Transient stratification force on particles crossing a density interface

Abstract Laboratory observations of the leeside hydraulic jump indicate it consists of a statistically stationary turbulent motion in an overturning wave. From the point of view of the shallow-water equations (SWE), the hydraulic jump is a discontinuity in fluid-layer depth and velocity at which kinetic energy is dissipated. To provide a deeper understanding of the leeside hydraulic jump, three-dimensional numerical solutions of the Navier–Stokes equations (NSE) are carried out alongside SWE solutions for nearly identical physical initial-value problems. Starting from a constant-height layer flowing over a two-dimensional obstacle at constant speed, it is demonstrated that the SWE solutions form a leeside discontinuity owing to the collision of upstream-moving characteristic curves launched from the obstacle. Consistent with the SWE solution, the NSE solution indicates the leeside hydraulic jump begins as a steepening of the initially horizontal density interface. Subsequently, the NSE solution indicates overturning of the density interface and a transition to turbulence. Analysis of the initial-value problem in these solutions shows that the tendency to form either the leeside height–velocity discontinuity in the SWE or the overturning density interface in the exact NSE is a feature of the inviscid, nonturbulent fluid dynamics. Dissipative turbulent processes associated with the leeside hydraulic jump are a consequence of the inviscid fluid dynamics that initiate and maintain the locally unstable conditions.

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On turbulent entrainment at a stable density interface

Journal of Fluid Mechanics ◽

10.1017/s0022112077000433 ◽

1977 ◽

Vol 79 (04) ◽

pp. 753 ◽

Cited By ~ 164

Author(s):

L. H. Kantha ◽

O. M. Phillips ◽

R. S. Azad

Keyword(s):

Density Interface ◽

Turbulent Entrainment

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Turbulence, waves and mixing at shear-free density interfaces. Part 2. Laboratory experiments

Journal of Fluid Mechanics ◽

10.1017/s0022112097006526 ◽

1997 ◽

Vol 347 ◽

pp. 235-261 ◽

Cited By ~ 27

Author(s):

J. L. MCGRATH ◽

H. J. S. FERNANDO ◽

J. C. R. HUNT

Keyword(s):

Flow Visualization ◽

Richardson Number ◽

Breaking Waves ◽

Companion Paper ◽

Motion Field ◽

Qualitative Properties ◽

Frequency Spectra ◽

Low Frequencies ◽

Density Interface ◽

Quantitative Measurements

A laboratory experimental study was performed to investigate turbulence, waves and mixing at a sharp density interface (with a jump in buoyancy Δb), subjected to shear-free turbulence induced by oscillating grids with typical velocity and length scales of uH and LH, respectively. The cases where turbulence is present on one side (single-sided stirring) or on both sides (double-sided stirring) of the interface were considered. Extensive flow visualization studies and quantitative measurements were performed on the motion field and mixing characteristics at the interface. It was found that, rather than any one mechanism controlling the mixing process, different mechanisms (namely engulfment, generation of waves and their breaking, eddy impingement and Kelvin–Helmholtz billows) play dominant roles over different ranges of the bulk Richardson number Ri(Ri =ΔbLH/u2H). For the Ri range where wave generation is significant, certain hypotheses and predictions of the companion paper by Fernando & Hunt (1997) were tested in detail, by flow visualization studies of the qualitative properties of interfacial motions and quantitative measurements of the r.m.s. fluctuations of interfacial velocity and displacement, the local gradient Richardson number within the stratified layer, the frequency spectra and the related fractal properties of the interface. The results are consistent with the hypothesis that, at high values of Ri(>35), the density interface consists of linear internal waves driven by turbulence at high frequencies and breaking waves with sharp horizontal gradients of density at low frequencies.

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