10B.4 THE ORIGIN AND DYNAMICS OF BANNER CLOUDS:AN ANALYSIS BASED ON LARGE EDDY SIMULATIONS

Daniel Reinert∗ and Volkmar WirthInstitute for Atmospheric Physics, Johannes Gutenberg-University, Mainz, Germany

1 INTRODUCTION

Banner clouds belong to the class of orographicclouds. They are known to occur in high moun-tain regions when sufficiently moist air flows acrosssteep mountain peaks or quasi 2D ridges. Pre-ferred places of occurrence are e.g. the Matter-horn in the Swiss Alps, Mount Everest, or MountZugspitze in the Bavarian Alps. Figure 1a,b showstwo typical examples.

Figure 1: Banner clouds forming leeward of apyramidal shaped mountain peak or a quasi 2Dridge. (a) Banner cloud at Matterhorn (Switzer-land). (b) Banner cloud at Mount Zugspitze(Bavarian Alps). Mean flow from right to left.

(a)

(b)

Banner clouds have the distinction of beingconfined to the immediate lee of the mountain,

∗Corresponding author address: Daniel Reinert, Jo-

hannes Gutenberg-University, Institute for Atmospheric

Physics, Becherweg 21, 55099 Mainz, Germany; e-mail:

dreinert@uni-mainz.de

whereas the windward side remains cloud-free.They typically have a banner-like appearance witha characteristic horizontal scale of O(1 km). Usu-ally their upwind end is directly attached to themountain tip while their downwind end flickersin the wind resembling a flag. Banner clouds arequasi-stationary and can often be observed for sev-eral hours. They must be clearly distinguishedfrom other orographically induced cloud patternslike cap clouds, lee wave clouds or rotor clouds.These either form on the windward side due toforced lifting or develop several kilometers down-wind of the mountain crest as a result of trappedlee waves.

Banner clouds, despite their regular appearance,were always on the fringe of scientific attention.The underlying mechanism of formation, as well asthe relative importance of dynamics versus ther-modynamics for formation and maintenance, arenot fully understood. Besides a number of draw-ings and photographs, very few investigations re-lated to banner clouds are documented in the sci-entific literature. We are aware of early mea-surements conducted by Peppler (1927) at Santis(Switzerland) and Joachim Kuettner (1946) (pers.comm.) at Mount Zugspitze. Unfortunately, thesemeasurements still do not provide a complete pic-ture of the phenomenon. The only numericalstudy we are aware of was conducted by Geerts(1992) using a model based on the Reynolds Aver-aged Navier-Stokes (RANS) equations. He focusedon the relative importance of surface friction forlee upslope flow behind an idealised tetrahedral-shaped obstacle.

In the scientific literature mainly three qualita-tive arguments are put forth in order to explain theoccurrence of banner clouds. According to themthe cloud develops due to:

I mixing of cold air near the ground withwarmer air from above (i.e. banner clouds be-ing essentially mixing fog) (e.g. Humphreys,1964)

II local adiabatic cooling near the mountain topdue to flow acceleration along quasi horizontaltrajectories originating on the windward side(Bernoulli-effect) (e.g. Beer, 1974)

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III adiabatic cooling due to forced upwelling inthe upward branch of a leeward vortex withhorizontal axis (e.g. Douglas, 1928) (see Fig.2).

Figure 2: Schematic, illustrating the postulatedformation mechanism of banner clouds leeward ofpyramidal shaped mountain peaks according to ar-gument III. Left: flow in x-z-plane. Right: lowlevel flow in x-y-plane. Light shading denotes thecloud.

We believe that argument III is the most rele-vant one, since it fits best with recent observationstaken by us at Mount Zugspitze (Schween et al,2007). Nevertheless, a distinct proof of argumentIII based on eddy-resolving numerical simulationsis still lacking.

This paper aims at providing more insight intothe dynamics of banner clouds with the aid ofLarge Eddy Simulations (LES). We will clarify thedominant formation mechanism and the necessityof additional leeward moisture sources, radiativeeffects or distinct air masses. Further we will in-vestigate the relative importance of thermodynam-ics regaring the reinforcement and maintenance ofbanner clouds.

