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All sourcesNASA NTRSDOE OSTI
NASA NTRS2022

The Harmonic Linearized Navier-Stokes Equations for Transition Prediction in Three-Dimensional Flows

The conventional method to predict the onset of laminar-turbulent transition in convectively unstable boundary-layer flows is based on the logarithmic amplification ratio, the so-called N-factor, of the linear instability waves. To calculate the N-factor, the flow variables are decomposed into a laminar basic state solution and the linear disturbances, which are assumed to be harmonic in time. The most commonly used linear stability analysis approaches include the locally parallel linear stability theory (LST) and the nonlocal, weakly nonparallel parabolized stability equations (PSE). However, these methods do not account for strong streamwise gradients that are encountered in several configurations of interest, such as those in the vicinity of roughness elements, steps, gaps, or corners. To compute the linear evolution of disturbances along such strongly nonparallel regions, the harmonic linearized Navier-Stokes equations (HLNSE) need to be solved. The discretization of the HLNSE for spanwise/azimuthally inhomogeneous laminar basic states yields a linear system of complex arithmetic with a leading dimension of the order of 10^(7) to 10^(8) even in relatively simple flows. A combined multithread and multiprocessor algorithm is implemented for the direct solution of such linear systems. Results for a supersonic boundary layer over a three-dimensional roughness patch show good agreement with experimental measurements when the evolution of the instability waves over the roughness patch is included via the HLNSE. Additionally, inflow-resolvent analysis based on the HLNSE for discrete-roughness-induced disturbances in the nose tip of a blunt cone at Mach 6 demonstrates the importance of including the disturbance amplification along the near vicinity of the roughness element and separation region.

Boundary Layer Stability↗
NASA NTRS1985

An observational study of a mesoscale area of convection under weak synoptic-scale forcing

This is a case study of a mesoscale area of convection which began at night over western Kansas on September 2, 1982 and lasted until the afternoon of September 3. Evidence from analyses of surface, upper-air radar, and satellite observations suggests that the thunderstorms probably formed in response to the lifting of an elevated layer of conditional instability. The lifting can be attributed qualitatively to quasi-geostrophic ascending motion resulting from a shallow layer of warm advection near 60 kPa. Two possible sources of moisture were midlevel moisture which had been advected around an upstream ridge and a localized area of turbulent transport of water vapor from below. The convective event could not have been forecast with synoptic-scale, mandatory-level analyses alone; it was difficult to explain even with detailed analyses at other levels.

Bluestein, H. B.↗
NASA NTRS1978

A method for determining the weak statistical stationarity of a random process

A method for determining the weak statistical stationarity of a random process is presented. The core of this testing procedure consists of generating an equivalent ensemble which approximates a true ensemble. Formation of an equivalent ensemble is accomplished through segmenting a sufficiently long time history of a random process into equal, finite, and statistically independent sample records. The weak statistical stationarity is ascertained based on the time invariance of the equivalent-ensemble averages. Comparison of these averages with their corresponding time averages over a single sample record leads to a heuristic estimate of the ergodicity of a random process. Specific variance tests are introduced for evaluating the statistical independence of the sample records, the time invariance of the equivalent-ensemble autocorrelations, and the ergodicity. Examination and substantiation of these procedures were conducted utilizing turbulent velocity signals.

