scholarly journals Transient solutions for stratified fluid flows

1976 ◽  
Vol 80B (1) ◽  
pp. 79
Author(s):  
David W. Fox
Keyword(s):  
Fluid Flows ◽  
Stratified Fluid ◽  
Transient Solutions

The hydraulics of a stratified fluid flowing through a contraction

1993 ◽  
Vol 251 ◽  
pp. 355-375 ◽  
Author(s):  
Laurence Armi ◽  
Richard Williams
Keyword(s):  
Flow Rate ◽  
Fluid Flows ◽  
Stratified Fluid ◽  
Wave Mode ◽  
Similar Solution ◽  
Constant Density ◽  
Self Similar Solution ◽  
Hydraulic Theory ◽  
Self Similar

The steady hydraulics of a continuously stratified fluid flowing from a stagnant reservoir through a horizontal contraction was studied experimentally and theoretically. As the channel narrows, the flow accelerates through a succession of virtual controls, at each of which the flow passes from sub-critical to supercritical with respect to a particular wave mode. When the narrowest section acts as a control, the flow is asymmetric about the narrowest section, supercritical in the divergent section and self- similar throughout the channel. With increased flow rate a new enclosed self-similar solution was found with level isopycnals and velocity uniform with depth. This flow is only symmetric in the immediate neighbourhood of the narrowest section, and in the divergent section remains supercritical with respect to higher internal modes, has separation isopycnals and splits into one or more jets separated by regions of stagnant, constant-density fluid. Flows which are subcritical with respect to lowest modes can also be asymmetric about the narrowest section for higher internal modes. The experiments are interpreted using steady, inviscid hydraulic theory. Solutions require separation isopycnals and regions of stationary, constant-density fluid in the divergent section.

Horizontal jets and vortex dipoles in a stratified fluid

1991 ◽  
Vol 227 ◽  
pp. 543-566 ◽  
Author(s):  
S. I. Voropayev ◽  
Ya. D. Afanasyev ◽  
I. A. Filippov
Keyword(s):  
Fluid Flows ◽  
Stratified Fluid ◽  
Theoretical Explanation ◽  
Thymol Blue ◽  
High Concentration ◽  
Governing Parameter ◽  
Aluminium Powder ◽  
Density Distributions ◽  
Vortex Dipoles ◽  
Short Period

When a horizontal force is applied locally to some volume of a viscous densitystratified fluid, flows with high concentration of vertically oriented vorticity (vortex dipoles) are generated. The processes of generation and evolution with time of these unsteady flows in a stratified fluid are studied. A convenient way to produce and study these flows in the laboratory is to use a submerged horizontal jet as a ‘point’ source of momentum. The main governing parameter (the ‘force’) is easily controlled in this case. Two regimes were studied: starting jets with dipolar vortex fronts (the force acts continuously) and impulsive vortex dipoles (the force acts for a short period of time). A conductivity microprobe, aluminium powder, shadowgraph, thymol-blue and other techniques have been used to measure the velocity and density distributions in the flows. It is found that in both regimes the flows are self-similar: the lengthscale of the flows increases with time as t½ for starting jets and as t1/3 for vortex dipoles. Detailed information about the generation mechanism, kinematics and dynamics of the flows is obtained. On the basis of similarity principles a theoretical explanation of the experimental results is given. The theory is in good agreement with the results obtained.

scholarly journals A limitation on Long's model in stratified fluid flows

1971 ◽  
Vol 48 (1) ◽  
pp. 161-179 ◽  
Author(s):  
Harvey Segur
Keyword(s):  
Froude Number ◽  
Barrier Height ◽  
Density Gradient ◽  
Dynamic Pressure ◽  
Fluid Flows ◽  
Critical Value ◽  
Stratified Fluid ◽  
Lee Wave ◽  
Finite Barrier ◽  
Internal Froude Number

The flow of a continuously stratified fluid into a contraction is examined, under the assumptions that the dynamic pressure and the density gradient are constant upstream (Long's model). It is shown that a solution to the equations exists if and only if the strength of the contraction does not exceed a certain critical value which depends on the internal Froude number. For the flow of a stratified fluid over a finite barrier in a channel, it is further shown that, if the barrier height exceeds this same critical value, lee-wave amplitudes increase without bound as the length of the barrier increases. The breakdown of the model, as implied by these arbitrarily large amplitudes, is discussed. The criterion is compared with available experimental results for both geometries.

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