The Connection between Carnot and CAPE Formulations of TC Potential Intensity

2021 ◽  
pp. 1-45
Keyword(s):  
Climate Model ◽  
Convective Available Potential Energy ◽  
Carnot Cycle ◽  
Moist Static Energy ◽  
Surface Evaporation ◽  
Physical Insight ◽  
The Difference ◽  
Static Energy ◽  
Insight Into ◽  
Multiple Conditions

Abstract Tropical cyclone (TC) potential intensity (PI) theory has a well known form, consistent with a Carnot cycle interpretation of TC energetics, which relates PI to mean environmental conditions: the difference between surface and TC outflow temperatures and the air–sea enthalpy disequilibrium. PI has also been defined as a difference in convective available potential energy (CAPE) between two parcels, and quantitative assessments of future changes make use of a numerical algorithm based on this definition. Here, an analysis shows the conditions under which these Carnot and CAPE-based PI definitions are equivalent. There are multiple conditions, not previously enumerated, which in particular reveal a role for irreversible entropy production from surface evaporation. This mathematical analysis is verified by numerical calculations of PI’s sensitivity to large changes in surface-air relative humidity. To gain physical insight into the connection between the CAPE and Carnot formulations of PI, we use a recently developed analytic theory for CAPE to derive, starting from the CAPE-based definition, a new approximate formula for PI which nearly recovers the previous Carnot PI formula. The derivation shows that the difference in undilute buoyancies of saturated and environmental parcels which determines CAPE PI can in fact be expressed as a difference in the parcels’ surface moist static energy, providing a physical link between the Carnot and CAPE formulations of PI. This combination of analysis and physical interpretation builds confidence in previous numerical CAPE-based PI calculations that use climate model projections of the future tropical environment.

scholarly journals MSE Minus CAPE is the True Conserved Variable for an Adiabatically Lifted Parcel

2015 ◽  
Vol 72 (9) ◽  
pp. 3639-3646 ◽  
Author(s):  
David M. Romps
Keyword(s):  
Potential Energy ◽  
Thermodynamic Equilibrium ◽  
Convective Available Potential Energy ◽  
Potential Temperature ◽  
Equivalent Potential Temperature ◽  
Moist Static Energy ◽  
Neutral Buoyancy ◽  
Equivalent Potential ◽  
Nonhydrostatic Pressure ◽  
Static Energy

Abstract For an adiabatic parcel convecting up or down through the atmosphere, it is often assumed that its moist static energy (MSE) is conserved. Here, it is shown that the true conserved variable for this process is MSE minus convective available potential energy (CAPE) calculated as the integral of buoyancy from the parcel’s height to its level of neutral buoyancy and that this variable is conserved even when accounting for full moist thermodynamics and nonhydrostatic pressure forces. In the calculation of a dry convecting parcel, conservation of MSE minus CAPE gives the same answer as conservation of entropy and potential temperature, while the use of MSE alone can generate large errors. For a moist parcel, entropy and equivalent potential temperature give the same answer as MSE minus CAPE only if the parcel ascends in thermodynamic equilibrium. If the parcel ascends with a nonisothermal mixed-phase stage, these methods can give significantly different answers for the parcel buoyancy because MSE minus CAPE is conserved, while entropy and equivalent potential temperature are not.

scholarly journals A Moisture-Stratiform Instability for Convectively Coupled Waves

2008 ◽  
Vol 65 (3) ◽  
pp. 834-854 ◽  
Author(s):  
Zhiming Kuang
Keyword(s):  
Realistic Model ◽  
Model Parameters ◽  
Convective Heating ◽  
Quasi Equilibrium ◽  
Moist Static Energy ◽  
Instability Mechanism ◽  
Convectively Coupled Waves ◽  
The Difference ◽  
Static Energy ◽  
The Waves

