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NASA NTRS1997

Hydrodynamic Instability in an Extended Landau/Levich Model of Liquid-Propellant Combustion at Normal and Reduced Gravity

The classical Landau/Levich models of liquid-propellant combustion, despite their relative simplicity, serve as seminal examples that correctly describe the onset of hydrodynamic instability in reactive systems. Recently, these two separate models have been combined and extended to account for a dynamic dependence, absent in the original formulations, of the local burning rate on the local pressure and temperature fields. The resulting model admits an extremely rich variety of both hydrodynamic and reactive/diffusive instabilities that can be analyzed either numerically or analytically in various limiting parameter regimes. In the present work, a formal asymptotic analysis, based on the realistic smallness of the gas-to-liquid density ratio, is developed to investigate the combined effects of gravity and other parameters on the hydrodynamic instability of the propagating liquid/gas interface. In particular, an analytical expression is derived for the neutral stability boundary A(p)(k), where A(p) is the pressure sensitivity of the burning rate and k is the wavenumber of the disturbance. The results demonstrate explicitly the stabilizing effect of gravity on long-wave disturbances, the stabilizing effect of viscosity (both liquid and gas) and surface tension on short-wave perturbations, and the instability associated with intermediate wavenumbers for negative values of A(p). In the limiting case of weak gravity, it is shown that hydrodynamic instability in liquid-propellant combustion is a long-wave instability phenomenon, whereas at normal gravity, this instability is first manifested through O(1) wavenumber disturbances. it is also demonstrated that, in general, surface tension and the viscosity of both the liquid and gas phases each produce comparable stabilizing effects in the long-wavenumber regime, thereby providing important modifications to previous analyses in which one or more of these effects were neglected.

Margolis, S. B.↗

NASA NTRS1998

Hydrodynamic Instability in an Extended Landau/Levich Model of Liquid-Propellant Combustion at Normal and Reduced Gravity

The classical Landau/Levich models of liquid-propellant combustion, despite their relative simplicity, serve as seminal examples that correctly describe the onset of hydrodynamic instability in reactive systems. Recently, these two separate models have been combined and extended to account for a dynamic dependence, absent in the original formulations, of the local burning rate on the local pressure and temperature fields. The resulting model admits an extremely rich variety of both hydrodynamic and reactive/diffusive instabilities that can be analyzed either numerically or analytically in various limiting parameter regimes. In the present work, a formal asymptotic analysis, based on the realistic smallness of the gas-to-liquid density ratio, is developed to investigate the combined effects of gravity and other parameters on the hydrodynamic instability of the propagating liquid/gas interface. In particular, an analytical expression is derived for the neutral stability boundary A(sub p)(k), where A(sub p) is the pressure sensitivity of the burning rate and k is the wavenumber of the disturbance. The results demonstrate explicitly the stabilizing effect of gravity on long-wave disturbances, the stabilizing effect of viscosity (both liquid and gas) and surface tension on short-wave perturbations, and the instability associated with intermediate wavenumbers for critical negative values of A(sub p). In the limiting case of weak gravity, it is shown that hydrodynamic instability in liquid-propellant combustion is a long-wave instability phenomenon, whereas at normal gravity, this instability is first manifested through O(1) wavenumber disturbances. It is also demonstrated that, in general, surface tension and the viscosity of both the liquid and gas phases each produce comparable stabilizing effects in the large-wavenumber regime, thereby providing important modifications to previous analyses in which one or more of these effects were neglected.

Margolis, Stephen B.↗

NASA NTRS2022

Nonlinear Evolution of Instabilities in a Laminar Separation Bubble at a Hypersonic Mach Number

