Sensitivity of Perturbation Variance and Fluxes in Turbulent Jets to Changes in the Mean Jet

2004 ◽  
Vol 61 (21) ◽  
pp. 2644-2652
Author(s):  
Brian F. Farrell ◽  
Petros J. Ioannou
Keyword(s):  
Stochastic Model ◽  
Storm Track ◽  
Turbulent Jets ◽  
Static Stability ◽  
Structure Change ◽  
Synoptic Scale ◽  
Single Jet ◽  
The Mean ◽  
Arbitrary Change ◽  
Jet Structure

Abstract Synoptic-scale eddy variance and fluxes of heat and momentum in midlatitude jets are sensitive to small changes in mean jet velocity, dissipation, and static stability. In this work the change in the jet producing the greatest increase in variance or flux is determined. Remarkably, a single jet structure change completely characterizes the sensitivity of a chosen quadratic statistical quantity to modification of the mean jet in the sense that an arbitrary change in the jet influences a chosen statistical quantity in proportion to the projection of the change on this single optimal structure. The method used extends previous work in which storm track statistics were obtained using a stochastic model of jet turbulence.

scholarly journals Meteorological Interpretation of Orographic Precipitation Gradients along an Andes West Slope Basin at 30°S (Elqui Valley, Chile)

2017 ◽  
Vol 18 (3) ◽  
pp. 713-727 ◽  
Author(s):  
Lucia Scaff ◽  
Jose A. Rutllant ◽  
David Rahn ◽  
Simon Gascoin ◽  
Roberto Rondanelli
Keyword(s):  
Storm Track ◽  
Coastal Region ◽  
Static Stability ◽  
Reanalysis Data ◽  
Orographic Precipitation ◽  
Synoptic Scale ◽  
Zonal Winds ◽  
The Andes ◽  
Northern Edge ◽  
Cutoff Low

Abstract To better forecast streamflow and water resource availability, it is important to have an understanding of the meteorological drivers of the orographic precipitation gradient (OPG), especially critical in semiarid mountainous areas. Although forced ascent over topography typically results in precipitation increasing with altitude (positive OPGs), mean annual OPGs and especially OPGs associated with individual storms can change widely in magnitude and even sign. Precipitation measurements from the Elqui Valley in the semiarid Andes of Chile (30°S) reveal a mean annual OPG of 6.3 mm km−1 (millimeters of precipitation over kilometers in elevation) ranging from −42 to 52 mm km−1 for individual storms over the last 35 years (1979–2013). Reanalysis data and precipitation measurements are used to characterize the observed OPG in this region in relation with their synoptic-scale flow. It is found that the Froude number correlates positively with the OPG, reflecting stronger zonal winds and less static stability during storms that have positive OPGs. Altitude of the Andes barrier jet shows only a weak relationship with the OPG. Significant storms with positive OPGs are typically linked with an austral blocking of the westerlies and an equatorward migration of the midlatitude storm track. For negative OPGs, either a cutoff low or the northern edge of a surface migratory cyclone reaches the Elqui Valley in such a way that significant rainfall only occurs in the near-coastal region without major snowfall accumulation over the Andes.

The Position of the Midlatitude Storm Track and Eddy-Driven Westerlies in Aquaplanet AGCMs

2010 ◽  
Vol 67 (12) ◽  
pp. 3984-4000 ◽  
Author(s):  
Jian Lu ◽  
Gang Chen ◽  
Dargan M. W. Frierson
Keyword(s):  
Global Warming ◽  
Coming Out ◽  
Storm Track ◽  
Lower Troposphere ◽  
Static Stability ◽  
Hadley Cell ◽  
Eddy Heat Flux ◽  
Circulation Regime ◽  
Wide Range ◽  
Single Jet

