Self-preservation in stratified momentum wakes

Meunier, Patrice; Diamessis, Peter; Spedding, Geoffrey

doi:10.1063/1.2361294

Cited by 41 publications

(47 citation statements)

References 32 publications

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“…Specifically, the initial mean and fluctuating velocity profiles are constructed to represent a self-similar axisymmetric nonstratified wake. 2,25 The erroneous assumption of self-similarity this close to the towed body is not critical for the purpose of these simulations, which focus on the intermediate-to-late time wake. Moreover, the specific choice of initial condition, described in detail elsewhere, 9 is found to reproduce a physically accurate transition into the NEQ regime, during and after which the numerical simulations exhibit power laws for the mean flow scaling and a vorticity field structure that agree very well with their experimental counterparts.…”

Section: B Numerical Methods and Initializationmentioning

confidence: 99%

“…1,2 Initially, in the "threedimensional" ͑3D͒ regime, the flow behaves very much like a wake in an unstratified fluid that grows unconstrained at the same rate in both spanwise and vertical directions. As the turbulence stirs the isopycnal surfaces and displaces them from their equilibrium position, the "nonequilibrium" ͑NEQ͒ regime is established, whereupon the flow begins to experience the restoring influence of buoyancy forces and the vertical growth of the wake is suppressed.…”

Section: Introductionmentioning

confidence: 99%

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Spatial characterization of vortical structures and internal waves in a stratified turbulent wake using proper orthogonal decomposition

2010

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Proper orthogonal decomposition ͑POD͒ has been applied to two-dimensional transects of vorticity obtained from numerical simulations of the stratified turbulent wake of a towed sphere at a Reynolds number Re= ͑UD͒ / =5ϫ 10 3 and Froude number Fr= 2U / ͑ND͒ =4 ͑U and D are characteristic velocity and length scales and N is the stratification frequency͒. At 231 times during the interval 12Ͻ Nt Ͻ 35, the streamwise and spanwise vorticity components are sampled on span-depth ͑yz͒ and stream-depth ͑xz͒ planes, respectively, at select streamwise and spanwise locations. POD appears to provide a natural decomposition of the vorticity field inside the wake core in terms of the relative influence of buoyancy on flow dynamics. The geometry of the individual eigenmodes shows a vorticity structure that is buoyancy-controlled at the lowest modes and is increasingly more actively turbulent as modal index is increased. In the wake ambient, i.e., the initially quiescent region outside the turbulent wake, the geometry of the POD modes consists of distinct internal wave rays whose angle to the horizontal is strongly dependent on modal index. Reconstruction of vorticity fields from subranges of POD modes indicates that, both inside the wake core but also in the wave-dominated ambient, each modal subrange is not only associated with a particular flow structure but also a characteristic timescale of motion. These preliminary findings suggest that POD may be a highly suitable alternative to globally defined basis functions in analyzing spatially localized internal wave fields emitted from a turbulent source that are also localized in space. In particular, it may serve as a platform toward an improved understanding of two fundamental questions associated with the nonequilibrium regime of stratified wake evolution: the structural transitions of the vorticity field within the wake core and the radiation of internal waves by the wake.

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Section: B Numerical Methods and Initializationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Spatial characterization of vortical structures and internal waves in a stratified turbulent wake using proper orthogonal decomposition

2010

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“…Similar flow anisotropization has been observed in stratified momentum wakes (Spedding 1997(Spedding , 2001) where the vertical spreading of the wake decreases while the horizontal spreading remains almost unaffected by stratification. Assuming the scales of the horizontal and vertical spreading of the wake proportional to the respective horizontal and vertical eddy viscosities (Meunier et al, 2006), one can trace this phenomenon directly to the behavior of ν h and ν z shown in Figure 2. With regard to the vertical mixing, both ν z and κ z decrease for Ri > 0.1.…”