The development of both convective stationary perturbation as well as global instabilities in the vicinity of a laminar separation bubble above an axisymmetric compression corner in a hypersonic flow is investigated using numerical simulations. The flow configuration of primary interest corresponds to the cone-cylinder-flare model used in experimental measurements in the Boeing/AFOSR Mach-6 Quiet Tunnel at Purdue University. For a flare angle of 10 degrees and a unit Reynolds number of 11.5 x 10 6 m -1 , their surface flow visualizations identified the presence of streamwise elongated thermal streaks near the reattachment position and the dominant azimuthal spacing between the streaks was determined to be approximately 10 degrees (i.e., an azimuthal mode number of 36). Previous linear stability analyses predicted that the amplification characteristics of small amplitude, unsteady, convective instabilities within this flow were consistent with the surface pressure fluctuations measured in the experiment. However, their accompanying analysis of global instabilities had found the separation bubble to be weakly unstable at the 10 degrees flare angle, with the most unstable global mode corresponding to a stationary disturbance with an azimuthal wavenumber of m ≈ 5, which was well below the measured wavenumber of m = 36. Besides confirming the presence of the global instability at these flow conditions, the present numerical simulations quantify the details of the stationary equilibrium state associated with the supercritical bifurcation resulting from the nonlinear saturation of the unstable global mode. Although velocity perturbations associated with the saturated global mode are dominated by the fundamental spanwise wavelength associated with the linear global instability, the surface heat flux downstream of reattachment is dominated by m = 36 in agreement with experimental measurements. However, the shorter wavelength peak ( m = 36) in the azimuthal spectrum is not manifested as streaks with an azimuthal spacing of 10 degrees. An additional simulation of the combined evolution of both unsteady convective and global instabilities indicates that the nonlinear interactions between a broadband spectrum of oblique Mack’s first mode instabilities generate stationary vortex modes with a higher dominant wavenumber ( m = 60) as that observed in the experiments. Additional analyses are performed to predict the global mode behavior at other flare angles and how it differs from the convective centrifugal instability due to concave streamline curvature over the compression corner.

Hypersonic flow↗

NASA NTRS2022

Nonlinear Evolution of Instability in a Laminar Separation Bubble at Hypersonic Mach Number

High speed flow↗

NASA NTRS2011

Spatial Distribution of Volcanic Hotspots and Paterae on Io: Implications for Tidal Heating Models and Magmatic Pathways

Io, the innermost of Jupiter's Galilean satellites, is the most volcanically active body in the Solar. System. Io's global mean heat flow is approximately 2 W/square m, which is approximately 20 times larger than on Earth. High surface temperatures concentrate within "hotspots" and, to date, 172 Ionian hotspots have been identified by spacecraft and Earth-based telescopes. The Laplace resonance between Io, Europa, and Ganymede maintains these satellites in noncircular orbits and causes displacement of their tidal bulges as the overhead position of Jupiter changes for each moon. Gravitational interactions between Jupiter and Io dominate the orbital evolution of the Laplacian system and generate enormous heat within to as tidal energy is dissipated. If this energy were transferred out of Io at the same rate as it is generated, then the associated surface heat flux would be 2.24 +/- 0.45 W/square m. This estimate is in good agreement with observed global heat flow, but to better constrain tidal dissipation mechanisms and infer how thermal energy is transferred to Io's surface, it is critical to closely examine the spatial distribution of volcanic features. End-member tidal dissipation models either consider that heating occurs completely in the mantle, or completely in the asthenosphere. Mixed models typically favor one-third mantle and two-thirds asthenosphere heating. Recent models also consider the effects of mantle-asthenosphere boundary permeability and asthenospheric instabilities. Deep-mantle heating models predict maximum surface heat flux near the poles, whereas asthenosphere heating models predict maxima near the equator-particularly in the Sub-Jovian and Anti-Jovian hemispheres, with smaller maxima occurring at orbit tangent longitudes. Previous studies have examined the global distribution of Ionian hotspots and patera (i.e., irregular or complex craters with scalloped edges that are generally interpreted to be volcanic calderas), but in this study, we combine a new geospatial analysis technique with an improved hotspot and paterae database .

Hamilton, C. W.↗

NASA NTRS1994

Baroclinic instability in the interiors of the giant planets: A cooling history of Uranus?

We propose a quasigeostrophic, baroclinic model for heat transport within the interior of a stably stratified Jovian planet, based on motion in thin cylindrical annuli. Density decreases from the center outward and is zero at the surface of the planet. In the homogeneous case (no core), we find instability for the poles hotter than the equator, but not for the reverse. If the motion is bounded by an impenetrable core, instability occurs for both cases. Much of the behavior can be explained by analogy to conventional baroclinic instability theory. Motivated by our results, we explore a possible connection between the highly inclined rotation axis of Uranus and its anomalously low surface heat flux. We assume that the planets formed hot. Our conjecture is that heat was efficiently convected outwards by baroclinic instability in Uranus (with the poles hotter than the equator), but not in the other three Jovian planets. The surface temperature was higher for the stably stratified case (Uranus), leading to a higher rate of infrared emission and faster cooling. Therefore, we propose that Uranus lost its internal heat sooner than Neptune because baroclinic motions, permitted by its inclination to the sun, were able to extract its internal heat while the surface was still warm.