Abstract A simple model of two vertical modes is constructed and analyzed to reveal the basic instability mechanisms of convectively coupled waves. The main novelty of this model is a convective parameterization based on the quasi-equilibrium concept and simplified for a model of two vertical modes. It hypothesizes 1) the approximate invariance of the difference between saturation moist static energy in the lower half of the troposphere and moist static energy in the subcloud layer, regardless of free troposphere humidity, and 2) that variations in the depth of convection are determined by moisture-deficit variations in the midtroposphere. Physical arguments for such a treatment are presented. For realistic model parameters chosen based on cloud system resolving model simulations (CSRMs) of an earlier study, the model produces unstable waves at wavelengths and with structures that compare well with the CSRM simulations and observations. A moisture–stratiform instability and a direct–stratiform instability are identified as the main instability mechanisms in the model. The former relies on the effect of midtroposphere humidity on the depth of convection. The latter relies on the climatological mean convective heating profile being top heavy, and it is identified to be the same as the stratiform instability mechanism proposed by B. E. Mapes. The moisture–stratiform instability appears to be the main instability mechanism for the convectively coupled wave development in the CSRM simulations. The finite response time of convection has a damping effect on the waves that is stronger at high wavenumbers. The net moistening effect of the second-mode convective heating also damps the waves, but more strongly at low wavenumbers. These effects help to shape the growth rate curve so that the most unstable waves are of a few thousand kilometers in scale.

Forced monsoon rainfall changes and the moist static energy budget: the Sahel and elsewhere

2020 ◽  
Author(s):  
Spencer Hill
Keyword(s):  
Global Warming ◽  
Climate Model ◽  
Monsoon Rainfall ◽  
Dominant Factor ◽  
Sahara Desert ◽  
Moist Static Energy ◽  
Model Simulations ◽  
Future Global Warming ◽  
Climate Model Simulations ◽  
Static Energy

<p>The Sahel is the semi-arid, transitional region separating the Sahara Desert from humid equatorial Africa, i.e. the poleward-most region to which appreciable rains from the West African monsoon extend during northern summer.  The severe drought it experienced in the 1970s and 1980s was one of the 20th century's most striking (and devastating) hydroclimatic events worldwide.  In climate model simulations of future global warming, Sahelian rainfall does anything from intense drying to even greater wettening depending on which climate model is used.  In this talk, I present recent research on rainfall in the Sahel using the moist static energy (MSE) budget -- what are the physical factors that drive its variations, and how do we expect them to change as the planet warms --- and the extent to which inferences from the Sahel can or cannot extend to other regions and other external forcings.<br><br>Using climate model simulations both of Earth's present-day conditions and of future global warming, I show that the drying influence of the Sahara Desert is a dominant factor in present-day and that this influence is strengthened with warming due to an increasing difference in moisture between the desert and the Sahel.  This enhancement of an existing moisture (and energy) gradient is a robust response of the atmosphere to mean ocean surface warming and has a firm theoretical basis.  By comparing climate model simulations of the present-day Sahel climate to real-world observations, I argue that this Sahara-driven drying mechanism is overly strong in those models that dry the Sahel most in future simulations.  This response to mean warming of global sea surface temperatures (SSTs) is readily explained using the MSE budget, whereas the Sahel rainfall response to changes in the spatial pattern of SSTs (such as during the 1970s-80s drought) are more easily interpreted via the popular energetic framework for Intertropical Convergence Zone (ITCZ) shifts.  I discuss the interplay between these and other theoretical frameworks for forced monsoon rainfall changes in the Sahel and other monsoon regions and offer ideas for refining and extending those theories.</p>

How Quartet Resonance Might or Might Not Amplify Large Waves Into Freak Waves

2011 ◽  
Author(s):  
Peter Tromans
Keyword(s):  
Spectral Response ◽  
Freak Waves ◽  
Freak Wave ◽  
Ocean Surface Waves ◽  
Surface Method ◽  
Random Seas ◽  
Time Marching ◽  
Physical Insight ◽  
The Difference ◽  
Insight Into

We have developed an approximate solution to Zakharov’s equations for the evolution of ocean surface waves. We have applied it with a spectral response surface method to estimate the probability of exceedance of crest elevation in random seas. The method avoids time-marching and allows probabilities to be estimated on practical time scales. The results indicate that quartet resonance can produce very large amplification of extreme crests in uni-directional seas. However, the effect is very much smaller in spread seas. Although the solution is approximate it provides a great deal of physical insight into the mechanisms by which a freak wave might develop and explains the difference in results between uni-directional and spread seas.

