physical limnology weta151 - jyväskylän...

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Physical limnology

WETA151

L4

Lake hydrodynamics I, watercurrents

1/15/2015 Timo Huttulahttp://personal.inet.fi/yritys/thec

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•Kärkinen 1967

•TampereenPyhäjärvi1963

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Several factors causing currents

• The value of velocity at certain point (x,y,z) vector v atcertain time v(t,x,y,z,) is a sum of vectors vi

• v(t,x,y,z,) = vi(t,x,y,z,)• vi , i=1, n, where most important components are• v1= current generated by wind• v2= current generated by run off• v3= convective currents• v4= currents related to periodic oscillations• v5• vn-1• vn= currents related to …. Virtausmalli 2DFemFlow


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Currents generated by wind

• Wind is the dominating factor causing lake currentsduring open water period

• Wind field over the lake is seldom uniform– Sheltering effects ==> the shelter effects to a distance,

which is 20*the height of the sheltering e object– Trees 20 m ==> shelter effect at maximum to 400 m– Considering all wind directions ==> lake with 1 km open

area is affected directly with wind,– On smaller lakes wind affects only indirectly– Air stratification affects to the sheltering

• Channelling effects due to the topography

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Wind driven currents: magnitude

• Air flow causes a shear ( s) onto the lake surface:

– where, Cd = drag coefficient, about 0.001, air = density of air f(air pressure,humidity and temperature) about 1 kgm-3 , U= wind velocity (ms-1)

• In practice surface current speed is about 2-3 % fromthe wind speed

• Typical current speed: 5 cm/s = 180 m/h = 4320 m/d =30 km/week

• Mean wind speed in Finland is about 3.2 ms-1 ==> typicalcurrent velocity is about 6-9 cms-1

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Wind driven currents:direction 1(3)

• Theoretically on an opendeep lake in NorthernHemisphere the direction ofsurface current is 45 o toright form the wind speed

• when going down in watercolumn the current directionis turning further right anddecaying (Ekman-spiral)

Lat Wind De

m/s m

4 5 81

4 10 162

60 5 23

60 10 46


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Wind drivencurrents: direction

2(3)• In practice the bottom

morphology determinesthe current direction in alake

– in shallow lakes(polymicitic , nonstratified)

– the current follows windon shallow regions

– compensation (=return)current is found ondeepest areas or on windsheltered areas

Suodenjoki

Riihonjoki

Lavijki

S3

S1

Ru

CSC

T

CM

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Wind driven currents: direction 3(3)• Stratified lakes

– the same structure is found inepilimnion as in shallow lakes,currents are highest there, whencompared to metalimnetic andhypolimnetic currents

– in metalimnion the currents aresporadic due to the indirect effects ofepilimnetic currents and periodicaloscillations

– in upper part of hypolimnion thecurrents are slowly following thecurrents in epilimnion and metalimnion

– current pattern is responding to thechanges of wind with a typical lag ofone to three hours in our lakes

• The highest current speeds are found atsteepest slopes and in narrow straights


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Run off generated currents

• called also as hydrological currents• tributary waters flowing through the

lake ( Q)• important during ice covered period

and in shallow lakes with high amountof river water

• currents calculated by continuityequation

• steady as compared to the windgenerated currents

• important during winter, when lake isnot affected by wind, also always inlakes with a short retention time

vi =mean velocity inthe cross section i

Ai =area of the crosssection i

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Example from Saimaa

• Annual mean outflow of Lake Saimaa ( Q) atTainionkoski is about 500 m3s-1.

• What is the mean run off generated current in astraight with 5 m depth and 1000 m width?

• v= Q/A = 500 m3 s-1/(5 m * 1000 m) =500/5000 ms-1 = 10.0 cms-1


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Convective currents 1(2)

• Caused by density differences in water• In summer time vertical mixing in night as surface

water is cooling down during the night, density is thusincreased and water sinks, typically down to themetalimnion

• In summer time in shallow bays water temperature willincrease to a higher level than that in deep waters, alsocooling of the waters in shallow bays happens quickerthat on deep waters ==> this leads to horizontalcurrents as the cooled dense water seeks water layerwith equivalent density and travels to the deep areas ofthe lake

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Convective currents 2(2)

• Sewage water can be warmer as ambient water ==>sinks to the bottom or to the equal density layer ==>flows slowly in thin concentrated layer long distances

