2017
DOI: 10.1017/jfm.2017.695
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Irreversible mixing by unstable periodic orbits in buoyancy dominated stratified turbulence

Abstract: We consider turbulence driven by a large-scale horizontal shear in Kolmogorov flow (i.e. with sinusoidal body forcing) and a background linear stable stratification with buoyancy frequency N 2 B imposed in the third, vertical direction in a fluid with kinematic viscosity ν. This flow is known to be organised into layers by nonlinear unstable steady states, which incline the background shear in the vertical and can be demonstrated to be the finite-amplitude saturation of a sequence of instabilities, originally … Show more

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Cited by 15 publications
(16 citation statements)
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“…Despite this recent progress in the understanding of stratified ECS, a connection with realistic fully turbulent stratified shear flow remains unresolved (although Lucas, Caulfield & Kerswell (2019) arguably see traces of underlying ECS in recent stratified plane Couette DNS results). In part this is due to the Prandtl number; prior stratified ECS studies have only dealt with unit Prandtl numbers (Eaves & Caulfield 2015; Deguchi 2017; Lucas & Caulfield 2017; Lucas et al. 2017; Olvera & Kerswell 2017) and full DNS of stratified shear flow turbulence is restricted in the Prandtl numbers it can access by issues of numerical resolution.…”
Section: Introductionmentioning
confidence: 99%
“…Despite this recent progress in the understanding of stratified ECS, a connection with realistic fully turbulent stratified shear flow remains unresolved (although Lucas, Caulfield & Kerswell (2019) arguably see traces of underlying ECS in recent stratified plane Couette DNS results). In part this is due to the Prandtl number; prior stratified ECS studies have only dealt with unit Prandtl numbers (Eaves & Caulfield 2015; Deguchi 2017; Lucas & Caulfield 2017; Lucas et al. 2017; Olvera & Kerswell 2017) and full DNS of stratified shear flow turbulence is restricted in the Prandtl numbers it can access by issues of numerical resolution.…”
Section: Introductionmentioning
confidence: 99%
“…As discussed in §3.4, different values of µ correspond to different assumptions about the involvement of third-order cumulants in the statistical equilibrium. Picking an arbitrary value of µ in equation (32) might result in the adjoint operator being close to singular and therefore yielding gradients that depend sensitively on the choice of µ. To illustrate this, figure 7 shows evaluations of the derivative of Q 6 with respect to r using equation (32) for values of µ in the vicinity of the optimal value µ * as determined by equation (29).…”
Section: Three-dimensional Convection (D = 9)mentioning
confidence: 99%
“…Picking an arbitrary value of µ in equation (32) might result in the adjoint operator being close to singular and therefore yielding gradients that depend sensitively on the choice of µ. To illustrate this, figure 7 shows evaluations of the derivative of Q 6 with respect to r using equation (32) for values of µ in the vicinity of the optimal value µ * as determined by equation (29). When r = 28.0 it is evident that some choices of µ result in a singular or near-singular adjoint operator and, therefore, a large amount of uncertainty in the resulting gradients.…”
Section: Three-dimensional Convection (D = 9)mentioning
confidence: 99%
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