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confidence: 94%

On the critical Richardson number in stably stratified turbulence

Galperin

Sukoriansky

Anderson

2007

Atmospheric Science Letters

236

146

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The gradient Richardson number, Ri, defined asis a measure of the relative strength of the density gradient in stably stratified shear flows. Here, N 2 = −g(∂ρ/∂z )/ρ 0 is the square of the buoyancy, or Brunt-Väisälä frequency, g is the gravity acceleration, ρ is the fluid density, ρ 0 is the reference density, S is the vertical shear of the horizontal velocity, and z is the vertical coordinate. The critical Richardson number, Ri c , appears in the classical papers by Miles (1961) Gage (1971).The increase of the Reynolds number causes nonstationarity of the basic field, bifurcations and transition to turbulence, and the analysis of the effect of stable stratification in this case needs to take into account the increasing complexity. Laval et al. (2003) considered the effect of the Reynolds number, Re = VL h /ν, on forced, stably-stratified shear layers (here, V and L h are the horizontal velocity and length scales, respectively, and ν is the kinematic viscosity). In order to be able to deal with shearless, freely decaying flows, Laval et al. (2003) also used a Froude number defined as Fr = V /NL v , where L v is a vertical length scale. Using the Kolmogorov scaling for the rate of viscous dissipation , = V 3 /L v , one can re-define the Froude number as Fr = /NK , where K = V 2 /2 is the turbulence kinetic energy. An increasing strength of stable stratification corresponds to decreasing Fr. With increasing Re, a simulated flow underwent a series of successive transitions to states with increasing anisotropy dominated by horizontal pancake-like vortices. These vortices, however, could become unstable with increasing Re. The study concluded that "for any Froude number, no matter how small, there are Reynolds numbers large enough so that a sequence of transitions to nonpancake motions will always occur and, conversely, for any Reynolds number, no matter how large, there are Froude numbers small enough so that these transitions are suppressed."From these results, one can surmise that the adaptation of the critical Richardson number to turbulent flows is not straightforward. Since turbulence is an unstable, stochastic phenomenon, it lacks

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“…Spedding 1997) that there is an initial stage in stratified wakes where the flow evolves much as it does in the absence of stratification. General and universal models have even been proposed for all wake defect magnitudes and signs provided they are not very close to zero (the momentumless condition) (Meunier & Spedding 2004, 2006, and simple analytical models have been constructed starting with this base condition over a wide range of Re and Fr (Meunier, Diamessis & Spedding 2006). The results presented here show that there can be no such universal initial condition.…”

Section: Discussionmentioning

confidence: 87%

The turbulent wake of a towed grid in a stratified fluid

et al. 2015

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In a stable background density gradient, initially turbulent flows eventually evolve into a state dominated by low-Froude-number dynamics and frequently also contain persistent pattern information. Much empirical evidence has been gathered on these latter stages, but less on how they first got that way, and how information on the turbulence generator may potentially be encoded into the flow in a robust and long-lasting fashion. Here an experiment is described that examines the initial stages of evolution in the vertical plane of a turbulent grid-generated wake in a stratified ambient. Refractive-index-matched fluids allow optically based measurement of early (Nt < 2) stages of the flow, even when there are strong variations in the local density gradient field. Suitably averaged flow measures show the interplay between internal wave motions and Kelvin-Helmholtz-generated vortical modes. The vertical shear is dominant at the wake edge, and the decay of horizontal vorticity is observed to be independent of Fr. Stratified turbulence, originating from Kelvin-Helmholtz instabilities, develops up to non-dimensional time Nt ≈ 10, and the scale separation between Ozmidov and Kolmogorov scales is independent of Fr at higher Nt. The detailed measurements in the near wake, with independent variation of both Reynolds and Froude numbers, while limited to one particular case, are sufficient to show that the initial turbulence in a stratified fluid is neither three-dimensional nor universal. The search for appropriately generalizable initial conditions may be more involved than hoped for.

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Self-preservation in stratified momentum wakes

Cited by 41 publications

References 32 publications

Spatial characterization of vortical structures and internal waves in a stratified turbulent wake using proper orthogonal decomposition

Spatial characterization of vortical structures and internal waves in a stratified turbulent wake using proper orthogonal decomposition

On the critical Richardson number in stably stratified turbulence

The turbulent wake of a towed grid in a stratified fluid

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