20 research outputs found
Disruption of SSP/VWI states by a stable stratification
We identify āminimal seedsā for turbulence, i.e. initial conditions of the smallest possible total perturbation energy density Ec that trigger turbulence from the laminar state, in stratified plane Couette flow, the flow between two horizontal plates of separation 2H, moving with relative velocity 2ĪU, across which a constant density difference 2ĪĻ from a reference density Ļr is maintained. To find minimal seeds, we use the ādirect-adjoint-loopingā (DAL) method for finding nonlinear optimal perturbations that optimise the time-averaged total dissipation of energy in the flow. These minimal seeds are located adjacent to the edge manifold, the manifold in state space that separates trajectories which transition to turbulence from those which eventually decay to the laminar state. The edge manifold is also the stable manifold of the systemās āedge stateā. Therefore, the trajectories from the minimal seed initial conditions spend a large amount of time in the vicinity of some states: the edge state; another state contained within the edge manifold; or even in dynamically slowly varying regions of the edge manifold, allowing us to investigate the effects of a stable stratification on any coherent structures associated with such states. In unstratified plane Couette flow, these coherent structures are manifestations of the self-sustaining process (SSP) deduced on physical grounds by Waleffe (Phys. Fluids, vol. 9, 1997, pp. 883ā900), or equivalently finite Reynolds number solutions of the vortexāwave interaction (VWI) asymptotic equations initially derived mathematically by Hall & Smith (J. Fluid Mech., vol. 227, 1991, pp. 641ā666). The stratified coherent states we identify at moderate Reynolds number display an altered form from their unstratified counterparts for bulk Richardson numbers RiBĀ = gĪĻH/(ĻrĪU2) = O(Re-1), and exhibit chaotic motion for larger RiB. We demonstrate that at hith Reynolds number the suppression of vertical motions by stratification strongly disrupts input from the waves to the roll velocity structures, thus preventing the waves from reinforcing the viscously decaying roll structures adequately, when RiB = O(Re-2)
Structured input-output analysis of stably stratified plane Couette flow
We employ a recently introduced structured input-output analysis (SIOA)
approach to analyze streamwise and spanwise wavelengths of flow structures in
stably stratified plane Couette flow. In the low-Reynolds number ()
low-bulk Richardson number () spatially intermittent regime, we
demonstrate that SIOA predicts high amplification associated with wavelengths
corresponding to the characteristic oblique turbulent bands in this regime.
SIOA also identifies quasi-horizontal flow structures resembling the
turbulent-laminar layers commonly observed in the high- high-
intermittent regime. An SIOA across a range of and values suggests
that the classical Miles-Howard stability criterion () is
associated with a change in the most amplified flow structures when Prandtl
number is close to one (). However, for , the most
amplified flow structures are determined by the product . For , SIOA identifies another quasi-horizontal flow structure that we show is
principally associated with density perturbations. We further demonstrate the
dominance of this density-associated flow structure in the high limit by
constructing analytical scaling arguments for the amplification in terms of
and under the assumptions of unstratified flow (with ) and
streamwise invariance.Comment: 27 pages, 12 figure
Growth and instability of a laminar plume in a strongly stratified environment
Experimental studies of laminar plumes descending under gravity into stably stratified environments have shown the existence of a critical injection velocity beyond which the plume exhibits a bifurcation to a coiling instability in three dimensions or a sinuous instability in a Hele-Shaw flow. In addition, flow visualization has shown that, prior to the onset of the instability, a stable base flow is established in which the plume penetrates to a depth significantly smaller than the neutral buoyancy depth. Moreover, the fresh water that is viscously entrained by the plume recirculates within a āconduitā whose boundary with the background stratification appears sharp. Beyond the bifurcation, the buckling plume takes the form of a travelling wave of varying amplitude, confined within the conduit, which disappears at the penetration depth. To determine the mechanisms underlying these complex phenomena, which take place at a strikingly low Reynolds number but a high Schmidt number, we study here a two-dimensional arrangement, as it is perhaps the simplest system which possesses all the key experimental features. Through a combination of numerical and analytical approaches, a scaling law is found for the plumeās penetration depth within the base flow (i.e. the flow where the instability is either absent or artificially suppressed), and the horizontal cross-stream velocity and concentration profile outside the plume are determined from an asymptotic analysis of a simplified model. Direct numerical simulations show that, with increasing flow rate, a sinuous global mode is destabilized giving rise to the self-sustained oscillations as in the experiment. The sinuous instability is shown to be a consequence of the baroclinic generation of vorticity, due to the strong horizontal gradients at the edge of the conduit, a mechanism that is relevant even at very low Reynolds numbers. Despite the strength of this instability, the penetration depth is not significantly affected by it, instead being determined by the properties of the plume in the vicinity of the source. This scenario is confirmed by a local stability analysis. A finite region of local absolute instability is found near the source for sinuous modes prior to the onset of the global instability. Sufficiently far from the source the flow is locally stable. Near the onset of the global instability, varicose modes are also found to be locally, but only convectively, unstable
