E ec s o Rayleigh numbe on he mal siphons in T iangula Wa e Bodies
Vassilios PAPAIOANNOU¹, Panagio is PRINOS²
¹ Senio Resea che , In o ma ion Technologies Ins i u e/ CERTH, Thessaloniki, G eece, email: aspapa@i i.g
² Eme i us P o esso , Dep . o Ci il Eng./ AUTh, Thessaloniki, G eece, email: p inosp@ci il.au h.g
h ps://sci o um.ne /e en /ECWS-9
INTRODUCTION & AIM
CONCLUSION
FUTURE WORK / REFERENCES
METHOD
Na u al con ec ion in enclosed o semi-enclosed wa e bodies (e.g., lakes, ese oi s) d i es
e ical and ho izon al hea and momen um exchange. Su ace cooling c ea es densi y
di e ences be ween shallow and deep egions, gene a ing he mal siphons [1], [2]. In iangula
o sloping-bo om basins, nea sho e a eas cool as e , igge ing downslope g a i y cu en s and
upwelling in deepe zones, a ec ing mixing, s a i ica ion, and hea dis ibu ion [3]. Mos
s udies ocus on low o mode a e Rayleigh numbe s (Ra) [4], while high-Ra u bulen lows
emain less explo ed.
This s udy aims o:
1. Examine he mal siphon o ma ion unde su ace cooling in iangula basins a high Ra.
2. Compa e La ge Eddy Simula ion (LES) wi h WALE subg id modeling o 2D DNS esul s.
3. Analyze empe a u e and low ields o assess in e ac ions be ween downslope cu en s
and con ec i e plumes.
Fu u e wo k will ex end simula ions o 3D, explo e LES-RANS hyb ids, and in es iga e e ec s o
une en cooling, wind, and seasonal changes, as well as ex eme Ra and long- e m cooling o
be e unde s and u bulen he mal siphons.
[1] Mao, Y., Lei, C., & Pa e son, J. C. (2010). Uns eady nea -sho e na u al con ec ion induced by
su ace cooling. Jou nal o Fluid Mechanics, 642,213–233.
h ps://doi.o g/10.1017/S0022112009991765
[2] Papaioannou, V., & P inos, P. (2023). Na u al con ec ion due o su ace cooling in sloping
wa e bodies wi h ege a ion. Jou nal o Hyd aulic Resea ch, 61,382–395.
h ps://doi.o g/10.1080/00221686.2023.2222094
[3] Ulloa, H. N., Ramón, C. L., Doda, T., Wües , A., & Bou a d, D. (2022). De elopmen o
o e u ning ci cula ion in sloping wa e bodies due o su ace cooling. Jou nal o Fluid
Mechanics, 930, A18.h ps://doi.o g/10.1017/j m.2021.883
[4] Doda, T., Ulloa, H. N., Ramón, C. L., Wües , A., & Bou a d, D. (2023). Pene a i e con ec ion
modi ies he dynamics o downslope g a i y cu en s. Geophysical Resea ch Le e s, 50.
h ps://doi.o g/10.1029/2022GL100633
The nume ical models o simula ing he mal siphons in wa e bodies, pa icula ly a high
Rayleigh numbe s ( u bulen na u al con ec ion), all in o wo ca ego ies:
1. La ge Eddy Simula ion (LES) models (2D), which equi e signi ican compu a ional
esou ces, and
2. Reynolds-A e aged Na ie –S okes (RANS) models, coupled wi h a u bulence model o
accoun o u bulence e ec s.
In his s udy, La ge Eddy Simula ion (LES) is employed o in es iga e he quasi-s eady s a e
beha io o he mal siphons induced by su ace cooling a high Ra numbe s, using he WALE
model o accoun o subg id-scale u bulence and compa es esul s wi h 2D DNS. Simula ions
use a ime s ep Δ = 0.1 s (CFL condi ion) o e 30,000 s. Bounda y condi ions (Fig. 1) a e igid,
non-slip, adiaba ic sides and bo om (∂𝑇/∂𝑛=0), a s ess- ee wa e su ace wi h an applied
he mal lux (−∂𝑇/∂𝑦=B0/(gβk), and an ini ially mo ionless wa e body a 293.15 K.