Vibration Analysis of Pipes Supported by a Flexible Tank Wall Considering the Support Clearances

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
M. Utsumi
Keyword(s):  
Stress Reduction ◽  
Tank Wall ◽  
Computationally Efficient ◽  
Element Analysis ◽  
Physical Insight ◽  
The Difference ◽  
Stress Behaviors ◽  
Semianalytical Method ◽  
Clearance Nonlinearity ◽  
Insight Into

The vibration of pipes supported by a flexible tank wall is analyzed taking into account the hydroelastic vibration of the tank and the nonlinearity caused by the support clearances. Because the support clearances increase the pipe displacement, it is important to examine whether the support clearances augment the pipe stress. We illustrate that the support clearances can cause an increase in the pipe stress not only due to the increase in pipe displacement but also to the difference between elastic behaviors of the tank wall and pipes. The tank wall and pipes are dominated by membrane and bending deformations, respectively. Furthermore, we illustrate that the support clearances render a stress reduction method ineffective. In this study, a semi-analytical method is applied, rather than a full finite element analysis. The semianalytical method is helpful not only for computationally efficient analysis but also for gaining physical insight into the clearance-nonlinearity-induced stress behaviors noted above.

Anthropogenic Influences on Tornadic Storms

2021 ◽  
pp. 1-57
Author(s):  
Emily Bercos-Hickey ◽  
Christina M. Patricola ◽  
William A. Gallus
Keyword(s):  
Climate Change ◽  
Climate Models ◽  
Climate Model ◽  
Convective Available Potential Energy ◽  
Future Climate Change ◽  
Storm Events ◽  
Climate Model Simulations ◽  
Tornadic Storms ◽  
The Impact ◽  
Insight Into

AbstractThe impact of climate change on severe storms and tornadoes remains uncertain, largely owing to inconsistencies in observational data and limitations of climate models. We performed ensembles of convection-permitting climate model simulations to examine how three tornadic storms would change if similar events were to occur in pre-industrial and future climates. The choice of events includes winter, nocturnal, and spring tornadic storms to provide insight into how the timing and seasonality of storms may affect their response to climate change. Updraft helicity (UH), convective available potential energy (CAPE), storm relative helicity (SRH), and convective inhibition (CIN) were used to determine the favorability for the three tornadic storm events in the different climate states. We found that from the pre-industrial to present, the potential for tornadic storms decreased in the winter event and increased in the nocturnal and spring events. With future climate change, the potential for tornadic storms increased in the winter and nocturnal events in association with increased CAPE, and decreased in the spring event despite greater CAPE.

Moist static energy solves storm track intensity puzzle for Snowball Earth

2020 ◽  
Author(s):  
Tiffany A Shaw ◽  
Robert J Graham
Keyword(s):  
Heat Flux ◽  
Latent Heat ◽  
Latent Heat Flux ◽  
Climate Model ◽  
Storm Track ◽  
Storm Tracks ◽  
Snowball Earth ◽  
Moist Static Energy ◽  
Energy Gradient ◽  
Static Energy

<p>Modern theories of the midlatitude storm tracks connect their intensity to surface baroclinicity (latitudinal surface temperature gradient). However, simulations show storm tracks were weaker during past cold, icy climates relative to the modern climate even though surface baroclinicity was stronger. We revisit this surface baroclinicity-intensity puzzle for Snowball Earth using simulations across the climate model hierarchy. Here we show the Moist Static Energy framework for storm track intensity solves the puzzle for Snowball Earth. It connects the weaker storm track to the increase of surface albedo, decrease of latent heat flux and decrease of latitudinal surface Moist Static Energy gradient. Weaker intensity can be predicted assuming a surface ice albedo and zero latent heat flux (large Bowen ratio) everywhere in Snowball Earth. The weaker storm track is also consistent with weaker Mean Available Potential Energy (weaker upper-tropospheric baroclinicity), however that cannot be predicted. Overall, the exotic Snowball Earth climate reveals storm track intensity follows the surface Moist Static Energy gradient and not surface baroclinicity. Our insights may help resolve the puzzle in other climates such as the Last Glacial Maximum.</p>

Analytical solution of equations describing slow axonal transport based on the stop-and-go hypothesis

Open Physics ◽  
2011 ◽  
Vol 9 (3) ◽  
Author(s):  
Andrey Kuznetsov
Keyword(s):  
Analytical Solution ◽  
Axonal Transport ◽  
Molecular Motor ◽  
Governing Equations ◽  
Slow Axonal Transport ◽  
Stop And Go ◽  
Solution Of Equations ◽  
Physical Insight ◽  
The Difference ◽  
Insight Into