Regimes of stratified turbulence at low Prandtl number
Quantifying transport by strongly stratified turbulence in low Prandtl number
() fluids is critically important for the development of better models for
the structure and evolution of stellar interiors. Motivated by recent numerical
simulations showing strongly anisotropic flows suggestive of scale-separated
dynamics, we perform a multiscale asymptotic analysis of the governing
equations. We find that, in all cases, the resulting slow-fast system naturally
takes a quasilinear form. Our analysis also reveals the existence of several
distinct dynamical regimes depending on the emergent buoyancy Reynolds and
P\'eclet numbers, and , respectively,
where is the aspect ratio of the large-scale turbulent flow
structures, and is the outer scale Reynolds number. Scaling relationships
relating the aspect ratio, the characteristic vertical velocity, and the
strength of the stratification (measured by the Froude number ) naturally
emerge from the analysis. When , the dynamics at all scales is
dominated by buoyancy diffusion, and our results recover the scaling laws
empirically obtained from direct numerical simulations by Cope et al. (2020).
For , diffusion is negligible (or at least subdominant) at all
scales and our results are consistent with those of Chini et al. (2022) for
strongly stratified geophysical turbulence at .Finally, we have
identified a new regime for , in which slow, large
scales are diffusive while fast, small scales are not. We conclude by
presenting a map of parameter space that clearly indicates the transitions
between isotropic turbulence, non-diffusive stratified turbulence, diffusive
stratified turbulence and viscously-dominated flows.Comment: 25 pages, 1 figur
Recommended from our members
Wake Induced Long Range Repulsion of Aqueous Dunes.
Sand dunes rarely occur in isolation, but usually form vast dune fields. The large scale dynamics of these fields is hitherto poorly understood, not least due to the lack of longtime observations. Theoretical models usually abstract dunes in a field as self-propelled autonomous agents, exchanging mass, either remotely or as a consequence of collisions. In contrast to the spirit of these models, here we present experimental evidence that aqueous dunes interact over large distances without the necessity of exchanging mass. Interactions are mediated by turbulent structures forming in the wake of a dune, and lead to dune-dune repulsion, which can prevent collisions. We conjecture that a similar mechanism may be present in wind driven dunes, potentially explaining the observed robust stability of dune fields in different environments
Mixing across stable density interfaces in forced stratified turbulence
Understanding how turbulence enhances irreversible scalar mixing in
density-stratified fluids is a central problem in geophysical fluid dynamics.
While isotropic overturning regions are commonly the focus of mixing analyses,
we here investigate whether significant mixing may arise in anisotropic
statically-stable regions of the flow. Focusing on a single forced direct
numerical simulation of stratified turbulence, we analyze spatial correlations
between the vertical density gradient and the
dissipation rates of kinetic energy and scalar variance , the
latter quantifying scalar mixing. The domain is characterized by relatively
well-mixed density layers separated by sharp stable interfaces that are
correlated with high vertical shear. While static instability is most prevalent
within the mixed layers, much of the scalar mixing is localized to the
intervening interfaces, a phenomenon not apparent if considering local static
instability or alone. While the majority of the domain is
characterized by the canonical flux coefficient
, often assumed in ocean mixing
parameterizations, extreme values of within the statically-stable
interfaces, associated with elevated , strongly skew the bulk
statistics. Our findings suggest that current parameterizations of turbulent
mixing may be biased by undersampling, such that the most common, but not
necessarily the most significant, mixing events are overweighted. Having
focused here on a single simulation of stratified turbulence, it is hoped that
our results motivate a broader investigation into the role played by stable
density interfaces in mixing, across a wider range of parameters and forcing
schemes representative of ocean turbulence.Comment: 17 pages, 7 figures. Version accepted for publication in the Journal
of Fluid Mechanics. DOI link to final typeset version provide
Time-Lapse Seismic Imaging of Oceanic Fronts and Transient Lenses within South Atlantic Ocean
Oceanic fronts play a pivotal role in controlling water mass transfer, although little is
known about deep frontal structure on appropriate temporal and spatial scales. Here,
we present a sequence of calibrated time-lapse images from a three-dimensional seismic
survey that straddles the Brazil-Malvinas Confluenceā a significant feature of the merid-
ional overturning circulation. Eight vertical transects reveal the evolution of a major front.