Sadeh, W. Z.↗
NASA NTRS1994

Crossflow instability control on a swept-wing: Preliminary studies

The pressure distribution on a swept wing causes the streamlines at the edge of the boundary layer to be curved. This pressure gradient normal to the external streamline creates a velocity component normal to the external streamline within the boundary layer which is referred to as the crossflow velocity. Because the crossflow velocity profile perpendicular to the wing surface has an inflection point, the profile is unstable. The stationary instability mode takes the form of crossflow vortices. Under these conditions, the boundary layer on the wing is extremely unstable and transition to turbulent flow takes place much closer to the leading edge of the wing than it would on an unswept wing. Higher skin friction drag is associated with turbulent flow, and so better aircraft performance could be obtained if the crossflow could be eliminated One method of controlling crossflow that is being investigated is boundary-layer suction. An extensive airfoil suction experiment in the 8 feet Transonic Pressure Tunnel (TPT) at NASA Langley Research Center will begin late in 1994. Because of the size, complexity, and expense associated with this test, a number of 'risk-reduction' tests are currently being conducted. The 20 x 28 in. Shear Flow Control Tunnel at NASA Langley is being used for some of these tests. Prior to the summer of 1994, a flat plate with a swept leading edge was installed in the 20 x 28 in. tunnel, with a displacement body mounted on the tunnel ceiling that created a pressure distribution on the plate similar to the pressure distribution on a swept wing. The flow over the plate was investigated during the summer of 1994 using a laser Doppler velocimeter (LDV) system. The LDV measurements indicated the possible presence of multiple disturbance modes, a rarely-seen phenomena since, in most tests, one disturbance mode dominates. The possible existence of multiple disturbance modes in the flat plate boundary layer, however, means that the flow in the 20 x 28 in. tunnel is of interest itself, and will be investigated more thoroughly in the future. With a view to these investigations, the boundary layer traverse mechanism in the 20 x 28 in. tunnel was modified to improve its performance, and strain gauges were mounted on the traverse in order to monitor its deflection during a test. Other preliminary work conducted in the 20 x 28 in. tunnel included the use of an infrared camera system. Previous work with this system showed that transition indeed could be detected, but the signal produced by the crossflow vortices was too weak to be detected. It was hoped that spraying the flat plate with naphthalene would augment the heat transfer associated with the crossflow vortices so that they would show up in a IR image; however, experiments showed that this would not work. Another set of tests was conducted in the 20 x 28 in. tunnel to determine the tripping requirements for a set of airfoil-shaped struts that will be used in the 8 feet TPT experiment. Since the Reynolds number associated with these struts is small, a laminar boundary layer would separate early, causing large fluctuations in the flow field. A turbulent boundary layer would remain attached further back, but tripping from laminar to turbulent flow at low Reynolds number is very difficult. However, trip strip configurations were found that should effectively trip the boundary layer at the required conditions. Currently underway is an investigation of the data acquisition requirements for the 8 feet TPT experiment, with the purpose of the finding the minimum amount of data needed to characterize sufficiently the swept-wing boundary layer. This study is being conducted using a numerically generated data set.

Bridges, David H.↗
NASA NTRS1999

Hydrodynamic Stability and Magnetic Reconnection in Disks and Stars

The purpose of this grant is to study parametric instability. The simplest example of parametric instability is a harmonic oscillator with a periodic modulation of the spring constant. If the modulation frequency is close to twice the natural frequency of the oscillator, the amplitude of oscillation tends to grow exponentially. The growth rate is proportional to the strength of the modulation, but it also depends upon the closeness to resonance of the two frequencies, and upon natural damping rate or "Q" of the oscillator. Parametric instabilities are very common in physics. A familiar example is a jogger's ponytail--normally a very strongly damped pendulum, it can be destabilized by the variation in effective gravity during the jogger's stride. Observation confirms that the period of the pendulum is half that of the jogger's vertical motion. In astrophysics, parametric instability may occur by external tidal forcing, or by interaction among eigenmodes. In the latter case, an energetic eigenmode may destabilize modes of half its frequency, provided some weak nonlinearity exists to couple them. Under a previous Astrophysical Theory grant (NAGW-2419), the PI discovered a parametric instability of tidally forced disks such as the accretion disks in cataclysmic variables and X ray binaries [2]. The destabilized modes are tightly-wound, incompressible, three-dimensional waves analogous to g-modes and r-modes in stars. Later work has confirmed our analysis [4]. It was hoped that these modes might provide a source of turbulence and angular momentum transport in accretion disks. However, a follow-up investigation of this instability by local numerical simulations, although confirming the analytically estimated growth rates, found negligible angular momentum flux [3]. Other work, partly supported by the ATP, now strongly indicates that the transport mechanism in such disks is magnetohydrodynamic turbulence [6]. Nevertheless, the parametric mechanism may truncate the outer edges of disks in close binaries [2], and it may be important in disks of very low ionization such as protostellar disks, or even cataclysmic-variable disks in quiescence where the MHD mechanism may be ineffective [5]. All analyses up to 1996 were done in a local approximation where the orbital frequency, shear rate, and tidal field were treated as constants. The locally computed growth rate turns out to depend strongly on radius, and it was unclear how to average these local rates to obtain the correct global rate. This is a critical issue for accretion disks in close binaries, because the local growth rate is comparable to the orbital frequency towards the outer edge of the disk but decreases rapidly inwards. Paper #1 examined this issue in a simplified global model where the destabilizing terms vary with position. We found that the global growth rate is essentially equal to the maximum local rate, provided that the latter is smoothed over a radial range equal to the distance that the destabilized wave propagates at its group speed in one growth time. Thus, in an accretion disk, waves would grow rapidly in the outer parts but would propagate both inwards and outwards at a maximum group speed of order the disk thickness divided by the orbital period.

