF model on the full planet and on an aquaplanet. Precipitation anomalies are estimated using the NOAA interpolated OLR and TRMM 3B42 datasets, as well as using model OLR and rainfall diagnostics. Derived variables from these datasets are used to examine assumptions of the theory. Large-scale characteristics of wave phenomena are robust in all datasets and models where Kelvin wave variance is large. Indices from the theory representing column moisture and convective inhibition are also robust. The results suggest that the CCKW is highly dependent on convective inhibition, while column moisture does not play an important role.

scholarly journals Secular evolution of close-in planets: the effects of general relativity

2020 ◽  
Vol 493 (1) ◽  
pp. 427-436
Author(s):  
F Marzari ◽  
M Nagasawa
Keyword(s):  
General Relativity ◽  
Numerical Integration ◽  
Time Scales ◽  
Initial Conditions ◽  
Outer Planet ◽  
Secular Perturbations ◽  
Secular Evolution ◽  
Eccentric Orbits ◽  
Wide Range ◽  
Comparable Time

ABSTRACT Pairs of planets in a system may end up close to their host star on eccentric orbits as a consequence of planet–planet scattering, Kozai, or secular migration. In this scenario, general relativity and secular perturbations have comparable time-scales and may interfere with each other with relevant effects on the eccentricity and pericenter evolution of the two planets. We explore, both analytically and via numerical integration, how the secular evolution is changed by general relativity for a wide range of different initial conditions. We find that when the faster secular frequency approaches the general relativity precession rate, which typically occurs when the outer planet moves away from the inner one, it relaxes to it and a significant damping of the proper eccentricity of the inner planet occurs. The proper eccentricity of the outer planet is reduced as well due to the changes in the secular interaction of the bodies. The lowering of the peak eccentricities of the two planets during their secular evolution has important implications on their stability. A significant number of two-planet systems, otherwise chaotic because of the mutual secular perturbations, are found stable when general relativity is included.

scholarly journals Tropical temperature variability and Kelvin-wave activity in the UTLS from GPS RO measurements

2017 ◽  
Vol 17 (2) ◽  
pp. 793-806 ◽  
Author(s):  
Barbara Scherllin-Pirscher ◽  
William J. Randel ◽  
Joowan Kim
Keyword(s):  
Large Scale ◽  
Deep Convection ◽  
Wave Activity ◽  
Kelvin Waves ◽  
Temperature Variability ◽  
Stationary Waves ◽  
Kelvin Wave ◽  
Quasi Biennial Oscillation ◽  
Tropical Tropopause ◽  
Tropopause Region

Abstract. Tropical temperature variability over 10–30 km and associated Kelvin-wave activity are investigated using GPS radio occultation (RO) data from January 2002 to December 2014. RO data are a powerful tool for quantifying tropical temperature oscillations with short vertical wavelengths due to their high vertical resolution and high accuracy and precision. Gridded temperatures from GPS RO show the strongest variability in the tropical tropopause region (on average 3 K2). Large-scale zonal variability is dominated by transient sub-seasonal waves (2 K2), and about half of sub-seasonal variance is explained by eastward-traveling Kelvin waves with periods of 4 to 30 days (1 K2). Quasi-stationary waves associated with the annual cycle and interannual variability contribute about a third (1 K2) to total resolved zonal variance. Sub-seasonal waves, including Kelvin waves, are highly transient in time. Above 20 km, Kelvin waves are strongly modulated by the quasi-biennial oscillation (QBO) in stratospheric zonal winds, with enhanced wave activity during the westerly shear phase of the QBO. In the tropical tropopause region, however, peaks of Kelvin-wave activity are irregularly distributed in time. Several peaks coincide with maxima of zonal variance in tropospheric deep convection, but other episodes are not evidently related. Further investigations of convective forcing and atmospheric background conditions are needed to better understand variability near the tropopause.

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