scholarly journals Modal Decay in the Australia–Antarctic Basin

2009 ◽  
Vol 39 (11) ◽  
pp. 2893-2909 ◽  
Author(s):  
Wilbert Weijer ◽  
Sarah T. Gille ◽  
Frédéric Vivier
Keyword(s):  
Potential Vorticity ◽  
Time Scale ◽  
Eddy Viscosity ◽  
Intraseasonal Variability ◽  
Normal Modes ◽  
Altimeter Data ◽  
Rapid Decay ◽  
Orthogonal Function ◽  
Southeast Indian Ridge ◽  
Flow Components

Abstract The barotropic intraseasonal variability in the Australia–Antarctic Basin (AAB) is studied in terms of the excitation and decay of topographically trapped barotropic modes. The main objective is to reconcile two widely differing estimates of the decay rate of sea surface height (SSH) anomalies in the AAB that are assumed to be related to barotropic modes. First, an empirical orthogonal function (EOF) analysis is applied to almost 15 years of altimeter data. The analysis suggests that several modes are involved in the variability of the AAB, each related to distinct areas with (almost) closed contours of potential vorticity. Second, the dominant normal modes of the AAB are determined in a barotropic shallow-water (SW) model. These stationary modes are confined by the closed contours of potential vorticity that surround the eastern AAB, and the crest of the Southeast Indian Ridge. For reasonable values of horizontal eddy viscosity and bottom friction, their decay time scale is on the order of several weeks. Third, the SW model is forced with realistic winds and integrated for several years. Projection of the modal velocity patterns onto the output fields shows that the barotropic modes are indeed excited in the model, and that they decay slowly on the frictional 𝒪(3 weeks) time scale. However, the SSH anomalies in the modal areas display rapid 𝒪(4 days) decay. Additional analysis shows that this rapid decay reflects the adjustment of unbalanced flow components through the emission of Rossby waves. Resonant excitation of the dominant free modes accounts for about 20% of the SSH variability in the forced-model run. Other mechanisms are suggested to explain the region of high SSH variability in the AAB.

scholarly journals The Tidally Averaged Momentum Balance in a Partially and Periodically Stratified Estuary

2010 ◽  
Vol 40 (11) ◽  
pp. 2418-2434 ◽  
Author(s):  
Mark T. Stacey ◽  
Matthew L. Brennan ◽  
Jon R. Burau ◽  
Stephen G. Monismith
Keyword(s):  
Water Column ◽  
Time Scale ◽  
Eddy Viscosity ◽  
Momentum Equation ◽  
Momentum Balance ◽  
Exchange Flow ◽  
Bed Stress ◽  
Turbulent Momentum ◽  
Stratified Estuary ◽  
Estuarine Exchange

Abstract Observations of turbulent stresses and mean velocities over an entire spring–neap cycle are used to evaluate the dynamics of tidally averaged flows in a partially stratified estuarine channel. In a depth-averaged sense, the net flow in this channel is up estuary due to interaction of tidal forcing with the geometry of the larger basin. The depth-variable tidally averaged flow has the form of an estuarine exchange flow (downstream at the surface, upstream at depth) and varies in response to the neap–spring transition. The weakening of the tidally averaged exchange during the spring tides appears to be a result of decreased stratification on the tidal time scale rather than changes in bed stress. The dynamics of the estuarine exchange flow are defined by a balance between the vertical divergence of the tidally averaged turbulent stress and the tidally averaged pressure gradient in the lower water column. In the upper water column, tidal stresses are important contributors, particularly during the neap tides. The usefulness of an effective eddy viscosity in the tidally averaged momentum equation is explored, and it is seen that the effective eddy viscosity on the subtidal time scale would need to be negative to close the momentum balance. This is due to the dominant contribution of tidally varying turbulent momentum fluxes, which have no specific relation to the subtidal circulation. Using a water column model, the validity of an effective eddy viscosity is explored; for periodically stratified water columns, a negative effective viscosity is required.

The effect of fast-time-scale turbulence on magnetohydrodynamical behaviour

1984 ◽  
Vol 31 (1) ◽  
pp. 81-92 ◽  
Author(s):  
R. O. Dendy ◽  
D. Ter Haar
Keyword(s):  
Time Scale ◽  
Normal Modes ◽  
Dispersion Relations ◽  
Magnetized Plasma ◽  
Fast Time ◽  
Fast Time Scale ◽  
Scale Turbulence ◽  
The Ideal

We show what corrections have to be made to the equations of ideal magneto-hydrodynamics when there is fast-time-scale turbulence present in a magnetized plasma. We show how the dispersion relations for the ideal Alfvén and magnetoacoustic MHD normal modes are modified when such turbulence is present. Finally, we discuss the relation of our work to that of other authors.