2 APPROACH

As a tool to investigate this phenomenon we de-veloped a new LES model which can handle moistatmospheric flow above highly complex terrain(Reinert et al, 2007; Reinert and Wirth, 2008).The model is able to treat orography with slopesup to 90◦ by applying the method of viscous topog-raphy (Mason and Sykes, 1978). Furthermore, tur-bulent inflow conditions can be generated by usinga modified perturbation recycling method (Lundet al, 1998; Reinert and Wirth, 2008). Precipi-tating clouds are accounted for with a 2-momentwarm microphysical bulk scheme. The model hasbeen tested in detail and was validated againstwind tunnel data.

Since pyramidal shaped mountains seem to bethe most preferred places for banner cloud occur-rence, we investigated the flow field around ide-

alised pyramidal shaped obstacles on experimen-tal as well as atmospheric scale. The numericalsimulations on experimental scale were also val-idated against wind tunnel data of Ikhwan andRuck (2006). Thus more insight could be gainedregarding the robustness of our findings for thebanner cloud problem.

Figure 3 gives a general idea of the model setup.In x-direction we applied open inflow/outflowboundaries while in y-direction cyclic boundaryconditions were used. Since in LES the inflow al-ready needs to comprise realistic turbulent struc-tures, we generated model consistent turbulencein a precursor run by using the perturbation recy-cling technique. Then, for each time step, slices ofthe generated turbulent data set were applied atthe inflow boundary. Table 1 provides an overviewabout chosen model parameters, like the horizon-tal (∆x) and vertical (∆z) resolution, the obstacleshape (edge length L and slope angle α), the ve-locity of the approaching flow at the top of thedomain U0 and the total number of grid pointsNxyz.

U0

periodic

periodic

inflow

y

α

outflow

9.13 L4.00 L

3.57

L

6.00 L

3.40 L

2.60

L

2.02 L 4.98 L

13.13 L 7.00 L

L x

z

Figure 3: Model setup on experimental (blue)and atmospheric (red) scale

L α ∆x ∆zm U0 Nxyz

[m] [◦] [m] [m] [ms−1] [#]

exp 0.2 70 1.3E-2 9E-3 5.4 0.91E6

atm 930 65 25 15 9.0 2.2E6

Table 1: Model parameters for experimental(exp) and atmospheric (atm) scale. L and α arethe edge length and slope angle of the obstacle, re-spectively, ∆x is the horizontal and ∆zm the min-imum vertical grid spacing (vertically stretchedgrid), U0 is the velocity at the top of the domainand Nxyz gives the total number of grid points.

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3 RESULTS

3.1 Simulations on experimentalscale

On experimental scale the simulations were con-ducted for a dry, neutrally stratified boundarylayer exhibiting a logarithmic velocity profile. Theinflow conditions were chosen according to thewind tunnel setup of Ikhwan and Ruck (2006).Figure 4a,b shows statistics of the generated tur-bulent inflow data set which is applied at the inlet.It can be seen that both the simulated mean veloc-ity profile and the normal stresses (lines) comparewell with the wind tunnel results (symbols). Thisconfirms the appropriateness of the applied inflowgeneration technique.

Figure 4: Statistics of the generated turbulentinflow data set (lines) compared to wind tunneldata (symbols). (a) profile of time averaged hor-izontal velocity <u>. (b) profiles of normalisedtotal (subgrid + resolved) standard deviations σu,σv, σw. Red line shows subgrid contribution to σu.

Figure 5 shows the simulated time averagedflow field in x-z-plane along the line of symme-try y/H=0. H denotes the pyramid height andthe colours show the time averaged vertical veloc-ity <w>. Red colours show upward, blue coloursdownward motion. The flow is characterised bya recirculation region in the lee with significantupwelling towards the pyramid’s tip. Moreover,the flow field is highly asymmetric, i.e. the verti-cal extent of the upwelling region is much largeron the leeward compared to the windward side.For the latter, air parcels approaching the pyra-mid at heights lower than the height of the stag-nation point Xs are deflected downward. Basedon these results, argument III, presented in Sect.1, seems to apply. Dynamically driven upwelling

in the lee may indeed be responsible for bannercloud formation.