Abstract The sensitivity of the midlatitude storm track and eddy-driven wind to the sea surface temperature (SST) boundary forcing is studied over a wide range of perturbations using both simple and comprehensive general circulation models over aquaplanet lower boundary conditions. Under the single-jet circulation regime similar to the conditions of the present climate in the Northern Hemisphere winter or the Southern Hemisphere summer, the eddy-driven jet shifts monotonically poleward with both the global mean and the equator-to-pole gradient of the SST. The eddy-driven jet can have a reverse relationship to the gradient if it is well separated from the subtropical jet and Hadley cell boundary in a double-jet circulation regime. A simple scaling is put forward to interpret the simulated sensitivity of the storm-track/eddy-driven westerly wind position within the single-jet regime in both models. The rationale for the scaling is based on the notion that the wave activity flux can propagate horizontally away from the source region, resulting in a broader distribution of eddy potential vorticity (PV) flux in the upper troposphere than that of the flux in the opposite direction in the lower troposphere. As a consequence, the position of the maximum of the eddy-driven westerlies tends to be controlled by the profile of the relatively sharp-peaked low-level PV flux, which is dominated by the eddy heat flux component of the Eliassen–Palm (EP) flux. Thus, the position of the eddy-driven surface westerlies may be inferred from the vertical EP flux coming out of the lower troposphere. The vertical EP flux can be parameterized by a measure of baroclinicity, whose latitudinal variations show a linear relationship with the meridional displacement of the eddy-driven westerlies and the storm track. This relationship still holds well within the single-jet regime, even when only the variation of static stability is taken into consideration in estimating the baroclinicity (the temperature gradient component of which is fixed). To the extent that the static stability is deterministically constrained by and hence can be predicted from the given SST conditions through a moist scaling for the midlatitude stratification, one may, given SST perturbations, predict which way the storm track and eddy-driven wind should shift with respect to a chosen reference climate state. The resultant anomaly-wise scaling turns out to be valid for both the idealized and comprehensive models, regardless of the details in the model physics. By corollary, it can be argued that the poleward shift of storm track found in the global warming simulations by fully coupled climate models may be attributed, at least partially, to the increase in the subtropical and midlatitude static stability with global warming.

Formation of Jets by Baroclinic Turbulence

2008 ◽  
Vol 65 (11) ◽  
pp. 3353-3375 ◽  
Author(s):  
Brian F. Farrell ◽  
Petros J. Ioannou
Keyword(s):  
Temperature Gradient ◽  
Power Law ◽  
Coupled System ◽  
Static Stability ◽  
Transient Growth ◽  
Stable States ◽  
Thermal Forcing ◽  
Confined Jets ◽  
The Mean ◽  
Jet Structure

Abstract Turbulent fluids are frequently observed to spontaneously self-organize into large spatial-scale jets; geophysical examples of this phenomenon include the Jovian banded winds and the earth’s polar-front jet. These relatively steady large-scale jets arise from and are maintained by the smaller spatial- and temporal-scale turbulence with which they coexist. Frequently these jets are found to be adjusted into marginally stable states that support large transient growth. In this work, a comprehensive theory for the interaction of jets with turbulence, stochastic structural stability theory (SSST), is applied to the two-layer baroclinic model with the object of elucidating the physical mechanism producing and maintaining baroclinic jets, understanding how jet amplitude, structure, and spacing is controlled, understanding the role of parameters such as the temperature gradient and static stability in determining jet structure, understanding the phenomenon of abrupt reorganization of jet structure as a function of parameter change, and understanding the general mechanism by which turbulent jets adjust to marginally stable states supporting large transient growth. When the mean thermal forcing is weak so that the mean jet is stable in the absence of turbulence, jets emerge as an instability of the coupled system consisting of the mean jet dynamics and the ensemble mean eddy dynamics. Destabilization of this SSST coupled system occurs as a critical turbulence level is exceeded. At supercritical turbulence levels the unstable jet grows, at first exponentially, but eventually equilibrates nonlinearly into stable states of mutual adjustment between the mean flow and turbulence. The jet structure, amplitude, and spacing can be inferred from these equilibria. With weak mean thermal forcing and weak but supercritical turbulence levels, the equilibrium jet structure is nearly barotropic. Under strong mean thermal forcing, so that the mean jet is unstable in the absence of turbulence, marginally stable highly nonnormal equilibria emerge that support high transient growth and produce power-law relations between, for example, heat flux and temperature gradient. The origin of this power-law behavior can be traced to the nonnormality of the adjusted states. As the stochastic excitation, mean baroclinic forcing, or the static stability are changed, meridionally confined jets that are in equilibrium at a given meridional wavenumber abruptly reorganize to another meridional wavenumber at critical values of these parameters. The equilibrium jets obtained with this theory are in remarkable agreement with equilibrium jets obtained in simulations of baroclinic turbulence, and the phenomenon of discontinuous reorganization of confined jets has important implications for storm-track reorganization and abrupt climate change.

scholarly journals The Role of Stationary Eddies in Shaping Midlatitude Storm Tracks

2013 ◽  
Vol 70 (8) ◽  
pp. 2596-2613 ◽  
Author(s):  
Yohai Kaspi ◽  
Tapio Schneider
Keyword(s):  
Energy Transport ◽  
Storm Track ◽  
Static Stability ◽  
Surface Heating ◽  
Storm Tracks ◽  
Mean Flow ◽  
Wavelength Scale ◽  
The Mean ◽  
And Control