Goodman, Jeremy↗
NASA NTRS2022

The Harmonic Linearized Navier-Stokes Equations for Transition Prediction in Three-Dimensional Flows

The conventional method to predict the onset of laminar-turbulent transition in convectively unstable boundary-layer flows is based on the logarithmic amplification ratio, the so-called N-factor, of the linear instability waves. To calculate the N-factor, the flow variables are decomposed into a laminar basic state solution and the linear disturbances, which are assumed to be harmonic in time. The most commonly used linear stability analysis approaches include the locally parallel linear stability theory (LST) and the non-local, weakly nonparallel parabolized stability equations (PSE). However, these methods do not account for strong streamwise gradients that are encountered in several configurations of interest, as roughness elements, steps, gaps, or corners. To solve the linear evolution of disturbances along such strongly nonparallel regions, the harmonic linearized Navier-Stokes equations (HLNSE) need to be solved. The discretization of the HLNSE for spanwise/azimuthally inhomogeneous laminar basic states yields a linear system of complex arithmetic with a leading dimension of the order of 107 to 108. A combined multithread and multiprocessor algorithm is implemented for the direct solution of such linear system. Results for a supersonic boundary layer over a three-dimensional roughness patch show good agreement with experimental measurements when the evolution of the instability waves over the roughness patch is included via the HLNSE.

Boundary Layer Stability↗
NASA NTRS1973

Swirling jet turbulent mixing and combustion computations

Computations are presented describing the mixing and combustion of swirling jets in a coaxial stream. It is demonstrated that the boundary layer equations represent the flow reasonably well until reversed flow is imminent. For the range of parameters investigated indications are that the edge velocity has little effect on the behavior of the flow. Furthermore, confining the flow with a constant pressure wall, or impressing a favorable pressure gradient on the coaxial flow, acts to reduce the severity of the centerline adverse pressure gradient created by the swirl decay. A simple scalar eddy viscosity model, including a potential core formulation, is shown to described the behavior of weak swirling flow in the far region but is only in fair agreement with observations in the near region. The effects of swirl on a burning hydrocarbon jet exhausting into a cold coaxial stream are shown to be intensified by the reduction of the density due to combustion. The enhanced mixing properties of high swirl flow produce rapid diffusion of the burning gases into the cold edge flow causing early cessation of the NO producing reactions. Computations show that doubling the initial jet swirl could reduce the NO production by 25 percent.

Rubel, A.↗
NASA NTRS1992

Atmospheric effects on sonic boom: A program review

The program goals were determined after consideration of the weaknesses in our understanding of atmospheric effects on sonic boom waveforms left in the wake of the cancellation of the U.S. SST in the 70's and the advancements in acoustics and atmospheric science since that time. For example, a considerable body of knowledge on molecular absorption has built up in the acoustics community over the last 15 years and this has not been incorporated into the sonic boom theory. Further, it was felt that the understanding of atmospheric turbulence had also advanced considerably during that time period. Therefore, key elements of the current program are the development of an improved atmospheric absorption model and an improved atmospheric turbulence model. The advances made in computer power over the last 15 years were also considered, and will be utilized to remove restrictions on the analytical model for turbulence effects on sonic boom waveforms. Although the majority of disturbing sonic booms will not occur at focuses or caustics, it was felt that this was an area that required further understanding, thus it will be looked into. Finally, in order to insure that the current effort, which is basically analytical in nature, retains a firm grasp on reality, a data base of sonic boom waveforms and associated weather data is being compiled, and a set of scale model experiments is being planned to guide the overall efforts.

