Abstract:Motivated by the variation of local shear produced by internal waves in the ocean, we use direct numerical simulations to investigate the effect of a time-dependent shear forcing on the evolution and mixing of turbulence produced by Kelvin–Helmholtz instability (KHI) at high Reynolds number. The forcing is implemented using a tilting coordinate system which causes the background shear to accelerate and decelerate periodically. We demonstrate that, with suitable timing between development of instability and the… Show more
“…2021; Issaev et al. 2022; Lewin & Caulfield 2022), we expect the need for an expanded set of scaling relationships due to the differences in the turbulence generation mechanism or large-scale forcing (Howland et al. 2020) and the energy exchange pathways among the different components of TKE and TPE (Yi & Koseff 2022).…”
Section: Discussionmentioning
confidence: 99%
“…Billant & Chomaz 2000a,b;Basak & Sarkar 2006;Deloncle, Chomaz & Billant 2007;Waite & Smolarkiewicz 2008;Lucas, Caulfield & Kerswell 2017;Cope, Garaud & Caulfield 2020) or flows with spatio-temporal variations (e.g. Williamson et al 2015;Kirkpatrick et al 2019Kirkpatrick et al , 2020Onuki et al 2021;Issaev et al 2022;Lewin & Caulfield 2022), we expect the need for an expanded set of scaling relationships due to the differences in the turbulence generation mechanism or large-scale forcing (Howland et al 2020) and the energy exchange pathways among the different components of TKE and TPE (Yi & Koseff 2022).…”
We revisit and extend the turbulent Froude number (
$Fr_k$
) scaling for the mixing coefficient (
$\varGamma$
) introduced by Garanaik & Venayagamoorthy (GV) (J. Fluid Mech., vol. 867, 2019, pp. 323–333) by directly incorporating the effects of mean shear through the non-dimensional shear parameter
$S_{\ast } = S k/\epsilon _k$
. For flows where the effects of mean shear are stronger than the background vertical stratification, we find
$\varGamma \sim Fr_k^{-2} S_\ast ^{-1}$
for weakly stratified sheared turbulence and
$\varGamma \sim Fr_k^{-1}S_\ast ^{-1}$
for moderately stratified sheared turbulence. The scaling procedure is inconclusive for strongly stratified sheared turbulence, but using two independent datasets of homogeneous, sheared, stably stratified turbulence, we empirically observe
$\varGamma \sim Fr_k^{-0.5} S_\ast ^{-1}$
. Our revised scaling better collapses both datasets compared with the original GV scaling, and we note that the moderately stratified sheared regime is extremely narrow (or maybe even non-existent). We also apply our scaling to the time-varying open channel simulations of Issaev et al. (J. Fluid Mech., vol. 935, 2022) and observe
$\varGamma \sim Fr_k^{-2}S_\ast ^{-1}$
for weakly stratified sheared turbulence, but we observe deviations from our revised scaling for moderate and strong stratifications due to time-varying mean shear and vertical transport. Finally, we apply our revised scaling to field measurements of Conry, Kit & Fernando (Environ. Fluid Mech., vol. 20, 2020, pp. 1177–1197) and observe
$\varGamma \sim Fr_k^{-2} S_\ast ^{-1}$
. We emphasize that our revised scaling is applicable only for stably stratified, vertically sheared turbulence with weak spatio-temporal variations of the mean shear and stratification, and we expect different scaling to apply when additional effects such as depth-varying radiative heating/cooling are present or when the orientation of the mean shear relative to the gravity vector is modified (e.g. horizontal shear).
“…2021; Issaev et al. 2022; Lewin & Caulfield 2022), we expect the need for an expanded set of scaling relationships due to the differences in the turbulence generation mechanism or large-scale forcing (Howland et al. 2020) and the energy exchange pathways among the different components of TKE and TPE (Yi & Koseff 2022).…”
Section: Discussionmentioning
confidence: 99%
“…Billant & Chomaz 2000a,b;Basak & Sarkar 2006;Deloncle, Chomaz & Billant 2007;Waite & Smolarkiewicz 2008;Lucas, Caulfield & Kerswell 2017;Cope, Garaud & Caulfield 2020) or flows with spatio-temporal variations (e.g. Williamson et al 2015;Kirkpatrick et al 2019Kirkpatrick et al , 2020Onuki et al 2021;Issaev et al 2022;Lewin & Caulfield 2022), we expect the need for an expanded set of scaling relationships due to the differences in the turbulence generation mechanism or large-scale forcing (Howland et al 2020) and the energy exchange pathways among the different components of TKE and TPE (Yi & Koseff 2022).…”
We revisit and extend the turbulent Froude number (
$Fr_k$
) scaling for the mixing coefficient (
$\varGamma$
) introduced by Garanaik & Venayagamoorthy (GV) (J. Fluid Mech., vol. 867, 2019, pp. 323–333) by directly incorporating the effects of mean shear through the non-dimensional shear parameter
$S_{\ast } = S k/\epsilon _k$
. For flows where the effects of mean shear are stronger than the background vertical stratification, we find
$\varGamma \sim Fr_k^{-2} S_\ast ^{-1}$
for weakly stratified sheared turbulence and
$\varGamma \sim Fr_k^{-1}S_\ast ^{-1}$
for moderately stratified sheared turbulence. The scaling procedure is inconclusive for strongly stratified sheared turbulence, but using two independent datasets of homogeneous, sheared, stably stratified turbulence, we empirically observe
$\varGamma \sim Fr_k^{-0.5} S_\ast ^{-1}$
. Our revised scaling better collapses both datasets compared with the original GV scaling, and we note that the moderately stratified sheared regime is extremely narrow (or maybe even non-existent). We also apply our scaling to the time-varying open channel simulations of Issaev et al. (J. Fluid Mech., vol. 935, 2022) and observe
$\varGamma \sim Fr_k^{-2}S_\ast ^{-1}$
for weakly stratified sheared turbulence, but we observe deviations from our revised scaling for moderate and strong stratifications due to time-varying mean shear and vertical transport. Finally, we apply our revised scaling to field measurements of Conry, Kit & Fernando (Environ. Fluid Mech., vol. 20, 2020, pp. 1177–1197) and observe
$\varGamma \sim Fr_k^{-2} S_\ast ^{-1}$
. We emphasize that our revised scaling is applicable only for stably stratified, vertically sheared turbulence with weak spatio-temporal variations of the mean shear and stratification, and we expect different scaling to apply when additional effects such as depth-varying radiative heating/cooling are present or when the orientation of the mean shear relative to the gravity vector is modified (e.g. horizontal shear).
