scholarly journals The structure and origin of confined Holmboe waves

2018 ◽  
Vol 848 ◽  
pp. 508-544 ◽  
Author(s):  
Adrien Lefauve ◽  
J. L. Partridge ◽  
Qi Zhou ◽  
S. B. Dalziel ◽  
C. P. Caulfield ◽  
...  
Keyword(s):  
Shear Flow ◽  
Coherent Structure ◽  
Shear Flows ◽  
Three Dimensional ◽  
Finite Amplitude ◽  
Geophysical Flows ◽  
Two Dimensional ◽  
Lateral Confinement ◽  
Stratified Shear Flow ◽  
Spatio Temporal

Finite-amplitude manifestations of stratified shear flow instabilities and their spatio-temporal coherent structures are believed to play an important role in turbulent geophysical flows. Such shear flows commonly have layers separated by sharp density interfaces, and are therefore susceptible to the so-called Holmboe instability, and its finite-amplitude manifestation, the Holmboe wave. In this paper, we describe and elucidate the origin of an apparently previously unreported long-lived coherent structure in a sustained stratified shear flow generated in the laboratory by exchange flow through an inclined square duct connecting two reservoirs filled with fluids of different densities. Using a novel measurement technique allowing for time-resolved, near-instantaneous measurements of the three-component velocity and density fields simultaneously over a three-dimensional volume, we describe the three-dimensional geometry and spatio-temporal dynamics of this structure. We identify it as a finite-amplitude, nonlinear, asymmetric confined Holmboe wave (CHW), and highlight the importance of its spanwise (lateral) confinement by the duct boundaries. We pay particular attention to the spanwise vorticity, which exhibits a travelling, near-periodic structure of sheared, distorted, prolate spheroids with a wide ‘body’ and a narrower ‘head’. Using temporal linear stability analysis on the two-dimensional streamwise-averaged experimental flow, we solve for three-dimensional perturbations having two-dimensional, cross-sectionally confined eigenfunctions and a streamwise normal mode. We show that the dispersion relation and the three-dimensional spatial structure of the fastest-growing confined Holmboe instability are in good agreement with those of the observed confined Holmboe wave. We also compare those results with a classical linear analysis of two-dimensional perturbations (i.e. with no spanwise dependence) on a one-dimensional base flow. We conclude that the lateral confinement is an important ingredient of the confined Holmboe instability, which gives rise to the CHW, with implications for many inherently confined geophysical flows such as in valleys, estuaries, straits or deep ocean trenches. Our results suggest that the CHW is an example of an experimentally observed, inherently nonlinear, robust, long-lived coherent structure which has developed from a linear instability. We conjecture that the CHW is a promising candidate for a class of exact coherent states underpinning the dynamics of more disordered, yet continually forced stratified shear flows.

The anatomy of the mixing transition in homogeneous and stratified free shear layers

2000 ◽  
Vol 413 ◽  
pp. 1-47 ◽  
Author(s):  
C. P. CAULFIELD ◽  
W. R. PELTIER
Keyword(s):  
Shear Layer ◽  
Three Dimensional ◽  
Streamwise Vortex ◽  
Shear Layers ◽  
Finite Amplitude ◽  
Small Scale ◽  
Two Dimensional ◽  
Streamwise Vortices ◽  
Free Shear Layers ◽  
Nonlinear Amplification

We investigate the detailed nature of the ‘mixing transition’ through which turbulence may develop in both homogeneous and stratified free shear layers. Our focus is upon the fundamental role in transition, and in particular the associated ‘mixing’ (i.e. small-scale motions which lead to an irreversible increase in the total potential energy of the flow) that is played by streamwise vortex streaks, which develop once the primary and typically two-dimensional Kelvin–Helmholtz (KH) billow saturates at finite amplitude.Saturated KH billows are susceptible to a family of three-dimensional secondary instabilities. In homogeneous fluid, secondary stability analyses predict that the stream-wise vortex streaks originate through a ‘hyperbolic’ instability that is localized in the vorticity braids that develop between billow cores. In sufficiently strongly stratified fluid, the secondary instability mechanism is fundamentally different, and is associated with convective destabilization of the statically unstable sublayers that are created as the KH billows roll up.We test the validity of these theoretical predictions by performing a sequence of three-dimensional direct numerical simulations of shear layer evolution, with the flow Reynolds number (defined on the basis of shear layer half-depth and half the velocity difference) Re = 750, the Prandtl number of the fluid Pr = 1, and the minimum gradient Richardson number Ri(0) varying between 0 and 0.1. These simulations quantitatively verify the predictions of our stability analysis, both as to the spanwise wavelength and the spatial localization of the streamwise vortex streaks. We track the nonlinear amplification of these secondary coherent structures, and investigate the nature of the process which actually triggers mixing. Both in stratified and unstratified shear layers, the subsequent nonlinear amplification of the initially localized streamwise vortex streaks is driven by the vertical shear in the evolving mean flow. The two-dimensional flow associated with the primary KH billow plays an essentially catalytic role. Vortex stretching causes the streamwise vortices to extend beyond their initially localized regions, and leads eventually to a streamwise-aligned collision between the streamwise vortices that are initially associated with adjacent cores.It is through this collision of neighbouring streamwise vortex streaks that a final and violent finite-amplitude subcritical transition occurs in both stratified and unstratified shear layers, which drives the mixing process. In a stratified flow with appropriate initial characteristics, the irreversible small-scale mixing of the density which is triggered by this transition leads to the development of a third layer within the flow of relatively well-mixed fluid that is of an intermediate density, bounded by narrow regions of strong density gradient.