Nevertheless, from this Eulerian point of view(Fig. 5) one cannot deduce, whether banner cloudformation is possible even for horizontal homo-geneous conditions in terms of temperature andhumidity or whether additional leeward moisturesources or air masses with distinct temperaturesare a necessary condition. Under horizontally ho-mogeneous conditions, the maximum vertical dis-placement of air parcels in the lee must exceedthe displacement on the windward side. Other-wise asymmetric (i.e. banner-like) cloud forma-tion would not be possible. Simply looking atthe vertical extent of the upwelling regions maylead to erroneous conclusions, since the flow fieldalso exhibits significant downwelling along the lat-eral faces of the pyramid (not shown). AdditionalLagrangian-like information is necessary.

Figure 5: Simulated time averaged flow on exper-imental scale along the line of symmetry y/H = 0.Colours show the time averaged vertical velocity<w>

For that reason we additionally advected a pas-sive tracer Φ, satisfying DΦ/Dt = 0. The tracerwas initialised as follows: Φ(xinlt, y, z) = z, i.e.the tracer concentration allocated to each air par-cel equals the starting height z of the air parcel atx = xinlt, where xinlt denotes the inflow bound-ary. The time averaged field of vertical air parceldisplacement ∆z can thus be deduced accordingto:

∆z(x, y, z) = Φ(xinlt, y, z)− < Φ > , (1)

where <Φ> denotes the simulated time averaged3D-field of Φ. Figure 6a,b shows contours of ∆z/Hin the x-z-plane along the line of symmetry and inthe x-y-plane near the pyramid’s tip.

It can be seen that the flow field is highly asym-metric regarding the Lagrangian vertical displace-ment. Air parcels which have been lifted to thetop in the upward branch of the induced vortex on

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Figure 6: (a) Time averaged vertical displace-ment ∆z/H along the line of symmetry y/H = 0.(b) ∆z/H in an x-y-plane at z/H = 0.86. Con-tours of ∆z/H = 0, 0.2, 0.3, 0.4 are addition-ally highlighted. (c) Displacement asymmetry∆zlws − ∆zwws, parallel to the obstacle slopes aty/H = 0.

the leeward side (lws) originate at lower levels (ex-hibit larger ∆z) than air parcels which have beenlifted on the windward side (wws). The asymme-try ∆zlws − ∆zwws is largest slightly below thepyramid’s tip, as shown in Fig. 6c. This is exactlythe place where banner clouds are known to occur.The maximum value of this asymmetry may be re-garded as a measure for the probability of bannercloud formation for the given obstacle geometry,since with increasing asymmetry there is a broaderrange of temperature and humidity profiles whichallow asymmetric (i.e. banner-like) cloud forma-tion. We investigated pyramids of various slopesα and heights H and found that this asymmetryincreases with increasing height and with increas-ing slope of the pyramid. This is in agreement withthe observation that banner clouds are usually re-stricted to very high and steep mountain peaks.

Due to the observed strong asymmetry it can bestated that banner clouds may indeed form underhorizontally homogeneous conditions in terms ofmoisture and temperature.

3.2 Simulations on atmosphericscale

In order to provide further evidence, the simu-lations were repeated on atmospheric scale for amoist boundary layer (BL) with the cloud physicsswitched on. The model was initialised horizon-tally homogeneous without any additional leewardmoisture sources, distinct air masses or radiativeeffects. The chosen background profiles of virtualpotential temperature θv and specific humidity qv

are shown in Fig. 7a.

Figure 7: (a) Environmental profiles of time av-eraged virtual potential temperature θv and spe-cific humidity qv. (b) Stability analysis for θv-profile shown in (a). Γdry is the dry adiabatic lapserate, Γmoist is the moist adiabatic lapse rate anddTv/dzenv is the chosen environmental lapse rate.

These profiles were motivated by measurementswhich were taken by us at Mount Zugspitze duringa banner cloud event. The measurements exhib-ited a well mixed turbulent BL slightly exceed-ing mountain peak height and a stable layer aloft.The vertical gradient of θv above the turbulent BLwas chosen such that the atmosphere was uncon-ditionally (moist) stable for z > 1000 m. This isillustrated in the stability analysis of Fig. 7b. Forz > 1000 m the moist adiabatic lapse rate Γmoist

exceeds the environmental lapse rate dTv/dzenv

which is indicative for a moist stable atmosphere.Without a moist stable layer aloft, triggering ofclouds in the lee would lead to convection, signif-icantly exceeding mountain peak height. As sug-gested in Schween et al (2007), we exclude predom-inantly convective clouds from the species of ban-ner clouds. The absolute values of θ and qv werechosen to yield Lifting Condensation Levels (LCL)which are below obstacle height H for large partsof the boundary layer depth. This is of course a

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necessary condition for banner cloud occurrence.The mean profile of horizontal velocity <u> againwas chosen to be logarithmic up to z = H witha constant value of U0 = 9 ms−1 above. Turbu-lent inflow data based on these mean profiles wereagain created in a precursor run.

