scholarly journals Layer formation in horizontally forced stratified turbulence: connecting exact coherent structures to linear instabilities

2017 ◽  
Vol 832 ◽  
pp. 409-437 ◽  
Author(s):  
Dan Lucas ◽  
C. P. Caulfield ◽  
Rich R. Kerswell
Keyword(s):  
Coherent Structures ◽  
Stable Stratification ◽  
Finite Amplitude ◽  
Shear Instability ◽  
Stratified Turbulence ◽  
Layer Formation ◽  
Horizontal Shear ◽  
Chaotic Flow ◽  
Background Shear ◽  
First Time

We consider turbulence in a stratified ‘Kolmogorov’ flow, driven by horizontal shear in the form of sinusoidal body forcing in the presence of an imposed background linear stable stratification in the third direction. This flow configuration allows the controlled investigation of the formation of coherent structures, which here organise the flow into horizontal layers by inclining the background shear as the strength of the stratification is increased. By numerically converging exact steady states from direct numerical simulations of chaotic flow, we show, for the first time, a robust connection between linear theory predicting instabilities from infinitesimal perturbations to the robust finite-amplitude nonlinear layered state observed in the turbulence. We investigate how the observed vertical length scales are related to the primary linear instabilities and compare to previously considered examples of shear instability leading to layer formation in other horizontally sheared flows.

scholarly journals Horizontal shear instabilities in rotating stellar radiation zones

2020 ◽  
Vol 635 ◽  
pp. A133 ◽  
Author(s):  
J. Park ◽  
V. Prat ◽  
S. Mathis
Keyword(s):  
Growth Rate ◽  
Thermal Diffusion ◽  
Turbulent Transport ◽  
Stable Stratification ◽  
Shear Instability ◽  
Inviscid Limit ◽  
Horizontal Shear ◽  
Wide Range ◽  
Inertial Instability ◽  
Shear Instabilities

Context. Rotational mixing transports angular momentum and chemical elements in stellar radiative zones. It is one of the key processes for modern stellar evolution. In the past two decades, an emphasis has been placed on the turbulent transport induced by the vertical shear instability. However, instabilities arising from horizontal shear and the strength of the anisotropic turbulent transport that they may trigger remain relatively unexplored. The weakest point of this hydrodynamical theory of rotational mixing is the assumption that anisotropic turbulent transport is stronger in horizontal directions than in the vertical one. Aims. This paper investigates the combined effects of stable stratification, rotation, and thermal diffusion on the horizontal shear instabilities that are obtained and discussed in the context of stellar radiative zones. Methods. The eigenvalue problem describing linear instabilities of a flow with a hyperbolic-tangent horizontal shear profile was solved numerically for a wide range of parameters. When possible, the Wentzel–Kramers–Brillouin–Jeffreys (WKBJ) approximation was applied to provide analytical asymptotic dispersion relations in both the nondiffusive and highly diffusive limits. As a first step, we consider a polar f-plane where the gravity and rotation vector are aligned. Results. Two types of instabilities are identified: the inflectional and inertial instabilities. The inflectional instability that arises from the inflection point (i.e., the zero second derivative of the shear flow) is the most unstable when at a zero vertical wavenumber and a finite wavenumber in the streamwise direction along the imposed-flow direction. While the maximum two-dimensional growth rate is independent of the stratification, rotation rate, and thermal diffusivity, the three-dimensional inflectional instability is destabilized by stable stratification, while it is stabilized by thermal diffusion. The inertial instability is rotationally driven, and a WKBJ analysis reveals that its growth rate reaches the maximum value of √f(1 − f) in the inviscid limit as the vertical wavenumber goes to infinity, where f is the dimensionless Coriolis parameter. The inertial instability for a finite vertical wavenumber is stabilized as the stratification increases, whereas it is destabilized by the thermal diffusion. Furthermore, we found a selfsimilarity in both the inflectional and inertial instabilities based on the rescaled parameter PeN2 with the Péclet number Pe and the Brunt–Väisälä frequency N.