It is manifest as a discrete planar surface that dips at less than 2 ā¦ and is traceable to
1.5ā2 km depth. Its shape and surface expression are consistent with sloping isopycnal
surfaces of the calculated potential density field and with coeval sea surface tempera-
ture measurements, respectively. Within the top ā¼1 km, where cold fresh water subducts
beneath warm salty water, a series of tilted lenses are banked up against the sharply de-
fined front. The largest of these structures is centered at 700 m depth and is cored by
cold fresh water. Time-lapse imagery demonstrates that this tilted lens grows and de-
cays over nine days. It has a maximum diameter of < 34 Ā± 0.13 km and a maximum
height of < 750Ā±10 m. Beneath 1 km, where horizontal density gradients are negligi-
ble, numerous deforming lenses and filaments on length scales of 10ā100 km are being
swept toward the advecting front
Prandtl number effects on extreme mixing events in forced stratified turbulence
Relatively strongly stratified turbulent flows tend to self-organise into a
'layered anisotropic stratified turbulence' (LAST) regime, characterised by
relatively deep and well-mixed density 'layers' separated by relatively thin
'interfaces' of enhanced density gradient. Understanding the associated mixing
dynamics is a central problem in geophysical fluid dynamics. It is challenging
to study 'LAST' mixing, as it is associated with Reynolds numbers and Froude numbers , ( and being
characteristic velocity and length scales, being the kinematic viscosity
and the buoyancy frequency). Since a sufficiently large dynamic range
(largely) unaffected by stratification and viscosity is required, it is also
necessary for the buoyancy Reynolds number where is the (appropriately volume-averaged) turbulent kinetic
energy dissipation rate. This requirement is exacerbated for oceanically
relevant flows, as the Prandtl number in
thermally-stratified water (where is the thermal diffusivity), thus
leading (potentially) to even finer density field structures. We report here on
four forced fully resolved direct numerical simulations of stratified
turbulence at various Froude () and Prandtl numbers ()
forced so that , with resolutions up to . We find that, as increases, emergent 'interfaces' become finer and
their contribution to bulk mixing characteristics decreases at the expense of
the small-scale density structures populating the well-mixed 'layers'. However,
extreme mixing events (as quantified by significantly elevated local
destruction rates of buoyancy variance ) are always preferentially
found in the (statically stable) interfaces, irrespective of the value of .Comment: 10 pages, 4 figure
Calibrated Seismic Imaging of Eddy-Dominated Warm-Water Transport across the Bellingshausen Sea, Southern Ocean
Seismic reflection images of thermohaline circulation from the Bellingshausen Sea, adjacent to the West Antarctica Peninsula, were acquired during February 2015. This survey shows that bright reflectivity occurs throughout the upper 300 m. By calibrating these seismic images with coeval hydrographic measurements, intrusion of warm water features onto the continental shelf at Marguerite and Belgica Troughs is identified and characterized. These features have distinctive lensāshaped patterns of reflectivity with lengths of 0.75ā11.00 km and thicknesses of 100ā150 m, suggesting that they are small mesoscale to submesoscale eddies. Abundant eddies are observed along a transect that crosses Belgica Trough. Near Alexander Island Drift, a large, of order urn:x-wiley:21699275:media:jgrc22803:jgrc22803-math-0001 km3, bowlālike feature, that may represent an anticyclonic Taylor column, is imaged on a pair of orthogonal images. A modified iterative procedure is used to convert seismic imagery into maps of temperature that enable the number and size of eddies being transported onto the shelf to be quantified. Finally, analysis of prestack shot records suggests that these eddies are advecting southward at speeds of urn:x-wiley:21699275:media:jgrc22803:jgrc22803-math-0002 m sā1, consistent with limited legacy hydrographic measurements. Concentration of observed eddies south of the Southern Antarctic Circumpolar Current Front implies they represent both a dominant, and a longālived, mechanism of warmāwater transport, especially across Belgica Trough. Our observations suggest that previous estimates of eddy frequency may have been underestimated by up to 1 order of magnitude, which has significant implications for calculations of ice mass loss on the shelf of the West Antarctic Peninsula