Figure 8 shows a snapshot of the simulated cloudstructures. The cloud is visualised by an isosurfaceof the cloud water content qc = 0.01 gkg−1 andcoloured with the instantaneous vertical velocity.The cloud strongly resembles naturally occurringbanner clouds. Except for some pieces of cloudwhich occur on the windward side as a result ofboundary layer turbulence, the cloud is almost en-tirely confined to the lee and is directly attachedto the upper part of the mountain. The colours in-dicate strong upwelling in the immediate lee anddownwelling about one obstacle height downwind.Figure 9 shows the corresponding time averagedcloud water content along the line of symmetryy = 0 m. Once again, the typical banner cloudshape is apparent.

Figure 8: Snapshot of simulated cloud structuresvisualised by an isosurface of the specific cloud wa-ter content (qc = 0.01 gkg−1). Colours show in-stantaneous vertical velocity w. Red colours showupwelling, blue colours downwelling.

Figure 9: Time averaged cloud water contentalong the line of symmetry y = 0 m.

The fact that we are able to numerically repro-duce banner-like cloud structures which stronglyresemble naturally occurring ones, strongly sug-

gests that this experiment captures the mainmechanism of formation. This strongly supportsargument III, since all other mechanisms underdiscussion, including local adiabatic cooling dueto the compressible Bernulli-effect, have been ex-cluded from this simulation. Furthermore, thissimulation clearly shows that, at least for pyra-midal shaped mountain peaks, there is no needfor additional leeward moisture sources, radiativeeffects or distinct air masses in order for bannerclouds to form.

3.3 Impact of moisture physics

As shown in Fig. 10, in situ measurements wereconducted at Mount Zugspitze in order to char-acterise the air masses on both sides of the ridge.N o r t h 9 mS o u t h

3 . 7 mFigure 10: Measuring poles located northern andsouthern to the tip of Mount Zugspitze.

Figure 11a,b shows timeseries of temperatureand specific humidity measured at the poles duringthe 16.10.2008. The solid and dashed lines showmeasurements at the leeward (northern) and wind-ward (southern) side, respectively. During thatday a banner cloud was observed on the northernside. The corresponding time span is shaded ingray. It can be seen that during the banner cloudevent the air in the lee was about 1.5 K warmerand 0.5 gkg−1 moister than the air on the wind-ward side (the additional cloud liquid water qc isnot taken into account). This is in accordance withthe measurements conducted by Joachim Kuttnerin 1946 (pers. comm.); the reason for the observeddifferences on windward versus leeward side wasunclear. Differences in temperature may resultfrom:

• radiative effects or heating of leeward air dueto contact with the ground

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Figure 11: Timeseries of (a) temperature T and(b) specific humidity qv at Mount Zugspitze for thewindward (dashed) and leeward (solid) side. Grayshading denotes time span during which a bannercloud was observed.

• latent heat release

The observed differences in specific humidity couldbe due to:

• additional leeward moisture sources at theground (such as lake Eibsee in the valley tothe north)

• distinct air masses on windward versus lee-ward side with different origins

• larger vertical displacement of air parcels onleeward compared to the windward side

For qualitative comparison, Fig. 12 shows timeseries of T and qt = qv + qc as derived from ournumerical simulations. The selected points are lo-cated on the windward and leeward side next tothe pyramid’s tip (see Fig. 12 for exact positions).It can be seen, that the model is able to qual-itatively reproduce the measurements at MountZugspitze. The air on the leeward side is about0.3 K warmer and about 0.6 gkg−1 moister than

Figure 12: Timeseries of (a) temperature T and(b) total water (qv+qc) next to the pyramid’s tip astaken from the numerical simulation. Dashed line:windward side; Solid line: leeward side. Thicklines indicate time averages.