“…Our canyon's length (~30 km), width (~8 km at its mouth), vertical extent (>1000 m from mouth to head), aspect ratio (~80º, denoting a relatively narrow canyon), V-shaped geometry (with axial slope near M2 tidal criticality, and steep, supercritical sidewalls), and characteristic barotropic tidal speeds (~0.08 m s -1 )all factors likely to shape the governing physics and intensity of the in-canyon mixing 30,31 are in line with those of many continental-slope canyons in the global ocean 20,21,30 . Second, observational and modelling investigations of nearboundary mixing in a range of oceanic 26,[33][34][35] , limnic 36,37 and idealized geophysical fluid 38,39 settings indicate that the convective process documented here may be of broad generality to oscillatory flows over sloping topography, regardless of the details of the flow or topographic configuration. We can thus surmise that the mechanism of rapid, convectively-induced along-boundary upwelling highlighted by our work is likely to operate elsewhere.…”
Deep-ocean upwelling, driven by small-scale turbulent mixing1,2, plays a central role in Earth’s climate by regulating the ocean’s capacity to sequester heat and carbon for decades to millennia3,4. Recent theoretical studies5-8 have hypothesized that this upwelling may primarily occur within a thin bottom boundary layer (BBL) adjacent to the sloping seafloor. However, little is known about the mixing processes that might drive such along-bottom upwelling, and the problem remains the subject of an enduring and vigorous debate8-11. Here, we elucidate the processes governing BBL-focussed upwelling in a typical continental-slope canyon, in which very rapid upwelling is observed12. We show that upwelling along the canyon stems from episodic cells of convective turbulent mixing up to 250 m in height, generated by tidal currents sweeping up- and down-canyon. Once per tidal cycle, these currents develop a vertical shear that conveys dense waters over slower-flowing lighter waters below, causing the dense waters to convectively mix, lighten and upwell. We argue that this upwelling mechanism is likely to be of wider representativeness, substantiating the view that deep-ocean upwelling can predominantly occur along the ocean’s sloping boundaries.
“…In the upper two rows the background shear oscillates sinusoidally, while in the bottom row the background shear initially is accelerated in the same way as in the other two simulations, but then not decelerated. Figure 3.Spanwise slices at various indicated times during stratified shear flows showing contours of density for three different simulations as described in more detail in Lewin & Caulfield (2022): ( a – d ) an oscillating shear flow initially perturbed with white noise; ( e – h ) an oscillating shear flow initially perturbed with the most unstable normal mode; ( i – l ) a shear flow which initially accelerates and then does not decelerate, initially perturbed with white noise. Only the central region (40 % of the total vertical extent) is shown.…”
mentioning
confidence: 99%
“…The data are stored as files (in this case simple text files) in the same directory as the notebook, and are available to the reader for download. The next example (figure 3) consists of a set of contour plots of snapshots of the time-evolving density field in three different simulations of stratified flow, as described in more detail in Lewin & Caulfield (2022). Figure 1 of that paper shows spanwise snapshots of the density field from the middle of the flow domain at four different times for three different simulations.…”
Ever since its inception, scientific publishing has used the printed page, a two-dimensional object, as its medium. Text, figures, photographs and drawings populate celebrated pages in our journals and libraries, pages that have been particularly effective in conveying the essence of science with its remarkable reductionist successes. Complex phenomena could be described with elegant compact theories and models, and graphs displaying cause and effect relationships have been a highly effective means of communication among scientists. The printed page has served to extend one-on-one communications between scientists where one scientist speaks or lectures (text), and draws a plot (x-y graph) or a sketch on a blackboard, trying to convince a colleague or audience of a new theory or implications of certain measurements. Our traditional paper containing pages with text and plots can encapsulate such interactions well, and enables interactions to be scaled up massively to reach many thousands of other scientist readers. These pages speak to us from nearby or far away, from recent or distant times. More recently, the online publishing phenomenon has revolutionized the access to such pages, making them available to scientists everywhere with remarkable ease and speed, aiming to accelerate the pace of learning and discovery. However, the online revolution has not yet changed the essence of the delivery mechanism of knowledge and insight, the static, two-dimensional page.In Batchelor's 1981 editorial 'Preoccupations of a journal editor' we are reminded that there is value in taking '. . . stock of the situation and to think about the general issues involved in the communication of scientific ideas and results from one research worker to another' (Batchelor 1981). For instance, we believe that a case can be made that the role of scientific publishing in general, and of the Journal of Fluid Mechanics in particular, is to enable prevailing information transmittal modes (however they may be practised at the time among individual scientists) to be scaled up to large numbers of people, the journal's readership. It is useful then to contemplate how, nowadays, an encounter between two scientists may proceed,
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