Holme, Richard↗

NASA NTRS1984

Progress in natural laminar flow research

For decades, since the earliest attempts to obtain natural laminar flow (NLF) on airplanes, three classical objections to its practicality have been held in the aeronautical community. These objectives concerned first, the capability to manufacture practical airframe surfaces smooth enough for NLF; second, the apparent inherent instability and sensitivity of NLF; and third, the accumulation of contamination such as insect debris in flight. This paper explains recent progress in our understanding of the achieveability and maintainability of NLF on modern airframe surfaces. This discussion explains why previous attempts to use NLF failed and what has changed regarding the three classical objections to NLF practicality. Future NASA research plans are described concerning exploring the limits of NLF usefulness, production tolerances, operational considerations, transition behavior and measurement methods, and NLF design applications.

Holmes, B. J.↗

NASA NTRS2023

Changing Characteristics of Tropical Extreme Precipitation-Cloud Regimes in Warmer Climates

In this paper, we have investigated the changing characteristics of climatic scale (monthly) tropical extreme precipitation in warming climates using the Energy Exascale Earth System Model (E3SM). Results are from Atmospheric Model Intercomparison Project (AMIP)-type simulations driven by a) control experiment with present-day sea surface temperature (SST) and CO 2 concentration, b) P4K, same as in a) but with uniform increase by 4K in SST globally, and c) same as in a), but with imposed SST and CO 2 concentration from outputs of coupled E3SM forced by 4xCO 2 concentration. We find that as the surface warms under P4K and 4xCO 2 , both convective and stratiform rain increase. Importantly, there is increasing fractional contribution of stratiform rain as a function of precipitation intensity, with the most extreme but rare events occurring preferentially over land more than ocean, more so under 4xCO 2 than P4K. Extreme precipitation is facilitated by increased precipitation efficiency, reflecting accelerated rates of recycling of precipitation-cloud water (both liquid and ice phases) in regions with colder anvil cloud tops. Changes in vertical profiles of clouds, condensation heating and vertical motions indicate increasing precipitation-cloud-circulation organization from control, P4K to 4xCO 2 . Results suggest that large-scale ocean warming, i.e., P4K, is the primary cause contributing to organization structure resembling the well-known Mesoscale Convective System (MCS) for increased extreme precipitation on shorter (hourly to daily) time scales. Additional 4xCO 2 atmospheric radiative heating, and dynamically consistent anomalous SST further amplifies the MCS organization under P4K. Analyses of the surface moist static energy distribution show that increase in surface moisture (temperature) under P4K and 4xCO 2 is the key driver leading to enhanced convective instability over tropical ocean (land). However, the fast and large increase in land surface temperature and lack of available local moisture result in strong reduction in land surface relative humidity, reflecting severe drying and enhanced convective inhibition (CIN). It is argued that very extreme and rare “record-breaking” precipitation events found over land under P4K, more so under 4xCO 2 , are likely due to the delayed onset of deep convection, i.e., the longer the suppression of deep convection by CIN, the more severe the extreme precipitation when eventually occur, due to the release of large amount of stored surplus convective available potential energy in the lower troposphere during prolonged CIN.

climate-scale extreme tropical precipitation↗

NASA NTRS2008

Aeroservoelastic Stability Analysis of the X-43A Stack

The first air launch attempt of an X-43A stack, consisting of the booster, adapter and Hyper-X research vehicle, ended in failure shortly after the successful drop from the National Aeronautics and Space Administration Dryden Flight Research Center (Edwards, California) B-52B airplane and ignition of the booster. The stack was observed to begin rolling and yawing violently upon reaching transonic speeds, and the grossly oscillating fins of the booster separated shortly thereafter. The flight then had to be terminated with the stack out of control. Very careful linear flutter and aeroservoelastic analyses were subsequently performed as reported herein to numerically duplicate the observed instability. These analyses properly identified the instability mechanism and demonstrated the importance of including the flight control laws, rigid-body modes, structural flexible modes and control surface flexible modes. In spite of these efforts, however, the predicted instability speed remained more than 25 percent higher than that observed in flight. It is concluded that transonic shock phenomena, which linear analyses cannot take into account, are also important for accurate prediction of this mishap instability.