Figu e 1. Cha ac e is ic low egions (le ) and concep ual model ( igh )
•The su ace buoyancy ou low, B0(m2/s3)is de ined as B0=gβI0/ρ0Cp,whe e g: g a i a ional
accele a ion [m/s2], β: he mal expansion coe icien [1/K]: su ace cooling lux I0[W/m2], ρ0:
luid densi y [kg/m3], Cp: wa e speci ic hea capaci y a cons an p essu e [J/(kg⋅K)].
•The Rayleigh numbe , Ra is de ined as Ra =𝐵0ℎ4/(𝜈𝑘2), whe e: 𝜈: kinema ic iscosi y [m2/s],
h: maximum wa e dep h [m], k: he mal di usi i y [m2/s].
•The P and l numbe , 𝑃𝑟 is P =𝜈/𝑘= 7.07 o wa e .
•Cha ac e is ic ime scales we e es ima ed ollowing Ulloa e al. [3] and adap ed o iangula
wa e bodies o :
▪ he onse o he mal ins abili ies a he ee su ace, τB≈ √657.5 √(ν/B0).I dec eases
om 1813.1 s up o 57.3 s wi h inc easing Ra om 1010 up o 1013
▪ he ime o plumes o each he bo om, τRB ≈h2/3/B01/3.I dec eases om 1710.0 s up
o 171.0 s wi h inc easing Ra numbe
▪ he quasi-s eady s a e, τSS (≈2L2/3/B01/3 ,L= o al body leng h). I also dec eases om
15873.7 s up o 1587.4 s wi h inc easing Ra numbe .
Figu e 5 shows he la ge ci cula ion pa e n o he highes Ra numbe . Bo h DNS and LES
cap u e he pe sis en la ge-scale ci cula ion, hough DNS e eals ansien small-scale o ices
mos ly absen in LES.
Figu e 2. Tempe a u e Ra io DNS (uppe ) & LES (lowe ) (Ra = 10¹¹, /τss = 1.07)
Figu e 3. S eam- unc ion DNS (uppe ) & LES (lowe ) (Ra = 10¹¹, /τss = 1.07)
Figu e 4. Tempe a u e a io DNS (uppe ) & LES (lowe ) (Ra = 10¹³, /τss = 5.04)
Figu e 5. S eam- unc ion DNS (uppe ) & LES (lowe ) (Ra = 10¹³, /τss = 5.04)
Fo Ra =10¹¹ a /τss = 1.07 he DNS ield exhibi s sha p he mal plumes and ine-scale
empe a u e luc ua ions, cap u ing he small-scale u bulen s uc u es. In con as , he LES
smoo hs hese g adien s due o i s subg id-scale modeling, which il e s ou he smalles scales
o mo ion. Despi e hese di e ences, bo h DNS and LES accu a ely ep oduce he g a i y
cu en esponsible o lushing he bo om laye .
Wi h inc easing Ra (Ra =10¹3), Bo h cases exhibi simila la ge-scale low s uc u es and he mal
pa e ns, indica ing compa able o e all mixing beha io . The DNS igu e shows sligh ly coole
egions and sha pe spa ial g adien s, e lec ed by he p esence o mo e blue- oned a eas.
RESULTS & DISCUSSION
The e ec o Ra numbe on empe a u e and s eam- unc ion o he wo highes Ra numbe s
s udied is shown in he ollowing igu es. Figu e 2 shows he empe a u e o Ra=1011. The DNS
empe a u e ield shows sha p plumes while he LES smoo hs g adien s and unde p edic s he
peak by ~6%, sligh ly damping small-scale hea ans e . The DNS s eam- unc ion (Fig. 3) shows
in ica e o ices and seconda y eddies, highligh ing in ense high-Ra u bulence. LES cap u es
ci cula ion, bu misses smalle -scale ea u es, wi h peak s eam- unc ion ψ₍DNS₎(=ψ/ρ0qc) equal
o 2.88 while is equal 2.82 o LES. The empe a u e Τ/Τ0(Fig. 4) ields a /τss = 5.04 show ha
he DNS exhibi s ine he mal s uc u es and la ge empe a u e a ia ions, while he LES
appea s smoo he and wa me . The LES ield spans a simila ange (0.983≤𝑇/𝑇0≤1.0) wi h ha o
DNS (0.982≤𝑇/𝑇0≤1.0).