Abstract Transient and stationary eddies shape the extratropical climate through their transport of heat, moisture, and momentum. In the zonal mean, the transports by transient eddies dominate over those by stationary eddies, but this is not necessarily the case locally. In particular, in storm-track entrance and exit regions during winter, stationary eddies and their interactions with the mean flow dominate the atmospheric energy transport. Here it is shown that stationary eddies can shape storm tracks and control where they terminate by modifying local baroclinicity. Simulations with an idealized aquaplanet GCM show that zonally localized surface heating alone (e.g., ocean heat flux convergence) gives rise to storm tracks, which have a well-defined length scale that is similar to that of Earth's storm tracks. The storm tracks terminate downstream of the surface heating even in the absence of continents, at a distance controlled by the stationary Rossby wavelength scale. Stationary eddies play a dual role: within about half a Rossby wavelength downstream of the heating region, stationary eddy energy fluxes increase the baroclinicity and therefore contribute to energizing the storm track; farther downstream, enhanced poleward and upward energy transport by stationary eddies reduces the baroclinicity by reducing the meridional temperature gradients and enhancing the static stability. Transports both of sensible and latent heat (water vapor) play important roles in determining where storm tracks terminate.

scholarly journals The Climatology of Synoptic-Scale Ascent over Western North America: A Perspective on Storm Tracks

2012 ◽  
Vol 140 (6) ◽  
pp. 1761-1778 ◽  
Author(s):  
Neil P. Lareau ◽  
John D. Horel
Keyword(s):  
United States ◽  
North America ◽  
Storm Track ◽  
Western United States ◽  
Storm Tracks ◽  
Western North America ◽  
Synoptic Scale ◽  
Regional Patterns ◽  
Mean Values ◽  
The Mean

Abstract The position and variability of storm tracks across western North America are examined during the October–April cool seasons spanning 1989–2010. The location and intensity of storms are represented by strong synoptic-scale ascent, which is diagnosed by the alternative balance omega equation applied to ECMWF Re-Analysis Interim data. This dynamically filtered method removes poorly resolved updrafts arising from subsynoptic-scale phenomena such as convection and mountain waves. The resulting vertical motions are illustrated for the case of a strong storm traversing the western United States. Summary statistics of synoptic-scale ascent are compiled over months, seasons, and the entire 21-yr period. Locations exhibiting high mean values of ascent are deemed to represent storm tracks. The climatological-mean storm track exhibits a sinusoidal shape across the eastern Pacific and western North America. The composite evolution of strong storms moving along specific segments of the storm track show regional differences (e.g., storms poleward of 50°N tend to result from progressive low-amplitude troughs progressing through the mean planetary ridge, while storms over the western United States are initiated by digging troughs that temporarily suppress the mean ridge). Seasonal shifts in the storm track are pronounced and exhibit coherent regional patterns. Interannual variations in synoptic-scale ascent indicate meridional shifts in position as well as changes in the degree of amplification within the dominant sinusoidal storm track. These changes in structure are related to the phase of ENSO: El Niño (La Niña) winters favor zonal (amplified) and southern (northern) storm tracks.

The global dynamics of stochastic Holling type II predator-prey models with non constant mortality rate

Filomat ◽  
2017 ◽  
Vol 31 (18) ◽  
pp. 5811-5825
Author(s):  
Xinhong Zhang
Keyword(s):  
Mortality Rate ◽  
Stochastic Model ◽  
Sufficient Conditions ◽  
Positive Periodic Solution ◽  
Global Dynamics ◽  
Type Ii ◽  
Predator Prey ◽  
Persistence In The Mean ◽  
The Mean ◽  
Predator Prey Models

In this paper we study the global dynamics of stochastic predator-prey models with non constant mortality rate and Holling type II response. Concretely, we establish sufficient conditions for the extinction and persistence in the mean of autonomous stochastic model and obtain a critical value between them. Then by constructing appropriate Lyapunov functions, we prove that there is a nontrivial positive periodic solution to the non-autonomous stochastic model. Finally, numerical examples are introduced to illustrate the results developed.

Distribution of the number of alleles in multigene families

1992 ◽  
Vol 29 (04) ◽  
pp. 759-769
Author(s):  
R. C. Griffiths
Keyword(s):  
Stochastic Model ◽  
Gene Conversion ◽  
Lower Bounds ◽  
Multigene Families ◽  
Expected Number ◽  
Allele Type ◽  
The Mean

The distribution of the number of alleles in samples from r chromosomes is studied. The stochastic model used includes gene conversion within chromosomes and mutation at loci on the chromosomes. A method is described for simulating the distribution of alleles and an algorithm given for computing lower bounds for the mean number of alleles. A formula is derived for the expected number of samples from r chromosomes which contain the allele type of a locus chosen at random.

scholarly journals Instability wave models for the near-field fluctuations of turbulent jets