Three-dimensional vortex formation from an oscillating, non-uniform cylinder

1992 ◽  
Vol 238 ◽  
pp. 31-54 ◽  
Author(s):  
F. Nuzzi ◽  
C. Magness ◽  
D. Rockwell
Keyword(s):  
Flow Structure ◽  
Phase Plane ◽  
Shear Flows ◽  
Vortex Formation ◽  
Excitation Frequency ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Near Wake ◽  
Shedding Frequency

A cylinder having mild variations in diameter along its span is subjected to controlled excitation at frequencies above and below the inherent shedding frequency from the corresponding two-dimensional cylinder. The response of the near wake is characterized in terms of timeline visualization and velocity traces, spectra, and phase plane representations. It is possible to generate several types of vortex formation, depending upon the excitation frequency. Globally locked-in, three-dimensional vortex formation can occur along the entire span of the flow. Regions of locally locked-in and period-doubled vortex formation can exist along different portions of the span provided the excitation frequency is properly tuned. Unlike the classical subharmonic instability in free shear flows, the occurrence of period-doubled vortex formation does not involve vortex coalescence; instead, the flow structure alternates between two different states.

The wall jet in a rotating fluid

1997 ◽  
Vol 335 ◽  
pp. 1-28 ◽  
Author(s):  
MELVIN E. STERN ◽  
ERIC P. CHASSIGNET ◽  
J. A. WHITEHEAD
Keyword(s):  
Vertical Wall ◽  
Three Dimensional ◽  
Point Vortex ◽  
Separation Distance ◽  
Finite Amplitude ◽  
Large Reynolds Number ◽  
Spatial Evolution ◽  
Two Dimensional ◽  
Rotating Fluid ◽  
Coriolis Parameter

The previously observed spatial evolution of the two-dimensional turbulent flow from a source on the vertical wall of a shallow layer of rapidly rotating fluid is strikingly different from the non-rotating three-dimensional counterpart, insofar as the instability eddies generated in the former case cause the flow to separate completely from the wall at a finite downstream distance. In seeking an explanation of this, we first compute the temporal evolution of two-dimensional finite-amplitude waves on an unstable laminar jet using a finite difference calculation at large Reynolds number. This yields a dipolar vorticity pattern which propagates normal to the wall, while leaving some of the near-wall vorticity (negative) of the basic flow behind. The residual far-field eddy therefore contains a net positive circulation and this property is incorporated in a heuristic point-vortex model of the spatial evolution of the instability eddies observed in a laboratory experiment of a flow emerging from a source on a vertical wall in a rotating tank. The model parameterizes the effect of Ekman bottom friction in decreasing the circulation of eddies which are periodically emitted from the source flow on the wall. Further downstream, the point vortices of the model merge and separate abruptly from the wall; the statistics suggest that the downstream separation distance scales with the Ekman spin-up time (inversely proportional to the square root of the Coriolis parameter f) and with the mean source velocity. When the latter is small and f is large, qualitative support is obtained from laboratory experiments.

