Edgar Knobloch
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View article: Spontaneous generation of helical flows by salt fingers
Spontaneous generation of helical flows by salt fingers Open
We study the dynamics of salt fingers in the regime of slow salinity diffusion (small inverse Lewis number) and strong stratification (large density ratio), focusing on regimes relevant to Earth’s oceans. Using three-dimensional direct num…
View article: Bridging the Rossby number gap in rapidly rotating thermal convection
Bridging the Rossby number gap in rapidly rotating thermal convection Open
Geophysical and astrophysical fluid flows are typically driven by buoyancy and strongly constrained at large scales by planetary rotation. Rapidly rotating Rayleigh–Bénard convection (RRRBC) provides a paradigm for experiments and direct n…
View article: Two-dimensional turbulent condensates without bottom drag
Two-dimensional turbulent condensates without bottom drag Open
The extent to which statistical equilibrium theory is applicable to driven dissipative dynamics remains an important open question in many systems. We use extensive direct numerical simulations of the incompressible two-dimensional (2D) Na…
View article: Traveling spatially localized convective structures in an inclined porous medium
Traveling spatially localized convective structures in an inclined porous medium Open
Multiple stationary, localized structures were recently found for inclined porous medium convection with constant-temperature boundaries. We analyze traveling asymmetric, localized convective structures, consisting of 1 to 5 pulses, in a 2…
View article: Rescaled Equations for Well-Conditioned Direct Numerical Simulations of Rapidly Rotating Convection
Rescaled Equations for Well-Conditioned Direct Numerical Simulations of Rapidly Rotating Convection Open
Convection is a ubiquitous process driving geophysical/astrophysical fluid flows, which are typically strongly constrained by planetary rotation on large scales. A celebrated model of such flows, rapidly rotating Rayleigh-Bénard convection…
View article: Bridging the Rossby number gap in rapidly rotating thermal convection
Bridging the Rossby number gap in rapidly rotating thermal convection Open
Geophysical and astrophysical fluid flows are typically driven by buoyancy and strongly constrained at large scales by planetary rotation. Rapidly rotating Rayleigh-Bénard convection (RRRBC) provides a paradigm for experiments and direct n…
View article: Fluctuation-induced transitions in anisotropic two-dimensional turbulence
Fluctuation-induced transitions in anisotropic two-dimensional turbulence Open
Two-dimensional (2D) turbulence features an inverse energy cascade that produces large-scale flow structures such as large-scale vortices (LSVs) and unidirectional jets. We investigate the dynamics of such large-scale structures using exte…
View article: Emergence of rogue-like waves in a reaction-diffusion system: Stochastic output from deterministic dissipative dynamics
Emergence of rogue-like waves in a reaction-diffusion system: Stochastic output from deterministic dissipative dynamics Open
Rogue waves are an intriguing nonlinear phenomenon arising across different scales, ranging from ocean waves through optics to Bose–Einstein condensates. We describe the emergence of rogue wave-like dynamics in a reaction-diffusion system …
View article: From a vortex gas to a vortex crystal in instability-driven two-dimensional turbulence
From a vortex gas to a vortex crystal in instability-driven two-dimensional turbulence Open
We study structure formation in two-dimensional turbulence driven by an external force, interpolating between linear instability forcing and random stirring, subject to nonlinear damping. Using extensive direct numerical simulations, we un…
View article: Time-dependent localized patterns in a predator-prey model
Time-dependent localized patterns in a predator-prey model Open
Numerical continuation is used to compute solution branches in a two-component reaction-diffusion model of Leslie–Gower type. Two regimes are studied in detail. In the first, the homogeneous state loses stability to supercritical spatially…
View article: Time-dependent localized patterns in a predator-prey model
Time-dependent localized patterns in a predator-prey model Open
Numerical continuation is used to compute solution branches in a two-component reaction-diffusion model of Leslie--Gower type. %in the vicinity of a Turing-Hopf interaction. Two regimes are studied in detail. In the first, the homogeneous …
View article: Fixed-flux Rayleigh-Bénard convection in doubly periodic domains: generation of large-scale shear
Fixed-flux Rayleigh-Bénard convection in doubly periodic domains: generation of large-scale shear Open
This work studies two-dimensional fixed-flux Rayleigh-Bénard convection with periodic boundary conditions in both horizontal and vertical directions and analyzes its dynamics using numerical continuation, secondary instability analysis and…
View article: Bifurcation delay and front propagation in the real Ginzburg-Landau equation on a time-dependent domain
Bifurcation delay and front propagation in the real Ginzburg-Landau equation on a time-dependent domain Open
This work analyzes bifurcation delay and front propagation in the one-dimensional real Ginzburg-Landau equation (RGLE) with periodic boundary conditions on monotonically growing or shrinking domains. First, we obtain closed-form expression…
View article: Fluctuation-Induced Transitions in Anisotropic Two-Dimensional Turbulence
Fluctuation-Induced Transitions in Anisotropic Two-Dimensional Turbulence Open
Two-dimensional (2D) turbulence features an inverse energy cascade that produces large-scale flow structures such as large-scale vortices (LSVs) and unidirectional jets. We investigate the dynamics of such structures using extensive direct…
View article: Traveling spiral wave chimeras in coupled oscillator systems: emergence, dynamics, and transitions
Traveling spiral wave chimeras in coupled oscillator systems: emergence, dynamics, and transitions Open