Pak, Chan-gi↗

NASA NTRS1992

Marangoni instability induced convection in an evaporating liquid droplet

The processes occurring when a liquid drop undergoes evaporation are described. When a liquid drop undergoes evaporation, its surface temperature decreases. If the droplet is free floating in a microgravity environment, the heat transfer process inside the droplet is initially condition controlled. As the process continues, a radial temperature gradient builds up at the free surface until the critical Marangoni number is exceeded. Then the onset of instability induces thermocapillary convective flows, which in turn speed up the evaporation. The convective flows will subside when the interior of the droplet reaches a certain equilibrium temperature, and the process will return to the diffusion controlled mode. Both preliminary modeling and recent laboratory data have confirmed that Marangoni instability induced convection can and does occur in the droplet evaporation process. Mathematical models representing Marangoni instability in an evaporating liquid drop are presented. An ideal space experiment to study and characterize the onset of Marangoni instability in an evaporating liquid droplet and to establish the effect of Marangoni instability induced convection on the droplet evaporation rate is outlined and the need for conducting such experiments in space is highlighted. However, before an opportunity to conduct experiments in space arises, ground based experiments have to be conducted to study feasibility issues and proof of concept. A ground based experiment of this type is outlined.

Chai, An-Ti↗

DOE OSTI2020

Unstable Invasion of Sedimenting Granular Suspensions

Here we investigate the development of mobility inversion and fingering when a granular suspension is injected radially between horizontal parallel plates of a cell filled with a miscible fluid. While the suspension spreads uniformly when the suspension and the displaced fluid densities are exactly matched, even a small density difference is found to result in a dense granular front which develops fingers with angular spacing that increase with granular volume fraction and decrease with injection rate. We show that the timescale over which the instability develops is given by the volume fraction dependent settling timescale of the grains in the cell. We then show that the mobility inversion and the nonequilibrium Korteweg surface tension due to granular volume fraction gradients determine the number of fingers at the onset of the instability in these miscible suspensions.

02 PETROLEUM↗

NASA NTRS2002

Fluid Mechanics of Capillary-Elastic Instabilities in Microgravity Environment

The aim of this project is to investigate the closure and reopening of lung airways due to surface tension forces, coupled with airway elasticity. Airways are liquid-lined, flexible tubes and closure of airways can occur by a Rayleigh instability of the liquid lining, or an instability of the elastic support for the airway as the surface tension of the air-liquid interface pulls the tube shut, or both. Regardless of the mechanism, the airway is closed because the liquid lining has created a plug that prevents axial gas exchange. In the microgravity environment, surface tension forces dominate lung mechanics and would lead to more prevalent, and more uniformly distributed air-way closure, thereby creating a potential for respiratory problems for astronauts. Once closed the primary option for reopening an airway is by deep inspiration. This maneuver will pull the flexible airways open and force the liquid plug to flow distally by the incoming air stream. Airway reopening depends to a large extent on this plug flow and how it may lead to plug rupture to regain the continuity of gas between the environment and the alveoli. In addition to mathematical modeling of plug flows in liquid-lined, flexible tubes, this work has involved benchtop studies of propagating liquid plugs down tube networks that mimic the human airway tree. We have extended the work to involve animal models of liquid plug propagation in rat lungs. The liquid is radio-opaque and x-ray video imaging is used to ascertain the movement and distribution of the liquid plugs so that comparisons to theory may be made. This research has other uses, such as the delivery of liquids or drugs into the lung that may be used for surfactant replacement therapy or for liquid ventilation.

Grotberg, James B.↗

NASA NTRS2014

Novel Epoxy Particulate Composites for Mitigation of Insect Residue Adhesion on Future Aircraft Surfaces

