Physical limnology WETA151 L4 Lake hydrodynamics I, water currents Tampereen Pyhäjärvi 1963 Kärkinen 1967 2 1
Several factors causing currents The value of velocity at certain point (x,y,z) vector v at certain time v(t,x,y,z,) is a sum of vectors v i v(t,x,y,z,) = v i (t,x,y,z,) v i, i=1, n, where most important components are v 1 = current generated by wind v 2 = current generated by run off v 3 = convective currents v 4 = currents related to periodic oscillations v 5 v n-1 v n = currents related to. Virtausmalli 2DFemFlow 3 4 2
5 Currents generated by wind Wind is the dominating factor causing lake currents during 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 6 3
7 Wind driven currents: magnitude Air flow causes a shear ( s ) onto the lake surface: where, C d = 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 % from the 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 ==> typical current velocity is about 6-9 cms -1 8 4
Wind driven currents: direction 1(3) Theoretically on an open deep lake in Northern Hemisphere the direction of surface current is 45 o to right form the wind speed when going down in water column the current direction is turning further right and decaying (Ekman-spiral) Lat Wind D e m/s m 4 5 81 4 10 162 60 5 23 60 10 46 9 Wind driven currents: direction 2(3) In practice the bottom morphology determines the current direction in a lake in shallow lakes (polymicitic, non stratified) the current follows wind on shallow regions compensation (=return) current is found on deepest areas or on wind sheltered areas R u S 1 Suode njoki Riihonjoki C T M C S 3 C S Lavij ki 10 5
Wind driven currents: direction 3(3) Stratified lakes the same structure is found in epilimnion as in shallow lakes, currents are highest there, when compared to metalimnetic and hypolimnetic currents in metalimnion the currents are sporadic due to the indirect effects of epilimnetic currents and periodical oscillations in upper part of hypolimnion the currents are slowly following the currents in epilimnion and metalimnion current pattern is responding to the changes of wind with a typical lag of one to three hours in our lakes The highest current speeds are found at steepest slopes and in narrow straights 11 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 amount of river water currents calculated by continuity equation steady as compared to the wind generated currents important during winter, when lake is not affected by wind, also always in lakes with a short retention time v i =mean velocity in the cross section i A i =area of the cross section i 12 6
Example from Saimaa Annual mean outflow of Lake Saimaa ( Q) at Tainionkoski is about 500 m 3 s -1. What is the mean run off generated current in a straight with 5 m depth and 1000 m width? v= Q/A = 500 m 3 s -1 /(5 m * 1000 m) = 500/5000 ms -1 = 10.0 cms -1 13 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 thus increased and water sinks, typically down to the metalimnion In summer time in shallow bays water temperature will increase to a higher level than that in deep waters, also cooling of the waters in shallow bays happens quicker that on deep waters ==> this leads to horizontal currents as the cooled dense water seeks water layer with equivalent density and travels to the deep areas of the lake 14 7
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 covered period Their typical speed is 1 cms -1 ==> during 160 days (= normal ice cover period) the travel distance could be 138 km!! In practice threshold at bottom will stop the flow and accumulation to deep basins will happen 15 Convection cells during summer night 16 8
Periodic oscillations 1(2) All water bodies (cups, swimming pools, lakes and seas have their characteristic oscillation periods Steady wind is causing the tilting of lake surface along the downwind Surface seiche movement, is formed when wind shear along the lake axis is relieved This happens as wind is ceasing or wind direction is turning Lake Jyväsjärvi:Lx= 3800 m, Ly=500 m, mean depth = 8.7 m. Wind: West 5 ms -1, air density = 1 kgm -3, C D = 0.001 s = 0.025 Nm -2 at 20 o C is 998. 28 kg/ m 3 h =1 mm. Period (n=1): 0.21 h 17 Periodic oscillations 2(2) Typical period for surface seiche is tens of minutes to hour in 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 100 m 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, Lake Erie 18 9
Esimerkkejä/Examples Järvi/Lake Pituus/Len gth Tuuli/W ind Keskisyvyys/ mean depth Pinnan nousu/amplitude m ms -1 m m h Periodi/P eriod (n=1) 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 19 Exercise Can water from Lake Päijänne reach Jyväsjärvi during 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 20 10
Lake Tanganyika Surface area=32 900 km 2, mean depth=572 m, maximum depth=1472 m, Watershed area= 263 000 km 2 Meromictic, surface temperature about 26 28 o C, hypolimnetic temperature 23.25 o C, thermocline depth around 50 120 m, Two main seasons: dry May- Sept and wet Very clear water Highly productive lake, important protein source for more than 10 Mill. people 21 Lake Tanganyika Research for Fisheries (LTR) by FAO in 1992-1996. Hydro and thermodynamics: understand the upwelling phenomena of the nutrient rich deep waters and their effects to biological production develop flow and upwelling model for predictions Lake Tanganyika Biodiversity Project/LTBP by UNDP/GEF. Hydro and thermodynamics in 1996-97: develop lake wide circulation model determine the transport and mixing river waters and suspended solid load Field courses in tropical limnology 2000 and 2001, joint effort by Universities of Kuopio, Turku, Jyväskylä and Helsinki 22 11
Surface seiche of Lake Tanganyika: typical period 4.7 h, phase sift of 180 0 between Bujumbura and Mplungu 23 Other currents 2(2): Internal seiches Are formed in a stratified lake, metalimnion is tilted to the opposite direction as compared to the surface seiche Typical amplitude is order of metres, typical period in Finnish lakes is from hours to tens of hours (=days) Can cause high local currents in narrow straights in the deep parts of the lake also can cause important vertical transport of substances (eq. Hypolimnetic pumping of nutrients) L=characteristick length of the basin n = mode h 1 =thickness of mixed layer or epilimnion h 2 =thickness of hypolimnion 1 =density of epilimnion 2 =density of hypolimnion 24 12
Internal seiche (Podsetchcine & Huttula, 1996): At Mplungu buoy during dry season the period for uninodal internal seiche was 23.4 d and during wet season 34.8 d Kigoma buoy during wet season period was 26.3 d 25 Other currents 1(2): Currents and waves 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 is seen current fluctuation!! 26 13