(k) Based on Stratification Stratified Flows When two fluids flow one over the other it is called Stratified flow. For example (i) The hot water flowing from a thermal power station, when let into a river or stream. In view of the density difference the hot water flows over cold water (or water at atmospheric temperature). (ii) Similarly in the estuary, the tide waves from sea when enters over the fresh water of the river, the stratified flow occurs (mass density of sea water is 1025 kg/m 3 mass density of fresh water is 1000 kg/m 3 ). Note: One may observe that using the word (upstream and downstream) is a relative term. In estuaries the flow will be bidirectional. (iii) In reservoir the dense sediment laiden flow occurs. This is known as density current which is again an example of stratified flows. (iv) Similarly the hot water is discharged through nozzles at the bottom of a river bed leads to stratification within a short distance. The strength of the density stratification is defined by the gradient Richardson number as ρ g = Ri 2 u ρ in which ρ is the density gradient, u velocity gradient in the vertical direction. (a) If u is small, ρ is large then stratification is stable. Then R i would be large (b) u is large, ρ is small, R i 0, flow system becomes homogeneous or neutral condition. In case of density stratified free surface flows the densimetric Froude number FD is defined which is inverse of Richardson number. u F D = = ρ g L ρ u g ' L ( 1 2) in which ( ),g' g ρ ρ = ρ ρ = ρ and L is the characteristic length. 1 2 ρ1
Richardson Number can also be defined as g θ θ z R = i 2 u z in which u is the velocity θ is the mean potential temperature R represents growth, decay or stability of the turbulent kinetic energy i Homogenous and Stratified flows Flows are classified as homogenous or Stratified on the basis of the variation of density within the flow. If the mass density of fluid in the flow field remains constant in all the spatial dimensions then it is known as homogenous. If the density of the flow varies in any direction then the flow is known as stratified. When the stable density stratification exists i.e., density increases with depth or lighter fluid overlies-- heavier fluid the effectiveness of turbulence mixing is reduced. Example Hot water ρ1 Cold water ρ2 Horizontal Stratification (ρ2 > ρ1) The hot water is discharged from a thermal power / Nuclear power station over the water at ambient temperature to a lake. Here the density is less because of the heating.
Fresh water from river ρ1 Sea water ρ2 (Bi-directional) Horizontal Stratification (ρ2 > ρ1) In estuaries the salt water is brought by the tide and the fresh water from upland is brought by the river. Warm- Isothermic, light epilimnion layer Vertical Stratification Intermediate-Sharp temperature change Meta Limnion layer Cool- (Cold Isothermic oxygen depleted nutrient enriched dark) Hyplimnion layer 0 m epilimnion Meta Limnion (THERMOCLINE LAYER) 1000 m DEEP WATER Hyplimnion layer 4000 m 5 10 15 Temperature in C not to scale B. Chemical stratification (Trophic status) 1. Oligotrophic lake deep depletion can be small. 2. Mesotrophic lake. 3. Eutrophic lake Epilimnion remains well oxygenated can become super saturated during the day as the result of photosynthetic activity.
Seechi disk transparency for above three types of lakes in metre. 1. > 3.7 m. 2. 2. 2 to 3.7 m 3. < 2.0 In range estuaries, a distinct salinity wedge exists as is the norm for many major rivers such as Mississippi, Amazon, Brahmaputra-Ganga-Megna System Godavari. Density current is due to the density gradient. A sediment laden inflow may move throughout the pool as a density current or layer of water with a density slightly different from the body of reservoir water. The density difference may arise due to temperature as well due to mass density of fluid mixture such as sediment in laden water. This can also be called two phase flows. Sea water ρ2 Interface Fresh water ρ1 Highly stratified estuary Lakes A. Patterns of (seasonality) stratification (due to turnover) a. Mononitic lakes (Single mixing)
Heating during Summer Warm water Cool water b. Dimictic pattern (Twice mixing annualy) - Deep lakes ice blocks Cooler water Warm water c. polymictic lakes (continously mixed-shallow lakes) d. oligmictic lakes in trophical areas and e. meromicitic lake (salinity gradients) Example: Red sea in Israel. Reference Water Resources Hand book edited by Lary W Mays Lakes and Reservoirs.