Drag is reduced significantly for airflow over surfaces when laminar flow can be maintained over greater chord lengths, the distance from the leading edge of an airfoil.1 However, surface imperfections, such as chipped paint, scratches, and events that change topography on a microscopic scale can introduce airflow instabilities resulting in premature transition to turbulent flow.1 Although many of these surface imperfections can be avoided with proper maintenance, advanced materials, and advanced manufacturing practices, topographical surface anomalies arising during flight from insect impacts cannot be controlled and can influence laminar flow stability. Practical solutions to this operational challenge need to be developed for future aircraft to have full advantage of laminar flow designs that improve fuel efficiency.2 Researchers have investigated various methods to mitigate insect residue adhesion for decades.3 Although several techniques have demonstrated efficacy including mechanical scrapers, active liquid discharge systems, and sacrificial paper coatings, they have not been commercially implemented due to increased manufacturing and operational complexity, environmental impact, and weight penalties. Coatings offer a simple route for passive insect residue adhesion prevention without many of the challenges associated with maintenance of laminar flow.4 In our previous work, we determined that most commercially available materials were not effective at insect residue adhesion.5 We also identified improvements when both surface energy could be controlled by surface modifying agents and the topography could be altered through the use of micron-sized and nanometer-sized filler materials.6 In this work, these general principles were applied to an epoxy system to evaluate the behavior of the surface modifying agent, a fluorinated alkyl ether oligomer, on surface energy and insect residue adhesion properties.

Wohl, Christopher J.↗

DOE OSTI2025

Silylsilane‐Substituted Polymers: Fluorine‐Free, Liquid Repellent, and Hydrolytically Stable Alternatives to Siloxanes

Abstract Per‐ and polyfluoroalkyl substances (PFAS) are omniphobic and exceptionally stable, making them ideal for a wide range of materials applications. However, as “forever chemicals”, their exceptional persistence and bioaccumulation have generated an increasing amount of environmental and health concerns, prompting the search for fluorine‐free alternatives. Siloxane‐based materials are therefore interesting to examine as PFAS alternatives due to their low surface energy and hydrophobicity but suffer from hydrolytic instability of Si─O linkages. To address this challenge, a novel methacrylate monomer, 3‐[tris(trimethylsilyl)silyl]propyl methacrylate (M‐silyl), is designed containing Si─Si bonds rather than Si─O bonds of siloxanes. Polymers derived from M‐silyl (P‐silyl) is prepared by controlled free radical polymerization and compared with their siloxane analogues after coating on silicon wafers. Contact angle (CA) measurements confirmed P‐silyl to be hydrophobic (advancing/receding water CA = 109.7°/83.0°), with a low‐hysteresis for oil (lyophobic) (hexadecane CA hysteresis = 2.0°), comparable to its siloxane‐based counterpart. Importantly, P‐silyl maintained these surface properties after exposure to acidic or basic conditions, while siloxane analogues lost hydrophobicity. Consequently, the incorporation of Si ─ Si linkages into the design of the polymer enables chemically stable, fluorine‐free alternatives for water‐repellent and low hysteresis surface coatings and advances the design of fluorine‐free functional materials.

fluorine-free↗

DOE OSTI2024

Severe Convective Storms in Limited Instability Organized by Pattern and Distribution

Abstract Severe convection occurring in high-shear, low-CAPE (HSLC) environments is a common cool-season threat in the southeastern United States. Previous studies of HSLC convection document the increased operational challenges that these environments present compared to their high-CAPE counterparts, corresponding to higher false-alarm ratios and lower probability of detection for severe watches and warnings. These environments can exhibit rapid destabilization in the hours prior to convection, sometimes associated with the release of potential instability. Here, we use self-organizing maps (SOMs) to objectively identify environmental patterns accompanying HSLC cool-season severe events and associate them with variations in severe weather frequency and distribution. Large-scale patterns exhibit modest variation within the HSLC subclass, featuring strong surface cyclones accompanied by vigorous upper-tropospheric troughs and northward-extending regions of instability, consistent with prior studies. In most patterns, severe weather occurs immediately ahead of a cold front. Other convective ingredients, such as lower-tropospheric vertical wind shear, near-surface equivalent potential temperature (θ e ) advection, and the release of potential instability, varied more significantly across patterns. No single variable used to train SOMs consistently demonstrated differences in the distribution of severe weather occurrence across patterns. Comparison of SOMs based on upper and lower quartiles of severe occurrence demonstrated that the release of potential instability was most consistently associated with higher-impact events in comparison to other convective ingredients. Overall, we find that previously developed HSLC composite parameters reasonably identify high-impact HSLC events. Significance Statement Even when atmospheric instability is not optimal for severe convective storms, in some situations they can still occur, presenting increased challenges to forecasters. These marginal environments may occur at night or during the cool season, when people are less attuned to severe weather threats. Here, we use a sorting algorithm to classify different weather patterns accompanying such storms, and we distinguish which specific patterns and weather system features are most strongly associated with severe storms. Our goals are to increase situational awareness for forecasters and to improve understanding of the processes leading to severe convection in marginal environments.