Thermoacoustic interplay between intrinsic thermoacoustic and acoustic modes: non-normality and high sensitivities

2019 ◽  
Vol 878 ◽  
pp. 190-220 ◽  
Author(s):  
Francesca M. Sogaro ◽  
Peter J. Schmid ◽  
Aimee S. Morgans
Keyword(s):  
Time Domain ◽  
Time Scale ◽  
Initial Conditions ◽  
Normal Modes ◽  
Time Domain Analysis ◽  
Normal Behaviour ◽  
Optimal Perturbation ◽  
Acoustic Modes ◽  
Energy Growth ◽  
The Time Domain

This study analyses the interplay between classical acoustic modes and intrinsic thermoacoustic (ITA) modes in a simple thermoacoustic system. The analysis is performed using a frequency-domain low-order network model as well as a time-domain spatially discretised model. Anti-correlated modal sensitivities are found to arise due to a pairwise interplay between acoustic and ITA modes. The magnitude of the sensitivities increases as the interplay between the modes grows stronger. The results show a global behaviour of the modes linked to the presence of exceptional points in the spectrum. The time-domain analysis results in a delay-differential equation and allows the investigation of non-normal behaviour and its consequences. Pseudospectral analysis reveals that energy amplification is crucially linked to an interplay between acoustic and ITA modes. While higher non-orthogonality between two modes is correlated with peaks in modal sensitivity, transient energy growth does not necessarily involve the most sensitive modes. In particular, growth estimates based on the Kreiss constant demonstrate that transient amplification relies critically on the proximity of the non-normal modes to the imaginary axis. The time scale for transient amplification is identified as the flame time delay, which is further corroborated by determining the optimal initial conditions responsible for the bulk of the non-modal energy growth. The flame is identified as an active and dominant contributor to energy gain. The frequency of the optimal perturbation matches the acoustic time scale, once more confirming an interplay between acoustic and ITA structures. Flame-based amplification factors of two to five are found, which are significant when feeding into the acoustic dynamics and eventually triggering nonlinear limit-cycle behaviour.

scholarly journals Geodesic stability and quasi normal modes via Lyapunov exponent for Hayward black hole

2020 ◽  
Vol 35 (30) ◽  
pp. 2050249
Author(s):  
Monimala Mondal ◽  
Parthapratim Pradhan ◽  
Farook Rahaman ◽  
Indrani Karar
Keyword(s):  
Black Hole ◽  
Lyapunov Exponent ◽  
Time Scale ◽  
Proper Time ◽  
Normal Modes ◽  
Schwarzschild Black Hole ◽  
Coordinate Time ◽  
Stability And Instability ◽  
The Stability ◽  
Asymptotic Observers

We derive proper time Lyapunov exponent [Formula: see text] and coordinate time Lyapunov exponent [Formula: see text] for a regular Hayward class of black hole. The proper time corresponds to [Formula: see text] and the coordinate time corresponds to [Formula: see text], where [Formula: see text] is measured by the asymptotic observers both for Hayward black hole and for special case of Schwarzschild black hole. We compute their ratio as [Formula: see text] for time-like geodesics. In the limit of [Formula: see text] that means for Schwarzschild black hole this ratio reduces to [Formula: see text]. Using Lyapunov exponent, we investigate the stability and instability of equatorial circular geodesics. By evaluating the Lyapunov exponent, which is the inverse of the instability time scale, we show that, in the eikonal limit, the real and imaginary parts of quasi-normal modes (QNMs) is specified by the frequency and instability time scale of the null circular geodesics. Furthermore, we discuss the unstable photon sphere and radius of shadow for this class of black hole.

Laboratory and numerical studies of baroclinic waves in an internally heated rotating fluid annulus: a case of wave/vortex duality?