The ‘zoo’ of secondary instabilities precursory to stratified shear flow transition. Part 1 Shear aligned convection, pairing, and braid instabilities

2012 ◽  
Vol 708 ◽  
pp. 5-44 ◽  
Author(s):  
A. Mashayek ◽  
W. R. Peltier
Keyword(s):  
Stagnation Point ◽  
Three Dimensional ◽  
Negative Influence ◽  
Finite Amplitude ◽  
Shear Instability ◽  
Background Flow ◽  
Shear Modes ◽  
Stratified Shear Flow ◽  
Secondary Instabilities ◽  
Background Shear

AbstractWe study the competition between various secondary instabilities that co-exist in a preturbulent stratified parallel flow subject to Kelvin–Helmholtz instability. In particular, we investigate whether a secondary braid instability might emerge prior to the overturning of the statically unstable regions that develop in the cores of the primary Kelvin–Helmholtz billows. We identify two groups of instabilities on the braid. One group is a shear instability which extracts its energy from the background shear and is suppressed by the straining contribution of the background flow. The other group, which seems to have no precedent in the literature, includes phase-locked modes which grow at the stagnation point on the braid and are almost entirely driven by the straining contributions of the background flow. For the latter group, the braid shear has a negative influence on the growth rate. Our analysis demonstrates that the probability of finite-amplitude growth of both braid instabilities is enhanced with increasing Reynolds number and Richardson number. We also show that the possibility of emergence of braid instabilities decreases with the Prandtl number for the shear modes and increases for the stagnation point instabilities. Through detailed non-separable linear stability analysis, we show that both braid instabilities are fundamentally three dimensional with the shear modes being of small wavenumbers and the stagnation point modes dominating at large wavenumber.

Frontogenesis and frontal arrest of a dense filament in the oceanic surface boundary layer

2017 ◽  
Vol 837 ◽  
pp. 341-380 ◽  
Author(s):  
Peter P. Sullivan ◽  
James C. McWilliams
Keyword(s):  
Boundary Layer ◽  
Turbulent Mixing ◽  
Shear Instability ◽  
Upper Ocean ◽  
Surface Boundary ◽  
Horizontal Shear ◽  
Boundary Layer Turbulence ◽  
Filament Axis ◽  
Small Width ◽  
The Cross

The evolution of upper ocean currents involves a set of complex, poorly understood interactions between submesoscale turbulence (e.g. density fronts and filaments and coherent vortices) and smaller-scale boundary-layer turbulence. Here we simulate the lifecycle of a cold (dense) filament undergoing frontogenesis in the presence of turbulence generated by surface stress and/or buoyancy loss. This phenomenon is examined in large-eddy simulations with resolved turbulent motions in large horizontal domains using${\sim}10^{10}$grid points. Steady winds are oriented in directions perpendicular or parallel to the filament axis. Due to turbulent vertical momentum mixing, cold filaments generate a potent two-celled secondary circulation in the cross-filament plane that is frontogenetic, sharpens the cross-filament buoyancy and horizontal velocity gradients and blocks Ekman buoyancy flux across the cold filament core towards the warm filament edge. Within less than a day, the frontogenesis is arrested at a small width,${\approx}100~\text{m}$, primarily by an enhancement of the turbulence through a small submesoscale, horizontal shear instability of the sharpened filament, followed by a subsequent slow decay of the filament by further turbulent mixing. The boundary-layer turbulence is inhomogeneous and non-stationary in relation to the evolving submesoscale currents and density stratification. The occurrence of frontogenesis and arrest are qualitatively similar with varying stress direction or with convective cooling, but the detailed evolution and flow structure differ among the cases. Thus submesoscale filament frontogenesis caused by boundary-layer turbulence, frontal arrest by frontal instability and frontal decay by forward energy cascade, and turbulent mixing are generic processes in the upper ocean.

scholarly journals Steep Shelf Stabilization of the Coastal Bransfield Current: Linear Stability Analysis