2011 ◽  
Vol 689 ◽  
pp. 97-128 ◽  
Author(s):  
K. Gudmundsson ◽  
Tim Colonius
Keyword(s):  
Flow Field ◽  
Large Scale ◽  
Microphone Array ◽  
Near Field ◽  
Turbulent Jets ◽  
Instability Wave ◽  
Mean Flow ◽  
Velocity Fluctuations ◽  
The Mean ◽  
Scale Structures

AbstractPrevious work has shown that aspects of the evolution of large-scale structures, particularly in forced and transitional mixing layers and jets, can be described by linear and nonlinear stability theories. However, questions persist as to the choice of the basic (steady) flow field to perturb, and the extent to which disturbances in natural (unforced), initially turbulent jets may be modelled with the theory. For unforced jets, identification is made difficult by the lack of a phase reference that would permit a portion of the signal associated with the instability wave to be isolated from other, uncorrelated fluctuations. In this paper, we investigate the extent to which pressure and velocity fluctuations in subsonic, turbulent round jets can be described aslinearperturbations to the mean flow field. The disturbances are expanded about the experimentally measured jet mean flow field, and evolved using linear parabolized stability equations (PSE) that account, in an approximate way, for the weakly non-parallel jet mean flow field. We utilize data from an extensive microphone array that measures pressure fluctuations just outside the jet shear layer to show that, up to an unknown initial disturbance spectrum, the phase, wavelength, and amplitude envelope of convecting wavepackets agree well with PSE solutions at frequencies and azimuthal wavenumbers that can be accurately measured with the array. We next apply the proper orthogonal decomposition to near-field velocity fluctuations measured with particle image velocimetry, and show that the structure of the most energetic modes is also similar to eigenfunctions from the linear theory. Importantly, the amplitudes of the modes inferred from the velocity fluctuations are in reasonable agreement with those identified from the microphone array. The results therefore suggest that, to predict, with reasonable accuracy, the evolution of the largest-scale structures that comprise the most energetic portion of the turbulent spectrum of natural jets, nonlinear effects need only be indirectly accounted for by considering perturbations to the mean turbulent flow field, while neglecting any non-zero frequency disturbance interactions.

scholarly journals Initial-Condition Sensitivities and the Predictability of Downslope Winds

2009 ◽  
Vol 66 (11) ◽  
pp. 3401-3418 ◽  
Author(s):  
Patrick A. Reinecke ◽  
Dale R. Durran
Keyword(s):  
Wave Breaking ◽  
Initial Conditions ◽  
Static Stability ◽  
Synoptic Scale ◽  
Wind Speeds ◽  
Downslope Winds ◽  
First Case ◽  
Downslope Wind ◽  
The Difference ◽  
Strong Winds

Abstract The sensitivity of downslope wind forecasts to small changes in initial conditions is explored by using 70-member ensemble simulations of two prototypical windstorms observed during the Terrain-Induced Rotor Experiment (T-REX). The 10 weakest and 10 strongest ensemble members are composited and compared for each event. In the first case, the 6-h ensemble-mean forecast shows a large-amplitude breaking mountain wave and severe downslope winds. Nevertheless, the forecasts are very sensitive to the initial conditions because the difference in the downslope wind speeds predicted by the strong- and weak-member composites grows to larger than 28 m s−1 over the 6-h forecast. The structure of the synoptic-scale flow one hour prior to the windstorm and during the windstorm is very similar in both the weak- and strong-member composites. Wave breaking is not a significant factor in the second case, in which the strong winds are generated by a layer of high static stability flowing beneath a layer of weaker mid- and upper-tropospheric stability. In this case, the sensitivity to initial conditions is weaker but still significant. The difference in downslope wind speeds between the weak- and strong-member composites grows to 22 m s−1 over 12 h. During and one hour before the windstorm, the synoptic-scale flow exhibits appreciable differences between the strong- and weak-member composites. Although this case appears to be more predictable than the wave-breaking event, neither case suggests that much confidence should be placed in the intensity of downslope winds forecast 12 or more hours in advance.

A stochastic model for polymer degradation

1972 ◽  
Vol 9 (1) ◽  
pp. 43-53 ◽  
Author(s):  
S. K. Srinivasan ◽  
K. M. Mehata
Keyword(s):  
Stochastic Model ◽  
General Model ◽  
Polymer Degradation ◽  
Mean Square ◽  
Product Density ◽  
The Mean ◽  
Number Of Segments

The stochastic model for breaking of molecular segments proposed by Bithell is analysed and some results relating to the distribution of the number of fragments are obtained by using a slightly more general model which allows multiple ruptures. The product density technique is employed to derive the mean and mean square number of segments at any time t and the number of segments with length greater than y at time of production.

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