Stratified flows
The flow in many fluids varies with density and depends upon the gravity. Due to which the fluid with lower density is always above the fluid with higher density. Stratified flows are very common such as the Earth's ocean and its atmosphere.[1]
Stratified fluid[edit]
A stratified fluid may be defined as the fluid with density variations in the vertical direction. For example, air and water; both are fluids and if we consider them together then they can be seen as a stratified fluid system. Density variations in the atmosphere profoundly affect the motion of water and air. Wave phenomena in air flow over the mountains and occurrence of smog are the examples of stratification effect in the atmosphere. When a fluid system having a condition in which fluid density decreases with height, is disturbed, then the gravity and friction restore the undisturbed conditions. If however the fluid tends to be stable if density decreases with height.[clarification needed][2]
Upstream motions in stratified flow[edit]
It is known that the sub critical flow of a stratified fluid past a barrier produce motions upstream of the barrier. Sub critical flow may be defined as a flow for which the Froude number based on channel height is less than 1/
Efficient mixing in stratified flows[edit]
Turbulent mixing in stratified flows is described by mixing efficiency. This mixing efficiency compares the energy used in irreversible mixing, enlarging the minimum gravitational potential energy that can be kept in the density field, to the entire change in mechanical energy during the mixing process. It can be defined either as an integral quantity, calculated between inert initial and final conditions or as a fraction of the energy flux to mixing and the power into the system. These two definitions can give different values if the system is not in steady state. Mixing efficiency is especially important in oceanography as mixing is required to keep the overall stratification in a steady-state ocean. The entire amount of mixing in the oceans is equal to the product of the power input to the ocean and the mean mixing efficiency.[4]
Stability criteria for stratified flow[edit]
Wallis and Dobson (1973) estimate their criterion with transition observations that they call “Slugging” and note that empirically the stability limit is described by
Here and where H is channel height and U, h and
According to [TD], a finite wave will grow in a horizontal rectangular channel of height H, when or for inclined pipe. D is the pipe diameter and A is the cross section area. Note that . If , , and this is compatible with the result of Wallis and Dobson(1973) The [TD] overall procedure result to a weak dependence on viscosity, through the calculation of .
[TD] also identify two kinds of stratified flow: stratified smooth (SS) and stratified wavy (SW). These waves, as they say, “are produced by the gas flow under conditions where the velocity of gas is enough to cause waves to form, but slower than that needed for the quick wave growth which leads transition to intermittent or annular flow.” [TD] suggest a standard to predict the transition from stratified smooth to stratified wavy flow, based on Jeffreys’ (1925, 1926) ideas.[5]
Effects of stratification on diffusion[edit]
Density stratification has significant effect on diffusion in fluids. For example, smoke which is coming from a chimney diffuses turbulently if the earth atmosphere is not stably stratified. When the lower air is in stable condition, as in morning or early evening, the smoke comes out and become flat into a long, thin layer. Strong stratification, or inversions as they are called sometimes, restrict contaminants to the lower regions of the earth atmosphere, and cause many of our current air-pollution problems.[6]
References[edit]
- ^ "Stratified Flows".
- ^ Long, Robert R. "Fluid film mechanics". Film Notes for Stratified Flows. 21618.
- ^ Castro, I.P.; Snyder, W.H. (20 May 1986). "J. Fluid Mech". Upstream Motions in Stratified Flow. 187 (5 August 1987)): 487.
- ^ Davies Wykes, Megan S.; Dalziel, Stuart B. (2014). "J. Fluid Mech". Efficient Mixing in Stratified Flows: Experimental Study of a Rayleigh-Taylor Unstable Interface within an Otherwise Stable Stratification. 756: 1027. doi:10.1017/jfm.2014.308. S2CID 53608663.
- ^ Mata, C.; Pereyra, E.; Trallero, J. L.; Joseph, D. D. (March 2002). "Intevep". Stability of Stratified Gas-liquid Flows: 5, 6, 7.
- ^ Long, Robert R. "Fluid film mechanics". Film Notes for Stratified Flows. 21618.