Stratified flow
A stratified fluid may be defined as the fluid with density variations in the vertical direction.
The flow in many fluids varies with density and depends upon the gravity due to which the fluid with lower density is always above of the fluid with higher density. Stratified flows are very common such as the Earth's ocean and its atmosphere.
A stratified fluid may be defined as a fluid with density variations in the vertical direction. For example, air and water considered together can be seen as a stratified fluid system. Density variations in the atmosphere profoundly affect the motion of water and air. Wave phenomena in the air flow over the mountains and occurrences of smog are examples of the stratification effect in the atmosphere.
When a fluid system in which fluid density decreases with height is disturbed, gravity and friction restore the undisturbed conditions.
It is known that the sub critical flow of a stratified fluid past an barrier produce motions upstream of the barrier. Sub critical flow is here may be defined as a flow for which the Froude number based on channel height is less than 1/π, so that one or more stationary lee waves would be present. Some of the upstream motions do not decompose with the distance upstream. These ‘columnar’ modes have zero frequency and a sinusoidal structure in the direction of the density gradient ; they effectively lead to a continuous change in upstream conditions. If the barrier is two-dimensional (i.e. of infinite extent in the direction perpendicular to the upstream flow and the direction of density gradient), inviscid theories show that the length of the upstream region affected by the columnar modes increases without bound as t->infinity. Non-zero viscosity (and/or diffusivity) will, however, limit the region affected, since the wave amplitudes will then slowly decay.
Turbulent mixing in stratified flows is describe 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.
Wallis and Dobson (1973) estimate their criterion with transition observations that they call “Slugging” and note that empirically the stability limit is described by
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