2014 ◽  
Vol 44 (2) ◽  
pp. 714-732 ◽  
Author(s):  
F. J. Poulin ◽  
A. Stegner ◽  
M. Hernández-Arencibia ◽  
A. Marrero-Díaz ◽  
P. Sangrà
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Baroclinic Instability ◽  
Shear Instability ◽  
Coastal Current ◽  
Horizontal Shear ◽  
Shelf Slope ◽  
Topographic Parameter ◽  
Selection Of

Abstract In situ measurements obtained during the 2010 COUPLING cruise were analyzed in order to fully characterize the velocity structure of the coastal Bransfield Current. An idealized two-layer shallow-water model was used to investigate the various instability processes of the realistic current along the coastal shelf. Particularly studied is how the topographic parameter To (ratio between the shelf slope and the isopycnal slope of the surface current) impacts the growth and the wavelength of the unstable perturbations. For small bottom slopes, when the evolution of the coastal current is controlled by the baroclinic instability, the increase of the topographic parameter To yields a selection of smaller unstable wavelengths. The growth rates increase with small values of To. For larger values of To (To ≳ 10, which is relevant for the coastal Bransfield Current), the baroclinic instability is strongly dampened and the horizontal shear instability becomes the dominant one. In this steep shelf regime, the unstable growth rate and the wavelength selection of the baroclinic coastal current remains almost constant and weakly affected by the amplitude of the bottom velocity or the exact value of the shelf slope. Hence, the linear stability analysis of an idealized Bransfield Current predicts a typical growth time of 7.7 days and an alongshore scale of 47 km all along the South Shetland Island shelf. The fact that these large growth times are identical to the typical transit time of water parcels along the shelf may explain why the current does not exhibit any unstable meanders.

scholarly journals Non-linear evolution of the resonant drag instability in magnetized gas

2019 ◽  
Vol 485 (3) ◽  
pp. 3991-3998 ◽  
Author(s):  
Darryl Seligman ◽  
Philip F Hopkins ◽  
Jonathan Squire
Keyword(s):  
Linear Theory ◽  
Coherent Structures ◽  
Magnetic Energy ◽  
Density Fluctuations ◽  
Linear Evolution ◽  
Drag Forces ◽  
Non Linear ◽  
Magnetohydrodynamic Simulations ◽  
First Time ◽  
Different Parts

Abstract We investigate, for the first time, the non-linear evolution of the magnetized ‘resonant drag instabilities’ (RDIs). We explore magnetohydrodynamic simulations of gas mixed with (uniform) dust grains subject to Lorentz and drag forces, using the gizmo code. The magnetized RDIs exhibit fundamentally different behaviour than purely acoustic RDIs. The dust organizes into coherent structures and the system exhibits strong dust–gas separation. In the linear and early non-linear regime, the growth rates agree with linear theory and the dust self-organizes into 2D planes or ‘sheets.’ Eventually the gas develops fully non-linear, saturated Alfvénic, and compressible fast-mode turbulence, which fills the underdense regions with a small amount of dust, and drives a dynamo that saturates at equipartition of kinetic and magnetic energy. The dust density fluctuations exhibit significant non-Gaussianity, and the power spectrum is strongly weighted towards the largest (box scale) modes. The saturation level can be understood via quasi-linear theory, as the forcing and energy input via the instabilities become comparable to saturated tension forces and dissipation in turbulence. The magnetized simulation presented here is just one case; it is likely that the magnetic RDIs can take many forms in different parts of parameter space.

scholarly journals Slug genesis in cylindrical pipe flow

2010 ◽  
Vol 663 ◽  
pp. 180-208 ◽  
Author(s):  
Y. DUGUET ◽  
A. P. WILLIS ◽  
R. R. KERSWELL
Keyword(s):  
Phase Space ◽  
Vortex Shedding ◽  
Coherent Structures ◽  
Pipe Flow ◽  
Edge State ◽  
Shear Layers ◽  
Finite Amplitude ◽  
Spatial Expansion ◽  
Cylindrical Pipe ◽  
Low Dimensional