• Convective currents are important during ice coveredperiod

• Their typical speed is 1 cms-1 ==> during 160 days (=normal ice cover period) the travel distance could be 138km !! In practice threshold at bottom will stop the flowand accumulation to deep basins will happen


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Convection cellsduring summer

night

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Periodic oscillations 1(2)

• All water bodies (cups, swimmingpools, lakes and seas have theircharacteristic oscillation periods

• Steady wind is causing the tilting oflake surface along the downwind

• Surface seiche movement, isformed when wind shear along thelake axis is relieved

• This happens as wind is ceasing orwind direction is turning

Lake Jyväsjärvi:Lx= 3800 m,Ly=500 m, mean depth = 8.7m.

Wind: West 5 ms-1, air density= 1 kgm-3, CD = 0.001 s =0.025 Nm-2

at 20 oC is 998. 28 kg/ m3

h =1 mm. Period (n=1):0.21 h


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Periodic oscillations2(2)

• Typical period for surface seiche is tens of minutes to hourin Finnish lakes

• Typical amplitude is about centimetre• Highest velocities in a straight, which is located at a node,

can be about 5 cms-1

– ==> during an oscillation period water travels only about 100m and then comes back

– ==> importance to local mixing not to the transportation• When interfering with wind periodicity, can cause rapid

and significant water level rise O(2-4 m), Neva-bay, LakeErie

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Esimerkkejä/Examples

Järvi/Lake Pituus/Length

Tuuli/Wind

Keskisyvyys/mean depth

Pinnannousu/Amplitude

Periodi/Period(n=1)

m ms-1 m m h

Päijänne 110000 5 18 0.05 4.6

Päijänne 110000 10 18 0.19 4.6

Tanganyika 632000 5 532 0.02 4.9

Tanganyika 632000 10 532 0.07 4.9

Jyväsjärvi 3800 5 7.8 0.002 0.23

Jyväsjärvi 3800 10 7.8 0.008 0.23

Exercise

• Can water from Lake Päijänne reach Jyväsjärviduring a half seiche period of Lake Päijänne

• Use karttapaikka• Determine length of Äijälänsalmi straight• Take velocity to be 0,1 m/s and 0,05 m/s


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Lake Tanganyika• Surface area=32 900 km2, mean

depth=572 m, maximumdepth=1472 m,

• Watershed area= 263 000 km2

• Meromictic, surface temperatureabout 26…28 oC, hypolimnetictemperature 23.25 oC,thermocline depth around50…120 m,

• Two main seasons: dry May-Sept and wet

• Very clear water• Highly productive lake,

important protein source formore than 10 Mill. people


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• Lake Tanganyika Research forFisheries (LTR) by FAO in 1992-1996.Hydro and thermodynamics:

– understand the upwelling phenomena of thenutrient rich deep waters and their effects tobiological production

– develop flow and upwelling model forpredictions

• Lake Tanganyika BiodiversityProject/LTBP by UNDP/GEF. Hydroand thermodynamics in 1996-97:

– develop lake wide circulation model

– determine the transport and mixing riverwaters and suspended solid load

• Field courses in tropical limnology 2000and 2001, joint effort by Universities ofKuopio, Turku, Jyväskylä and Helsinki

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• Surface seiche of Lake Tanganyika: typicalperiod 4.7 h, phase sift of 1800 betweenBujumbura and Mplungu


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Other currents 2(2):Internal seiches

• Are formed in a stratified lake,metalimnion is tilted to theopposite direction as comparedto the surface seiche

• Typical amplitude is order ofmetres, typical period in Finnishlakes is from hours to tens ofhours (=days)

• Can cause high local currentsin narrow straights in the deepparts of the lake also can causeimportant vertical transport ofsubstances (eq. Hypolimneticpumping of nutrients)

L=characteristick length of the basin

n = mode

h1=thickness of mixed layer orepilimnion

h2=thickness of hypolimnion

1=density of epilimnion

2=density of hypolimnion

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• Internal seiche (Podsetchcine & Huttula, 1996):– At Mplungu buoy during dry season the period for

uninodal internal seiche was 23.4 d and during wetseason 34.8 d

– Kigoma buoy during wet season period was 26.3 d


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Other currents 1(2): Currents andwaves caused by short term regulation

• Meaning full on our narrow water courses• Near Lappeenranta the short term regulation

at Tainionkoski in the distance of 40 km isseen current fluctuation!!

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