Mcaninch, Gerry L.↗
NASA NTRS1987

Particle-laden swirling free jets: Measurements and predictions

A theoretical and experimental investigation of single-phase and particle-laden weakly swirling jets was conducted. The jets were injected vertically downward from a 19 mm diameter tube with swirl numbers ranging from 0 to 0.33. The particle-laden jets had a single loading ratio (0.2) with particles having a SMD of 39 microns. Mean and fluctuating properties of both phases were measured using nonintrusive laser based methods while particle mass flux was measured using an isokinetic sampling probe. The continuous phase was analyzed using both a baseline kappa-epsilon turbulence model and an extended version with modifications based on the flux Richardson number to account for effects of streamline curvature. To highlight effects of interphase transport rates and particle/turbulence interactions, effects of the particles were analyzed as follows: (1) locally homogeneous flow (LHF) analysis, where interphase transport rates are assumed to be infinitely fast; (2) deterministic separated flow (DSF) analysis, where finite interphase transport rates are considered but particle/turbulence interactions are ignored; and (3) stochastic separated flow (SSF) analysis, where both effects are considered using random-walk computations.

Bulzan, D. L.↗
NASA NTRS1987

Particle-laden swirling free jets - Measurements and predictions

A theoretical and experimental investigation of single-phase and particle-laden weakly swirling jets was conducted. The jets were injected vertically downward from a 19 mm diameter tube with swirl numbers ranging from 0 to 0.33. The particle-laden jets had a single loading ratio (0.2) with particles having an SMD of 39 micrometers. Mean and fluctuating properties of both phases were measured using nonintrusive laser based methods while particle mass flux was measured using an isokinetic sampling probe. The continuous phase was analyzed using both a baseline k-epsilon turbulence model and an extended version with modifications based on the flux Richardson number to account for effects of streamline curvature. To highlight effects of interphase transport rates and particle/turbulence interactions, effects of the particles were analyzed as follows: (1) locally homogeneous flow (LHF) analysis, where interphase transport rates are assumed to be infinitely fast; (2) deterministic separated flow (DSF) analysis, where finite interphase transport rates are considered but particle/turbulence interactions are ignored; and (3) stochastic separated flow (SSF) analysis, where both effects are considered using random-walk computations.

Bulzan, D. L.↗
NASA NTRS1979

Magnetic field effects on ionization inhomogeneities advected by motions of the neutral gas

A theory is developed for the ambipolar diffusion, drift, distortion, and production of ionization inhomogeneities within weakly ionized plasma in the presence of the geomagnetic field and motions of the neutral gas. The theory developed includes spatially varying velocity fields of the neutral gas, with a special emphasis on investigating the length scale restrictions necessary for the plasma to be treated as spatially homogeneous. Several effects of the magnetic field on ionization inhomogeneities are discussed. These include the anisotropy of ambipolar diffusion, the distortion and drift due to a gravitational field, the production of irregularities due to the turbulent acceleration field, the drift relative to the neutral gas, and the distortion of ionization inhomogeneities due to the effects of a uniform wind. Pertinent equations are derived for a multispecies plasma containing positive or negative ions, and for the case of electrons and one species of positive ions.

Hill, R. J.↗
NASA NTRS1981

Instability and transition in rotating disk flow

The stability of three-dimensional rotating disk flow is investigated, including the effects of Coriolis forces and streamline curvature. The numerical results show that the critical Reynolds number for establishment of stationary vortex flow is 287. These vortices spiral outward at an angle of about 11.2 deg, and transition to turbulence occurs when their total amplification is about e to the 11th. New experimental results are also reported on the spatial growth rates of the stationary vortices. It is shown that the analysis gives growth rates that compare much better with the experimental results than do results obtained using the Orr-Sommerfeld equation. The experimental results tend to support the numerical prediction that the number of stationary vortices varies directly with the Reynolds number. The calculations also indicate the existence of weakly unstable propagating (type II) modes at low Reynolds numbers (Critical Reynolds Number being approximately equal to 49).