Transition to uniform turbulence in cylindrical pipe flow occurs experimentally via the spatial expansion of isolated coherent structures called ‘slugs’, triggered by localized finite-amplitude disturbances. We study this process numerically by examining the preferred route in phase space through which a critical disturbance initiates a ‘slug’. This entails first identifying the relative attractor – ‘edge state’ – on the laminar–turbulent boundary in a long pipe and then studying the dynamics along its low-dimensional unstable manifold, leading to the turbulent state. Even though the fully turbulent state delocalizes at Re ≈ 2300, the edge state is found to be localized over the range Re = 2000–6000, and progressively reduces in both energy and spatial extent as Re is increased. A key process in the genesis of a slug is found to be vortex shedding via a Kelvin–Helmholtz mechanism from wall-attached shear layers quickly formed at the edge state's upstream boundary. Whether these shedded vortices travel on average faster or slower downstream than the developing turbulence determines whether a puff or a slug (respectively) is formed. This observation suggests that slugs are out-of-equilibrium puffs which therefore do not co-exist with stable puffs.

scholarly journals Numerical Study of Horizontal Shear Instability Waves along Narrow Cold Frontal Rainbands

2011 ◽  
Vol 68 (4) ◽  
pp. 878-903 ◽  
Author(s):  
Masayuki Kawashima
Keyword(s):  
Numerical Study ◽  
Leading Edge ◽  
Shear Instability ◽  
Vertical Shear ◽  
Horizontal Shear ◽  
Edge Waves ◽  
Instability Waves ◽  
Low Level ◽  
Wide Range ◽  
The Mean

Abstract The effects of variations in low-level ambient vertical shear and horizontal shear on the alongfront variability of narrow cold frontal rainbands (NCFRs) that propagate into neutral and slightly unstable environments are investigated through a series of idealized cloud-resolving simulations. In cases initialized with slightly unstable sounding and weak ambient cross-frontal vertical shears, core-gap structures of precipitation along NCFRs occur that are associated with wavelike disturbances that derive their kinetic energy mainly from the mean local vertical shear and buoyancy. However, over a wide range of environmental conditions, core-gap structures of precipitation occur because of the development of a horizontal shear instability (HSI) wave along the NCFRs. The growth rate and amplitude of the HSI wave decrease significantly as the vertical shear of the ambient cross-front wind is reduced. These decreases are a consequence of the enhancement of the low-level local vertical shear immediately behind the leading edge. The strong local vertical shear acts to damp the vorticity edge wave on the cold air side of the shear zone, thereby suppressing the growth of the HSI wave through the interaction of the two vorticity edge waves. It is also noted that the initial wavelength of the HSI wave increases markedly with increasing horizontal shear. The local vertical shear around the leading edge is shown to damp long HSI waves more strongly than short waves, and the horizontal shear dependency of the wavelength is explained by the decrease in the magnitude of the vertical shear relative to that of the horizontal shear.

scholarly journals Insights into the mixing efficiency of submesoscale Centrifugal-Symmetric instabilities

2021 ◽  
Author(s):  
Tomas Chor ◽  
Jacob Wenegrat ◽  
John Taylor
Keyword(s):  
Boundary Layer ◽  
Vertical Shear ◽  
Mixing Efficiency ◽  
Surface Boundary ◽  
Stratified Turbulence ◽  
Horizontal Shear ◽  
Surface Boundary Layer ◽  
Turbulent Dissipation ◽  
Balanced Flow ◽  
Shear Production