AbstractThis paper presents an analytical solution for slow axonal transport in an axon. The governing equations for slow axonal transport are based on the stop-and-go hypothesis which assumes that organelles alternate between short periods of rapid movement on microtubules (MTs), short on-track pauses, and prolonged off-track pauses, when they temporarily disengage from MTs. The model includes six kinetic states for organelles: two for off-track organelles (anterograde and retrograde), two for running organelles, and two for pausing organelles. An analytical solution is obtained for a steady-state situation. To obtain the analytical solution, the governing equations are uncoupled by using a perturbation method. The solution is validated by comparing it with a high-accuracy numerical solution. Results are presented for neurofilaments (NFs), which are characterized by small diffusivity, and for tubulin oligomers, which are characterized by large diffusivity. The difference in transport modes between these two types of organelles in a short axon is discussed. A comparison between zero-order and first-order approximations makes it possible to obtain a physical insight into the effects of organelle reversals (when organelles change the type of a molecular motor they are attached to, an anterograde versus retrograde motor).

Observed Long-Term Trends of the Atmospheric Circulation and of Dry and Moist Static Energies

2021 ◽  
Author(s):  
Christian Franzke ◽  
Nili Harnik
Keyword(s):  
Global Warming ◽  
Atmospheric Circulation ◽  
Zonal Wind ◽  
Energy Transport ◽  
Climate Model ◽  
Heat Fluxes ◽  
Specific Humidity ◽  
Storm Tracks ◽  
Moist Static Energy ◽  
Static Energy

<p>The atmospheric circulation response to global warming is an important problem which is theoretically still not well understood. This is a particular problem since climate model simulations provide uncertain, and at times contradictory, projections of future climate. In particular, it is still unclear how a warmer and moister atmosphere will affect the atmospheric circulation and mid-latitude storms. Here we perform a trend analysis of various atmospheric circulation measures and of the budgets of dry and moist static energy transports, which will contribute to our understanding of the role of moisture in circulation changes. Our analysis is based on the JRA-55 reanalysis data covering the period 1958 through 2018 for both winter and summer seasons. We focus our analysis on zonal mean quantities for the full latitudinal circles as well as for the Atlantic and Pacific sectors.</p><p>We find significant trends in zonal wind, eddy kinetic energy, Eady growth rate, diabatic heating rates, and specific humidity. The zonal wind changes appear to be in thermal wind balance. We also find that the increase in specific humidity is intensifying the trend in eddy moist static energy transport when compared with eddy dry static energy transport. Since band-pass filtered eddy moist static energy transports are related to storm tracks this suggests that increasing moisture in the atmosphere is contributing to the intensification and meridional shifts of storm tracks. Furthermore, our results suggest that global warming predominantly enhance heat fluxes and to a lesser extend momentum fluxes.</p>

Reexamining the Moisture Mode Theories of the Madden–Julian Oscillation Based on Observational Analyses

2021 ◽  
Vol 34 (2) ◽  
pp. 839-853
Author(s):  
Feng Hu ◽  
Tim Li ◽  
Jianyun Gao ◽  
Lisheng Hao
Keyword(s):  
Boundary Layer ◽  
Positive Column ◽  
The Other ◽  
Madden Julian Oscillation ◽  
Moist Static Energy ◽  
Maritime Continent ◽  
Budget Analysis ◽  
Moisture Mode ◽  
The Difference ◽  
Static Energy

AbstractTwo existing moisture mode theories of the MJO, one emphasizing boundary layer moisture asymmetry (MA) and the other emphasizing column-integrated moist static energy (MSE) tendency asymmetry (TA), were validated with the diagnosis of observational data during 1979–2012. A total of 2343 MJO days are selected. While all these days show a clear phase leading of the boundary layer moisture, 20% of these days do not show a positive column-integrated MSE tendency in front of MJO convection (non-TA). A further MSE budget analysis indicates that the difference between the non-TA composite and the TA composite lies in the zonal extent of anomalously vertical overturning circulation in front of the MJO convection. A background mean precipitation modulation mechanism is proposed to explain the distinctive circulation responses. Dependent on the MJO location, an anomalous Gill response to the heating is greatly modulated by the seasonal mean and ENSO induced precipitation fields. Despite the negative MSE tendency in front of MJO convection in the non-TA group, the system continues moving eastward due to the effect of the boundary layer moistening, which promotes a convectively unstable stratification ahead of MJO convection. The analysis result suggests that the first type of moisture mode theories, the moisture asymmetry mechanism, appears more robust, particularly over the eastern Maritime Continent and western Pacific.

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