Systems of coupled nonlinear oscillators often exhibit states of partial synchrony in which some of the oscillators oscillate coherently while the rest remain incoherent. If such a state emerges spontaneously, in other words, if it cannot …
View article: From a vortex gas to a vortex crystal in instability-driven two-dimensional turbulence
From a vortex gas to a vortex crystal in instability-driven two-dimensional turbulence Open
We study structure formation in two-dimensional turbulence driven by an external force, interpolating between linear instability forcing and random stirring, subject to nonlinear damping. Using extensive direct numerical simulations, we un…
View article: Front propagation and global bifurcations in a multivariable reaction-diffusion model
Front propagation and global bifurcations in a multivariable reaction-diffusion model Open
We study the existence and stability of propagating fronts in Meinhardt’s multivariable reaction-diffusion model of branching in one spatial dimension. We identify a saddle-node-infinite-period bifurcation of fronts that leads to episodic …
View article: Suppression of Wall Modes in Rapidly Rotating Rayleigh-Bénard Convection by Narrow Horizontal Fins
Suppression of Wall Modes in Rapidly Rotating Rayleigh-Bénard Convection by Narrow Horizontal Fins Open
The heat transport by rapidly rotating Rayleigh-Bénard convection is of fundamental importance to many geophysical flows. Laboratory measurements are impeded by robust wall modes that develop along vertical walls, significantly perturbing …
View article: Data supplement for "Stationary broken parity states in active matter models''
Data supplement for "Stationary broken parity states in active matter models'' Open
Data sets and python codes that produce all figures in "Stationary broken parity states in active matter models''. Additionally it contains example Matlab codes that perform the numerical path continuation with pde2path.
View article: Data supplement for "Stationary broken parity states in active matter models''
Data supplement for "Stationary broken parity states in active matter models'' Open
Data sets and python codes that produce all figures in "Stationary broken parity states in active matter models''. Additionally it contains example Matlab codes that perform the numerical path continuation with pde2path.
View article: Suppression of wall modes in rapidly rotating Rayleigh-Bénard convection by narrow horizontal fins
Suppression of wall modes in rapidly rotating Rayleigh-Bénard convection by narrow horizontal fins Open
The heat transport by rapidly-rotating Rayleigh-Bénard convection is of fundamental importance to many geophysical flows. Laboratory measurements are impeded by robust wall modes which develop along vertical walls, significantly perturbing…
View article: Front propagation and global bifurcations in a multivariable reaction-diffusion model
Front propagation and global bifurcations in a multivariable reaction-diffusion model Open
We study the existence and stability of propagating fronts in Meinhardt's multivariable reaction-diffusion model of branching in one spatial dimension. We identify a saddle-node-infinite-period (SNIPER) bifurcation of fronts that leads to …
View article: Collisions of localized patterns in a nonvariational Swift-Hohenberg equation
Collisions of localized patterns in a nonvariational Swift-Hohenberg equation Open
The cubic-quintic Swift-Hohenberg equation (SH35) has been proposed as an order parameter description of several convective systems with reflection symmetry in the layer midplane, including binary fluid convection. We use numerical continu…
View article: Elastic fingering in a rotating Hele-Shaw cell
Elastic fingering in a rotating Hele-Shaw cell Open
We consider the steady-state fingering instability of an elastic membrane separating two fluids of different density under external pressure in a rotating Hele-Shaw cell. Both inextensible and highly extensible membranes are considered, an…
View article: Single-Mode Solutions for Convection and Double-Diffusive Convection in Porous Media
Single-Mode Solutions for Convection and Double-Diffusive Convection in Porous Media Open
This work employs single-mode equations to study convection and double-diffusive convection in a porous medium where the Darcy law provides large-scale damping. We first consider thermal convection with salinity as a passive scalar. The si…
View article: Spontaneous suppression of inverse energy cascade in instability-driven 2-D turbulence
Spontaneous suppression of inverse energy cascade in instability-driven 2-D turbulence Open
Instabilities of fluid flows often generate turbulence. Using extensive direct numerical simulations, we study two-dimensional turbulence driven by a wavenumber-localised instability superposed on stochastic forcing, in contrast to previou…
View article: Instability mechanisms of repelling peak solutions in a multi-variable activator–inhibitor system
Instability mechanisms of repelling peak solutions in a multi-variable activator–inhibitor system Open
We study the linear stability properties of spatially localized single- and multi-peak states generated in a subcritical Turing bifurcation in the Meinhardt model of branching. In one spatial dimension, these states are organized in a foli…
View article: Instability mechanisms of repelling peak solutions in a multi-variable activator-inhibitor system
Instability mechanisms of repelling peak solutions in a multi-variable activator-inhibitor system Open
We study the linear stability properties of spatially localized single- and multi-peak states generated in a subcritical Turing bifurcation in the Meinhardt model of branching. In one spatial dimension, these states are organized in a foli…
View article: Universal wrinkling of supported elastic rings
Universal wrinkling of supported elastic rings Open
An exactly solvable family of models describing the wrinkling of substrate-supported inextensible elastic rings under compression is identified. The resulting wrinkle profiles are shown to be related to the buckled states of an unsupported…