Submesoscale processes provide a pathway for energy to transfer from the balanced circulation to turbulent dissipation. One class of submesoscale phenomena that has been shown to be particularly effective at removing energy from the balanced flow are centrifugal-symmetric instabilities (CSIs), which grow via geostrophic shear production. CSIs have been observed to generate significant mixing in both the surface boundary layer and bottom boundary layer flows along bathymetry, where they have been implicated in the mixing and watermass transformation of Antarctic Bottom Water. However, the mixing efficiency (i.e. the fraction of the energy extracted from the flow used to irreversibly mix the fluid) of these instabilities remains uncertain, making estimates of mixing and energy dissipation due to CSI difficult.In this work we use large-eddy simulations to investigate the mixing efficiency of CSIs in the submesoscale range. We find that centrifugally-dominated CSIs (i.e. CSI mostly driven by horizontal shear production) tend to have a higher mixing efficiency than symmetrically-dominated ones (i.e. driven by vertical shear production). The mixing efficiency associated with CSIs can therefore alternately be significantly higher or significantly lower than the canonical value used by most studies. These results can be understood in light of recent work on stratified turbulence, whereby CSIs control the background state of the flow in which smaller-scale secondary overturning instabilities develop, thus actively modifying the characteristics of mixing by Kelvin-Helmholtz instabilities. Our results also suggest that it may be possible to predict the mixing efficiency with more readily measurable parameters (namely the Richardson and Rossby numbers), which would allow for parameterization of this effect.

scholarly journals Vortex pairing in an unstable anticyclonic shear flow: discrete subharmonics of one pendulum day

2001 ◽  
Vol 440 ◽  
pp. 401-409 ◽  
Author(s):  
PIERRE FLAMENT ◽  
RICK LUMPKIN ◽  
JEAN TOURNADRE ◽  
LAURENCE ARMI
Keyword(s):  
Reynolds Number ◽  
Shear Flow ◽  
Finite Amplitude ◽  
North Equatorial Current ◽  
Horizontal Shear ◽  
Vortex Pairing ◽  
Centrifugal Instability ◽  
Equatorial Current ◽  
Geometric Sequence ◽  
Orbital Periods

Observations of the downstream evolution of an oceanic zonal horizontal shear flow at a Reynolds number of about 1011, formed as the westward North Equatorial Current passes the island of Hawai‘i, reveal finite-amplitude anticyclonic vortices resulting from instability of the shear. The initial orbital period of the vortices is exactly one pendulum day (3.1 days at this latitude), centrifugal instability presumably inhibiting stronger vortices from forming. As they move downstream, they appear to pair and merge into successively larger vortices, in a geometric sequence of longer orbital periods; three subharmonic transitions are suggested with final orbital periods near 6, 12 and 24 days.

scholarly journals Shear Instability Wave along a Snowband: Instability Structure, Evolution, and Energetics Derived from Dual-Doppler Radar Data

2005 ◽  
Vol 62 (2) ◽  
pp. 351-370 ◽  
Author(s):  
Masayuki Kawashima ◽  
Yasushi Fujiyoshi
Keyword(s):  
Linear Growth ◽  
Doppler Radar ◽  
Growth Period ◽  
Radar Data ◽  
Shear Instability ◽  
Instability Wave ◽  
Horizontal Shear ◽  
Pressure Work ◽  
Doppler Radar Data ◽  
Dual Doppler Radar

Abstract This article presents a detailed analysis of a meso-γ-scale (∼17 km wavelength) shear instability wave along a snowband using a series of dual-Doppler radar data. The wave developed along a low-level shear line that formed under the strain wind field caused by an adjacent mesoscale vortex. The horizontal wind shear across the line was largest at lower levels, and the eddy-component horizontal winds and the retrieved pressure anomaly showed a bottom-intensified structure as well. The resultant vertical pressure gradient force was found to be responsible for the enhancement of alternating updrafts and downdrafts that were subsequently related to the formation of the reflectivity core/gap structure of the wave. Eddy kinetic energy (EKE) budgets of the evolving disturbance were investigated using time series of retrieved kinematic and thermodynamic data. The wave grew at an approximately constant growth rate for about 40 min from its onset. The EKE in this quasi-linear growth period was primarily generated by the horizontal shear that decreased with height. The pressure work was found to remove about two-thirds of this generation in the layer below 1 km, while in the upper layer it was constructive to EKE generation and comparable to the generation of EKE by horizontal shear. These results indicate that the source of EKE was basically located at low levels and the energy was transported upward mainly by the pressure work. After the quasi-linear growth period, horizontal shear generation rapidly decreased and EKE peaked. The buoyancy generation of EKE was small but positive in the quasi-linear growth period, then became negative because of the development of thermally indirect circulations.

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