the air on the windward side. For the numeri-cal simulation these differences can be explainedas follows: Since the oncoming turbulent BL waschosen to be almost neutrally stratified, the differ-ences in temperature can purely be ascribed to lee-ward condensation and corresponding latent heatrelease. The differences in qt result from differ-ences in the Lagrangian vertical displacement onwindward versus leeward side (specific humiditytypically decreases with increasing distance fromthe ground, as given in Fig. 7a). Thus in or-der to qualitatively explain the observations atMount Zugspitze, explanations involving radiativeeffects, distinct air masses or additional leewardmoisture sources are not necessary. Neverthe-less, due to the observed quantitative differencesit can not be ruled out that for quasi-2D ridgeslike Mount Zugspitze other effects, like those men-tioned above, play an additional role.

Our simulations suggest that the differences intemperature and humidity, as observed on MountZugspitze, should be a common feature of banner

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clouds. While differences in moisture are inducedby the dynamics, the differences in temperatureare a result of moisture physics.

From the observed and simulated differences thefollowing consequence results: Since the relativelydry and cold air on the windward side is forcedto flow over the warmer and moister air on theleeward side, banner clouds give rise to a desta-bilisation of the lee near the mountain’s tip. Thisis illustrated in Fig. 13a, where modelled verticalprofiles of the Brunt-Vaisala frequency

N2 =g

θv

∂θv

∂z(2)

are shown for the immediate lee. The thick solidline shows results from the full simulation, aspresented in Sect. 3.2 (here referred to as moist

run). In a saturated atmosphere the moist Brunt-Vaisala frequency N2

m (Durran and Klemp, 1982)is probably a better representation of the ac-tual static stability. For the cloudy region (grayshaded) this parameter is given by the dashed line.It can be seen that the effective Brunt-Vaisala fre-quency is lower when the atmosphere is saturatedthan when it is dry. To explicitly determine theimportance of moist physics (i.e. latent heat re-lease) this model run was reconducted with thesource terms in the θ-equation switched off (herereferred to as dry run). Thus the effect of latentheat release/consumption onto the dynamics wasneglected. The resulting N2-profile is given by thedotted line.

For the moist run, the N2-profile exhibitsa dipole-like structure with positive values for770 m < z < 1120 m. Thus compared to the dryrun, the atmosphere is stabilised within the lowerpart of the cloudy region, while the upper partis destabilised and is even statically unstable onaverage. When considered in terms of the moistBrunt-Vaisala frequency N2

m, the destablizing ef-fect is even larger.

The observed dipole in N2 should impact lee-ward turbulence. Regions with N2 < 0 shouldgive rise to buoyant production of turbulence whileregions with N2 > 0 should give rise to a nega-tive contribution to the TKE budget (in terms ofthe buoyant production term). Figure 13b showsvertical profiles of the total TKE for the moist(solid line) and dry (dotted line) run. These pro-files were derived by averaging over the region487 m < x < 937 m. The TKE-profiles showsimilar shapes, indicating that most of the lee-ward turbulence was generated mechanically inboth runs, associated with flow separation. The

Figure 13: (a) time and space averaged verticalprofiles of the Brunt-Vaisala frequency N2 (solidline) and its moist counterpart N2

m (dashed line)in the mountain’s lee (space averaged for 237 m <x < 687 m at y = 0 m) for the moist run. Thedotted line shows N2 for the dry run. (b) time andspace averaged vertical profiles of resolved TKE forthe moist and dry run (space averaged for 487 m <x < 937 m at y = 0 m). Vertical extent of the cloud(moist run) is shaded in gray.

maxima of both profiles coincide with the verti-cal position of the separating shear layer. Thebuoyant generation/decay of leeward turbulenceseems to be of secondary importance. Neverthe-less, consistent with the N2-profiles shown in Fig.13a, TKE is enhanced in the moist run for the al-titude range with N2 < 0. Likewise, the compar-atively low values of TKE for the moist run in theregion 900 m < z < 1000 m could be a manifesta-tion of the positive N2-anomaly apparent in Fig.13a. Furthermore the vertical position of thoselow TKE values agrees well with the vertical po-sition where N2

m slightly exceeds N2 for the dryrun. We verified that the observed differences inTKE far below the cloudy region do not resultfrom differences in the TKE-profiles upstream ofthe mountain peak; although intermittent clouddevelopment can also be observed far upstream ofthe mountain within the oncoming boundary layer,differences in the upstream TKE-profiles are neg-ligible. Thus the slightly enhanced TKE far belowthe cloudy region (moist run) must be a result ofthe moist physics, too.