1997 ◽  
Vol 337 ◽  
pp. 155-191 ◽  
Author(s):  
P. L. READ ◽  
S. R. LEWIS ◽  
R. HIDE
Keyword(s):  
Numerical Simulations ◽  
Potential Vorticity ◽  
Axisymmetric Flow ◽  
Zonal Flow ◽  
Chaotic Advection ◽  
Rotating Fluid ◽  
Mean Flow ◽  
Baroclinic Waves ◽  
Vortex Merging ◽  
Flow Components

The structure, transport properties and regimes of flow exhibited in a rotating fluid annulus, subject to internal heating and sidewall cooling, are studied both in the laboratory and in numerical simulations. The performance of the numerical model is verified quantitatively to within a few per cent in several cases by direct comparison with measurements in the laboratory of temperature and horizontal velocity fields in the axisymmetric and regular wave regimes. The basic azimuthal mean flow produced by this distribution of heat sources and sinks leads to strips of potential vorticity in which the radial gradient of potential vorticity changes sign in both the vertical and horizontal directions. From diagnosis of the energy budget of numerical simulations, the principal instability of the flow is shown to be predominantly baroclinic in nature, though with a non-negligible contribution towards the maintenance of the non-axisymmetric flow components from the barotropic wave–zonal flow interaction. The structure of the regime diagram for the internally heated baroclinic waves is shown to have some aspects in common with conventional wall-heated annulus waves, but the former shows no evidence for time-dependence in the form of ‘amplitude vacillation’. Internally heated flows instead evidently prefer to make transitions between wavenumbers in the regular regime via a form of vortex merging and/or splitting, indicating a mixed vortex/wave character to the non-axisymmetric flows in this system. The transition towards irregular flow occurs via a form of wavenumber vacillation, also involving vortex splitting and merging events. Baroclinic eddies are shown to develop from an initial axisymmetric flow via a mixed sinuous/varicose instability, leading to the formation of detached vortices of the same sign as the ambient axisymmetric potential vorticity at that level, in a manner which resembles recent simulations of atmospheric baroclinic frontal instability and varicose barotropic instabilities. Dye tracer experiments confirm the mixed wave/vortex character of the equilibrated instabilities, and exhibit chaotic advection in time-dependent flows.

scholarly journals Features of Intraseasonal Variability Observed in the Upper-Layer Current in the Northern South China Sea

2021 ◽  
Vol 8 ◽  
Author(s):  
Wen Xu ◽  
Yeqiang Shu ◽  
Dongxiao Wang ◽  
Ju Chen ◽  
Jinghong Wang ◽  
...  
Keyword(s):  
South China Sea ◽  
South China ◽  
Northern South China Sea ◽  
Intraseasonal Variability ◽  
Mesoscale Eddy ◽  
Luzon Strait ◽  
Altimeter Data ◽  
China Sea ◽  
Spatial Differences ◽  
Long Time

This study reveals the features of the strong intraseasonal variability (ISV) of the upper-layer current in the northern South China Sea (NSCS) based on four long-time mooring observations and altimeter data. The ISV of the upper-layer current in the NSCS consists of two dominant periods of 10–65 days and 65–110 days. The ISV with period of 10–65 days is much strong in the Luzon Strait and decays rapidly westward along the slope. The ISV with the period of 65–110 days is relatively strong along the slope with two high cores at 115 and 119°E, whereas it is weak in the Luzon Strait. The 10–65-day ISV can propagate directly from the western Pacific into the NSCS for most of the time. However, due to its long wavelength, the 65–110-day ISV propagates into the NSCS indirectly, possibly similar to the wave diffraction phenomenon. The spatial differences between the two main frequency bands are primarily due to the baroclinic and barotropic instabilities. The spatial distribution of the upper-layer ISV is closely associated with the mesoscale eddy radius of the NSCS. The eddy radius is directly proportional to the strength of 65–110-day ISV, but it is inversely proportional to the strength of 10–65-day ISV.

scholarly journals A Realizable Version of the k-w Turbulence Model

2017 ◽  
Vol 4 (1) ◽  
pp. 1
Author(s):  
Uriel Goldberg
Keyword(s):  
Turbulence Model ◽  
Time Scale ◽  
Eddy Viscosity ◽  
Normal Strain ◽  
Strain Gradients ◽  
Predictive Quality ◽  
Major Disadvantage ◽  
Large Eddy ◽  
Impinging Flows ◽  
Near Wall

This paper describes improvements in predictive quality to the original Wilcox k-ω turbulence model. A major disadvantage in the near-wall formulation of this model is usage of the large eddy inverse time-scale, ω ~ ε/k, even though small, dissipative eddies popular the immediate vicinity of walls. The present work suggests a correction to this problemthrough a realizable constraint introduced by the Kolmogorov time-scale. A second realizability constraint, the Schwarz condition, limits eddy viscosity magnitude in flow zones involving large normal strain gradients. Several examples demonstrate the improvements enabled due to these corrections, particularly in transonic and impinging flows where significant normal strain gradients occur.

Sign in / Sign up

Export Citation Format

Share Document