Compressible magnetoconvection in three dimensions: planforms and nonlinear behaviour

1995 ◽  
Vol 305 ◽  
pp. 281-305 ◽  
Author(s):  
P. C. Matthews ◽  
M. R. E. Proctor ◽  
N. O. Weiss
Keyword(s):  
Magnetic Field ◽  
Shear Flow ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Nonlinear Behaviour ◽  
Two Dimensional ◽  
Horizontal Shear ◽  
Mean Flow ◽  
The Magnetic Field

Convection in a compressible fiuid with an imposed vertical magnetic field is studied numerically in a three-dimensional Cartesian geometry with periodic lateral boundary conditions. Attention is restricted to the mildly nonlinear regime, with parameters chosen first so that convection at onset is steady, and then so that it is oscillatory.Steady convection occurs in the form of two-dimensional rolls when the magnetic field is weak. These rolls can become unstable to a mean horizontal shear flow, which in two dimensions leads to a pulsating wave in which the direction of the mean flow reverses. In three dimensions a new pattern is found in which the alignment of the rolls and the shear flow alternates.If the magnetic field is sufficiently strong, squares or hexagons are stable at the onset of convection. Both the squares and the hexagons have an asymmetrical topology, with upflow in plumes and downflow in sheets. For the squares this involves a resonance between rolls aligned with the box and rolls aligned digonally to the box. The preference for three-dimensional flow when the field is strong is a consequence of the compressibility of the layer- for Boussinesq magnetoconvection rolls are always preferred over squares at onset.In the regime where convection is oscillatory, the preferred planform for moderate fields is found to be alternating rolls - standing waves in both horizontal directions which are out of phase. For stronger fields, both alternating rolls and two-dimensional travelling rolls are stable. As the amplitude of convection is increased, either by dcereasing the magnetic field strength or by increasing the temperature contrast, the regular planform structure seen at onset is soon destroyed by secondary instabilities.

scholarly journals Global bifurcations to subcritical magnetorotational dynamo action in Keplerian shear flow

2013 ◽  
Vol 731 ◽  
pp. 1-45 ◽  
Author(s):  
A. Riols ◽  
F. Rincon ◽  
C. Cossu ◽  
G. Lesur ◽  
P.-Y. Longaretti ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Shear Flow ◽  
Shear Flows ◽  
Three Dimensional ◽  
Transition To Turbulence ◽  
Global Bifurcations ◽  
Magnetic Field Generation ◽  
Dynamo Action ◽  
Systems Research ◽  
Hydrodynamic Shear

AbstractMagnetorotational dynamo action in Keplerian shear flow is a three-dimensional nonlinear magnetohydrodynamic process, the study of which is relevant to the understanding of accretion processes and magnetic field generation in astrophysics. Transition to this form of dynamo action is subcritical and shares many characteristics with transition to turbulence in non-rotating hydrodynamic shear flows. This suggests that these different fluid systems become active through similar generic bifurcation mechanisms, which in both cases have eluded detailed understanding so far. In this paper, we build on recent work on the two problems to investigate numerically the bifurcation mechanisms at work in the incompressible Keplerian magnetorotational dynamo problem in the shearing box framework. Using numerical techniques imported from dynamical systems research, we show that the onset of chaotic dynamo action at magnetic Prandtl numbers larger than unity is primarily associated with global homoclinic and heteroclinic bifurcations of nonlinear magnetorotational dynamo cycles born out of saddle-node bifurcations. These global bifurcations are found to be supplemented by local bifurcations of cycles marking the beginning of period-doubling cascades. The results suggest that nonlinear magnetorotational dynamo cycles provide the pathway to injection of both kinetic and magnetic energy for the problem of transition to turbulence and dynamo action in incompressible magnetohydrodynamic Keplerian shear flow in the absence of an externally imposed magnetic field. Studying the nonlinear physics and bifurcations of these cycles in different regimes and configurations may subsequently help to understand better the physical conditions of excitation of magnetohydrodynamic turbulence and instability-driven dynamos in a variety of astrophysical systems and laboratory experiments. The detailed characterization of global bifurcations provided for this three-dimensional subcritical fluid dynamics problem may also prove useful for the problem of transition to turbulence in hydrodynamic shear flows.

Possibilities of Incorporating Coherent Structure Models in Turbulent Shear Flow Calculations

1990 ◽  
Vol 43 (5S) ◽  
pp. S210-S213
Author(s):  
J. T. C. Liu
Keyword(s):  
Shear Flow ◽  
Coherent Structure ◽  
Shear Flows ◽  
Hydrodynamic Instability ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Wall Bounded Flows ◽  
Dynamical Instabilities

We discuss possibilities of using coherent structure models in turbulent shear flow description. The nonuniversality of different classes of such flows is directly attributed to the nonuniversality of hydrodynamic instability mechanisms. This is fully explored in discussions of free shear flows, where dynamical instabilities are important and in wall-bounded flows where longitudinal vorticity system and its nonlinear consequence are at play.

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