Malik, M. R.↗
DOE OSTI2022

Effect of triangularity on ion-temperature-gradient-driven turbulence

The linear and nonlinear properties of ion-temperature-gradient-driven turbulence with adiabatic electrons are modeled for axisymmetric configurations for a broad range of triangularities δ, both negative and positive. Peak linear growth rates decrease with negative δ but increase and shift toward a finite radial wavenumber kx with positive δ. The growth-rate spectrum broadens as a function of kx with negative δ and significantly narrows with positive δ. Here, the effect of triangularity on linear instability properties can be explained through its impact on magnetic polarization and curvature. Nonlinear heat flux is weakly dependent on triangularity for |δ|≤0.5, decreasing significantly with extreme δ, regardless of sign. Zonal modes play an important role in nonlinear saturation in the configurations studied, and artificially suppressing zonal modes increased nonlinear heat flux by a factor of about four for negative δ, increasing with positive δ by almost a factor of 20. Proxies for zonal-flow damping and drive suggest that zonal flows are enhanced with increasing positive δ.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1992

Venus lower thermosphere studies

Studies undertaken in this project have sought to understand lower thermospheric structure and dynamics (less than or equal to 145 km), particularly the processes responsible. This is a region just below the reach of in-situ instruments onboard PVO (Pioneer Venus Orbiter) during the first few diurnal cycles. PVO remote airglow observations (nitric oxide, O2, visible, O 1304A) have been coupled with ground-based observations (CO densities, winds, temperatures, O2 IR nightglow) to address the behavior of lower thermospheric winds and chemistry over 95 to 150 km. This interpretation of PVO and related data is accomplished by using the NCAR Venus thermospheric general circulation model (VTGCM) (Bougher et al., 1988; 1990). This model has been modified over the last two years to improve its ability to calculate O, CO, and O2 densities, temperatures, nightglow, and subsolar-to-antisolar and zonal winds over 95 to 150 km (Bougher and Borucki, 1992). Our VTGCM studies show that: (1) O2 visible and IR nightglow distributions can be used to trace lower thermosphere / upper mesosphere winds over 100-130 km. Typically, weak zonal winds (less than or equal to 25 m/sec) and nightglow maximum patches near 0100 LT prevail. Occasionally, strong zonal winds (30-60 m/sec) and airglow patches peaking near 0300 LT characterize the Venus lower thermosphere. (2) It is clear that the dynamics of the Venus 90-130 km region is highly variable on time scales as short as an hour. This is most likely due to the time variable nature of upward propagating gravity waves, which grow in amplitude and eventually break. The resulting turbulence gives rise to local time variable eddy diffusion and momentum drag, both of which strongly impact global density and nightglow distributions. (3) The oxygen chemistry (O, O2, etc.) over 90-120 km is strongly dependent on HO(x) and CLO(x) tracer species that must be properly included in any coupled chemical dynamical model. (4) The density profiles of light species (O, CO, N, He) are strongly affected by large-scale transport by the winds. Strong eddy diffusion is not a suitable model parameterization for approximating these light species, especially for extrapolation into the region below 140 km where PVO in-situ data is lacking. Instead, the fully coupled chemical dynamical VTGCM model should be used to improve estimates of densities within the VTS3 empirical model (Hedin et al., 1983) below 140 km.

Bougher, Stephen W.↗
NASA NTRS1995

Effects of confinement on partially premixed flames

Partially premixed combustion is an intermediate regime between the limiting cases of premixed and nonpremixed combustion. Although combustion problems are generally approached from one of these two limiting cases, there are many practical situations where flames cannot be considered as purely premixed or nonpremixed, and thus the partially premixed approach must be used. In partially premixed combustion, mechanisms from the premixed and nonpremixed regimes can coexist, and as a result some interesting new phenomena can arise. One such phenomenon is the flame stabilization in laminar mixing layers by triple flames. One of the first observations of triple flames was made by Phillips (1965), who investigated a triple flame propagating in a methane mixing layer. Kioni et al. (1993) also examined triple flames both experimentally and numerically. There have also been numerous analytical studies on the shape and propagation of triple flames under various assumptions by Dold (1989), Dold et al. (1991), and Hartley and Dold (1991). In terms of modeling, Muller et al. (1994) have combined the flamelet formulations for premixed and nonpremixed combustion in order to treat lifted diffusion flames. One common feature in the analytical and numerical studies mentioned above is the assumption of zero heat release, which is necessary to make the problem tractable. The effect of heat release on triple flames was investigated by Ruetsch et al. (1995), where for the unconfined case, flame speeds larger than their premixed counterparts were found. One of the most important practical situations in which these conditions arise is in lifted turbulent jet diffusion flames. At a critical velocity the burning zone of a fuel jet lifts off from the nozzle, moves to increasing distances as the jet velocity increases, and finally blows off. The mechanisms that control these phenomena, i.e. that determine the stability of these flames, are still not understood. In addition to regions where diffusion flame stabilization takes place, partially premixed conditions also exist during the ignition process in nonpremixed systems. Numerical simulations by Reveillon et al. (1994) of the ignition process in a weakly stirred mixture of fuel and oxidizer show that triple flames propagate along lines of stoichiometric mixture fraction throughout the fluid. In addition, Peters (1994) notes that NO(x) emissions are likely to be large in such transient cases, and therefore an understanding of triple flames can provide information concerning pollutant formation. This study extends the work previously done and examines the effects of lateral confinement on partially premixed flames. Once again, we study both the flame structure and propagation.