Apart from the influence on leeward TKE, onecould imagine that moist physics also have the po-tential to reinforce or sustain the upward branchof the leeward vortex which could help to sustainbanner clouds during episodes with minor dynam-

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Figure 14: Contours of<∆w>=<wmoist>−<wdry> along y = 0 m,showing differences between the time averagedvertical velocity for the moist and dry run, respec-tively. Contour interval: 0.05 ms−1. Solid linesshow <∆w> > 0. The zero line is omitted. Thesolid and dashed thick lines distinguish regionswith up- and downwelling for the dry and moistrun, respectively. The shading highlights areaswith downward motion for the dry run.

ical forcing. In order to estimate the impact ofmoist physics on the mean flow, we compared timeaveraged fields of vertical velocity <w> along theline of symmetry y = 0 m. Figure 14 shows con-tours of <∆w>=<wmoist>−<wdry> which is thedifference in <w> between the moist and dry run,respectively. For the dry run, in addition, regionswith upward and downward motion are separatedby the thick solid line. Regions with downwardmotion are shaded in gray. Correspondingly, thethick dashed line separates up- and downwellingregions for the moist run. While differences be-tween those thick lines provide some informationabout structural differences regarding the positionand shape of up- and downwelling regions, the con-tours emphasise its absolute change in strength.

As can be seen, structural differences betweenthe moist and the dry run are small. Differ-ences are somewhat more pronounced regardingthe strength of the up- and downwelling regions.The downward directed branch of the secondarycirculation is weakened for the moist run, which isindicated by a positive <∆w> in Fig. 14 withinthe gray shaded region. This is of course directlyrelated to latent heat release during cloud for-mation which counteracts the dynamically forceddownwelling in this region. On the other hand, la-tent heat release barely impacts the strength of theupward branch of the secondary circulation. Forthe moist run, the upward branch is only slightlyenhanced nearby the mountain’s tip and its foot.This enhancement is far to small for being an ef-

fective process to systain banner clouds when dy-namical forcing breaks down. Overall, there is amuch stronger impact on the downward- comparedto the upward branch. This is embodied in thechange of the maximum positive and negative ver-tical velocities. Relative to the dry run, the maxi-mum vertical velocity in the upward branch hardlychanges, while the maximum vertical velocity inthe downward branch decreases about 11%.

4 CONCLUSIONS

This paper aims at providing more insight intothe origin and dynamics of orographically inducedbanner clouds. We numerically investigated airflow around idealised pyramidal shaped obstacleson both experimental and atmospheric scale, in-cluding model runs with moisture physics switchedon and off. We were able to present the first LESof a realistically shaped banner cloud. The sim-ulations provide evidence that banner clouds arepredominantly a dynamical phenomenon. Theyform due to dynamically forced upwelling and adi-abatic cooling in the upward branch of a secondaryleeward circulation. Since the flow field was foundto be highly asymmetric regarding the Lagrangianvertical displacement on leeward versus windwardside, banner cloud formation was even possiblefor horizontally homogeneous conditions regard-ing both moisture and temperature. These re-sults lead us to conclude that additional leewardmoisture sources, distinct air masses and radia-tion effects are no necessary condition for ban-ner cloud formation. This contradicts earlier ex-planations given in classical textbooks (e.g. Beer(1974) or Humphreys (1964)), which are basedupon Bernoulli- or mixing fog theories.

A comparison of model runs with the cloudmodel switched on and off indicated that (at leastfor the thermodynamical situation given in Fig.7a) thermodynamics (i.e. latent heat release) donot significantly impact the mean flow and are un-likely to significantly reinforce or sustain the flowfield giving rise to banner cloud formation. Onthe other hand, thermodynamics do impact theleeward stratification. Latent heat release leadsto a destabilisation of the upper part of the ban-ner cloud which results in a moderate increase ofleeward turbulence.

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