Meteorology & Atmospheric Sciences↗

DOE OSTI2021

Mode spectrum characteristics and onset of the low-shear MHD stability regime

Equilibria with extended regions of weak magnetic shear, including some tokamak scenarios and stellarators, can be susceptible to pressure-driven internal MHD instabilities even though there is no mode rational surface in the plasma. Nonresonant modes, in particular, can have properties that are unattractive for confinement, including displacing substantial volumes of the plasma and leading to more efficient pressure gradient flattening in the nonlinear regime. The onset and linear properties of the low shear stability regime are examined using the initial-value, extended-MHD code M3D-C. For monotonic q-profiles, we demonstrate a clear correlation between the convergents associated with the continued fraction representation of q 0 and the spectrum of unstable modes. Nonresonant modes are observed to be destabilized preferentially to any other resonant instability with the same toroidal mode number when n > 1. Using the observed connection between the spectrum associated with q 0 and the overall equilibrium stability properties, we suggest a technique for reducing the uncertainty on both q 0 and magnetic shear in the core region, obtained either via measurement or through the analysis and reconstruction of experimental results.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1992

Stability analysis of surface tension effects on a double-diffusive layer

The linear stability characteristics of a fluid layer with simultaneous temperature and concentration gradients in a reduced gravity field are examined. The surface tension of the fluid is assumed to be a linear function of temperature and concentration. It is concluded that a small amount of gravity may damp out oscillatory instability or may alter its dynamics so that instability appears as steady convection. The onset of salt-finger instability may be in the overstable mode due to the surface tension method. The Lewis and Prandtl numbers of the material have a strong influence on the stability boundaries and onset characteristics of the system.

Chen, C. F.↗

DOE OSTI2023

Changing Characteristics of Tropical Extreme Precipitation–Cloud Regimes in Warmer Climates

In this study, we investigated the changing characteristics of climatic scale (monthly) tropical extreme precipitation in warming climates using the Energy Exascale Earth System Model (E3SM). The results are from Atmospheric Model Intercomparison Project (AMIP)-type simulations driven by (a) a control experiment with the present-day sea surface temperature (SST) and CO 2 concentration, (b) P4K, the same as in (a) but with a uniform increase of 4K in the SST globally, and (c) the same as in (a), but with an imposed SST and CO 2 concentration from the outputs of the coupled E3SM forced by a 4xCO 2 concentration. We found that as the surface warmed under P4K and 4xCO 2 , both convective and stratiform rain increased. Importantly, there was an increasing fractional contribution of stratiform rain as a function of the precipitation intensity, with the most extreme but rare events occurring preferentially over land more than the ocean, and more so under 4xCO 2 than P4K. Extreme precipitation was facilitated by increased precipitation efficiency, reflecting accelerated rates of recycling of precipitation cloud water (both liquid and ice phases) in regions with colder anvil cloud tops. Changes in the vertical profiles of clouds, condensation heating, and vertical motions indicate increasing precipitation–cloud–circulation organization from the control and P4K to 4xCO 2 . The results suggest that large-scale ocean warming, that is, P4K, was the primary cause contributing to an organization structure resembling the well-known mesoscale convective system (MCS), with increased extreme precipitation on shorter (hourly to daily) time scales. Additional 4xCO 2 atmospheric radiative heating and dynamically consistent anomalous SST further amplified the MCS organization under P4K. Analyses of the surface moist static energy distribution show that increases in the surface moisture (temperature) under P4K and 4xCO 2 was the key driver leading to enhanced convective instability over tropical ocean (land). However, a fast and large increase in the land surface temperature and lack of available local moisture resulted in a strong reduction in the land surface relative humidity, reflecting severe drying and enhanced convective inhibition (CIN). It is argued that very extreme and rare “record-breaking” precipitation events found over land under P4K, and more so under 4xCO 2 , are likely due to the delayed onset of deep convection, that is, the longer the suppression of deep convection by CIN, the more severe the extreme precipitation when it eventually occurs, due to the release of a large amount of stored surplus convective available potential energy in the lower troposphere during prolonged CIN.

54 ENVIRONMENTAL SCIENCES↗