1,712 research outputs found
Invariant Solution underlying Oblique Stripe Patterns in Plane Couette Flow
When subcritical shear flows transition to turbulence, laminar and turbulent
flow often coexists in space, giving rise to turbulent-laminar patterns. Most
prominent are regular stripe patterns with large-scale periodicity and oblique
orientation. Oblique stripes are a robust phenomenon, observed in experiments
and flow simulations, yet their origin remains unclear. We demonstrate the
existence of an invariant equilibrium solution of the fully nonlinear 3D
Navier-Stokes equations that resembles the oblique pattern of turbulent-laminar
stripes in plane Couette flow. We uncover the origin of the stripe equilibrium
and show how it emerges from the well-studied Nagata equilibrium via two
successive symmetry-breaking bifurcations
Studying edge geometry in transiently turbulent shear flows
In linearly stable shear flows at moderate Re, turbulence spontaneously
decays despite the existence of a codimension-one manifold, termed the edge of
chaos, which separates decaying perturbations from those triggering turbulence.
We statistically analyse the decay in plane Couette flow, quantify the breaking
of self-sustaining feedback loops and demonstrate the existence of a whole
continuum of possible decay paths. Drawing parallels with low-dimensional
models and monitoring the location of the edge relative to decaying
trajectories we provide evidence, that the edge of chaos separates state space
not globally. It is instead wrapped around the turbulence generating structures
and not an independent dynamical structure but part of the chaotic saddle.
Thereby, decaying trajectories need not cross the edge, but circumnavigate it
while unwrapping from the turbulent saddle.Comment: 11 pages, 6 figure
Snakes and ladders: localized solutions of plane Couette flow
We demonstrate the existence of a large number of exact solutions of plane
Couette flow, which share the topology of known periodic solutions but are
localized in space. Solutions of different size are organized in a
snakes-and-ladders structure strikingly similar to that observed for simpler
pattern-forming PDE systems. These new solutions are a step towards extending
the dynamical systems view of transitional turbulence to spatially extended
flows.Comment: submitted to Physics Review Letter
Edge states control droplet break-up in sub-critical extensional flows
A fluid droplet suspended in an extensional flow of moderate intensity may
break into pieces, depending on the amplitude of the initial droplet
deformation. In subcritical uniaxial extensional flow the non-breaking base
state is linearly stable, implying that only a finite amplitude perturbation
can trigger break-up. Consequently, the stable base solution is surrounded by
its finite basin of attraction. The basin boundary, which separates initial
droplet shapes returning to the non-breaking base state from those becoming
unstable and breaking up, is characterized using edge tracking techniques. We
numerically construct the edge state, a dynamically unstable equilibrium whose
stable manifold forms the basin boundary. The edge state equilibrium controls
if the droplet breaks and selects a unique path towards break-up. This path
physically corresponds to the well-known end-pinching mechanism. Our results
thereby rationalize the dynamics observed experimentally [Stone & Leal, J.
Fluid Mech. 206, 223 (1989)
Identifying invariant solutions of wall-bounded three-dimensional shear flows using robust adjoint-based variational techniques
Invariant solutions of the Navier-Stokes equations play an important role in
the spatiotemporally chaotic dynamics of turbulent shear flows. Despite the
significance of these solutions, their identification remains a computational
challenge, rendering many solutions inaccessible and thus hindering progress
towards a dynamical description of turbulence in terms of invariant solutions.
We compute equilibria of three-dimensional wall-bounded shear flows using an
adjoint-based matrix-free variational approach. To address the challenge of
computing pressure in the presence of solid walls, we develop a formulation
that circumvents the explicit construction of pressure and instead employs the
influence matrix method. Together with a data-driven convergence acceleration
technique based on dynamic mode decomposition, this yields a practically
feasible alternative to state-of-the-art Newton methods for converging
equilibrium solutions. We successfully converge multiple equilibria of plane
Couette flow starting from inaccurate guesses extracted from a turbulent time
series. The variational method significantly outperforms the standard
Newton-hookstep method, demonstrating its superior robustness and suggesting a
considerably larger convergence radius
Superspreading events suggest aerosol transmission of SARS-CoV-2 by accumulation in enclosed spaces
Viral transmission pathways have profound implications for public safety; it
is thus imperative to establish a complete understanding of viable infectious
avenues. Mounting evidence suggests SARS-CoV-2 can be transmitted via the air;
however, this has not yet been demonstrated. Here we quantitatively analyze
virion accumulation by accounting for aerosolized virion emission and
destabilization. Reported superspreading events analyzed within this framework
point towards aerosol mediated transmission of SARS-CoV-2. Virion exposure
calculated for these events is found to trace out a single value, suggesting a
universal minimum infective dose (MID) via aerosol that is comparable to the
MIDs measured for other respiratory viruses; thus, the consistent infectious
exposure levels and their commensurability to known aerosol-MIDs establishes
the plausibility of aerosol transmission of SARS-CoV-2. Using filtration at a
rate exceeding the destabilization rate of aerosolized SARS-CoV-2 can reduce
exposure below this infective dose.Comment: 6 pages, 4 figure
- …