Ruetsch, G. R.↗
NASA NTRS2005

Particle Image Velocimetry Measurements of a Two/Three-dimensional Separating/Reattaching Boundary Layer Downstream of an Axisymmetric Backward-facing Step

Planar Particle Image Velocimetry measurements were obtained in the separating/reattaching flow region downstream of an axisymmetric backward-facing step. Data were acquired for a two-dimensional (2D) separating boundary layer at five different Reynolds numbers based on step height (Re(sub h)), spanning 5900-33000, and for a three-dimensional (3D) separating boundary layer at Re(sub h) = 5980 and 8081. Reynolds number effects were investigated in the 2D cases using mean-velocity field, streamwise and wall-normal turbulent velocity, and Reynolds stress statistics. Results show that both the reattachment length (x(sub r)) and the secondary separation point are Reynolds number dependent. The reattachment length increased with rising Re(sub h) while the secondary recirculation region decreased in size. These and other Re(sub h) effects were interpreted in terms of changes in the separating boundary layer thickness and wall-shear stress. On the other hand, in the 3D case, it was found that the imposed cross-flow component was relatively weak in comparison to the streamwise component. As a result, the primary influences of three dimensionality only affected the near-separation region rather than the entire separation bubble.

Hudy, Laura M.↗
NASA NTRS1993

Mixing in a stratified shear flow: Energetics and sampling

Direct numerical simulations of the time evolution of homogeneous stably stratified shear flows have been performed for Richardson numbers from 0 to 1 and for Prandtl numbers between 0.1 and 2. The results indicate that mixing efficiency R(sub f) varies with turbulent Froude number in a manner consistent with laboratory experiments performed with Prandtl numbers of 0.7 and 700. However, unlike the laboratory results, for a particular Froude number, the simulations do not show a clear dependence on the magnitude of R(sub f) on Pr. The observed maximum value of R(sub f) is 0.25. When averaged over vertical length scales of an order of magnitude greater than either the overturning or Ozmidov scales of the flow, the simulations indicate that the dissipation rate epsilon is only weakly lognormally distributed with an intermittency of about 0.01 whereas estimated values in the ocean are 3 to 7.

Ivey, G. N.↗
DOE OSTI2022

Observed Covariations in Boundary Layer and Cumulus Cloud Layer Processes

In this paper we examine variations in boundary-layer processes spanning the shallow to deep cumulus transition. This is accomplished by differentiating boundary layer properties on the basis of convective outcomes, ranging from shallow to deep, as observed at the Atmospheric Radiation Measurement (ARM) Southern Great Plains (SGP) site in Oklahoma, USA. Doppler lidar, radar, and radiosonde data are combined to determine statistical differences in boundary layer and cloud layer properties using a large sample (236) of days with a range of convective outcomes: shallow, congestus, and deep convection. In these analyses, the radar characterizes diurnal cloud depth, the lidar quantifies updraft and downdraft properties in the subcloud layer, and daily radiosonde data provides the convective inhibition (CIN). Combined, these data are used to test the hypothesis that deep convection occurs when the strength of the boundary layer turbulence (i.e., TKE) exceeds the strength of the energy barrier (i.e., CIN) at the top of the CBL. Results show that days with deep convective clouds have significantly lower vertical velocity variance and weaker updrafts within the subcloud layer. However, CIN values are also found to be significantly lower on deep convective days, allowing for these weaker updrafts to penetrate the energy barrier and reach the level of free convection (LFC). In contrast, shallow convective outcomes occur when the updrafts are strong in an absolute sense, but are weak when compared to the strength of the energy barrier. These findings support the use of the CIN/TKE framework in parameterizing convection in coarse resolution models.

54 ENVIRONMENTAL SCIENCES↗