Jacob Page
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View article: Characterizing the Reynolds number dependence of the chaotic attractor in two-dimensional turbulence with dimension-minimizing autoencoders
Characterizing the Reynolds number dependence of the chaotic attractor in two-dimensional turbulence with dimension-minimizing autoencoders Open
Deep autoencoder neural networks can generate highly accurate, low-order representations of turbulence. We design a family of autoencoders which are a combination of a “dense-block” encoder-decoder structure [Page , ], an "implicit rank mi…
View article: Dynamical relevance of periodic orbits under increasing Reynolds number and connections to inviscid dynamics
Dynamical relevance of periodic orbits under increasing Reynolds number and connections to inviscid dynamics Open
Large numbers of relative periodic orbits (RPOs) have been found recently in doubly periodic, two-dimensional Kolmogorov flow at moderate Reynolds numbers ${\textit{Re}} \in \{40, 100\}$ . While these solutions lead to robust statistical r…
View article: Characterizing the Reynolds number dependence of the chaotic attractor in two-dimensional turbulence with dimension-minimizing autoencoders
Characterizing the Reynolds number dependence of the chaotic attractor in two-dimensional turbulence with dimension-minimizing autoencoders Open
Deep autoencoder neural networks can generate highly accurate, low-order representations of turbulence. We design a new family of autoencoders which are a combination of a 'dense-block' encoder-decoder structure (Page et al, J. Fluid Mech.…
View article: Dynamical relevance of periodic orbits under increasing Reynolds number and connections to inviscid dynamics
Dynamical relevance of periodic orbits under increasing Reynolds number and connections to inviscid dynamics Open
Large numbers of relative periodic orbits (RPOs) have been found recently in doubly-periodic, two-dimensional Kolmogorov flow at moderate Reynolds numbers $Re \in \{40, 100\}$. While these solutions lead to robust statistical reconstructio…
View article: Super-resolution of turbulence with dynamics in the loss
Super-resolution of turbulence with dynamics in the loss Open
Super-resolution of turbulence is a term used to describe the prediction of high-resolution snapshots of a flow from coarse-grained observations. This is typically accomplished with a deep neural network and training usually requires a dat…
View article: Transition route to elastic and elasto-inertial turbulence in polymer channel flows
Transition route to elastic and elasto-inertial turbulence in polymer channel flows Open
Viscoelastic shear flows support additional chaotic states beyond simple Newtonian turbulence. In vanishing Reynolds number flows, the nonlinearity in the polymer evolution equation alone can sustain inertialess “elastic” turbulence (ET) w…
View article: Super-resolution with dynamics in the loss
Super-resolution with dynamics in the loss Open
Super-resolution of turbulence is a term used to describe the prediction of high-resolution snapshots of a flow from coarse-grained observations. This is typically accomplished with a deep neural network and training usually requires a dat…
View article: Transition route to elastic and elasto-inertial turbulence in polymer channel flows
Transition route to elastic and elasto-inertial turbulence in polymer channel flows Open
Viscoelastic shear flows support additional chaotic states beyond simple Newtonian turbulence. In vanishing Reynolds number flows, the nonlinearity in the polymer evolution equation alone can sustain inertialess 'elastic' turbulence (ET) w…
View article: Exact coherent structures in two-dimensional turbulence identified with convolutional autoencoders
Exact coherent structures in two-dimensional turbulence identified with convolutional autoencoders Open
Convolutional autoencoders are used to deconstruct the changing dynamics of two-dimensional Kolmogorov flow as $Re$ is increased from weakly chaotic flow at $Re=40$ to a chaotic state dominated by a domain-filling vortex pair at $Re=400$ .…
View article: Asymptotics of the centre-mode instability in viscoelastic channel flow: with and without inertia
Asymptotics of the centre-mode instability in viscoelastic channel flow: with and without inertia Open
Motivated by the recent numerical results of Khalid et al. ( Phys. Rev. Lett. , vol. 127, 2021, 134502), we consider the large-Weissenberg-number ( $W$ ) asymptotics of the centre mode instability in inertialess viscoelastic channel flow. …
View article: Recurrent flow patterns as a basis for two-dimensional turbulence: Predicting statistics from structures
Recurrent flow patterns as a basis for two-dimensional turbulence: Predicting statistics from structures Open
A dynamical systems approach to turbulence envisions the flow as a trajectory through a high-dimensional state space [Hopf, Commun. Appl. Maths 1 , 303 (1948)]. The chaotic dynamics are shaped by the unstable simple invariant solutions pop…
View article: Multistability of elasto-inertial two-dimensional channel flow
Multistability of elasto-inertial two-dimensional channel flow Open
Elasto-inertial turbulence (EIT) is a recently discovered two-dimensional chaotic flow state observed in dilute polymer solutions. Two possibilities are currently hypothesized to be linked to the dynamical origins of EIT: (i) viscoelastic …
View article: Inertial enhancement of the polymer diffusive instability
Inertial enhancement of the polymer diffusive instability Open
Beneitez et al. ( Phys. Rev. Fluids , vol. 8, 2023, L101901) have recently discovered a new linear ‘polymer diffusive instability’ (PDI) in inertialess rectilinear viscoelastic shear flow using the finitely extensible nonlinear elastic con…
View article: Inertial enhancement of the polymer diffusive instability
Inertial enhancement of the polymer diffusive instability Open
Beneitez et al. (Phys. Rev. Fluids, 8, L101901, 2023) have recently discovered a new linear “polymer diffusive instability” (PDI) in inertialess rectilinear viscoelastic shear flow using the FENE-P model when polymer stress diffusion is pr…
View article: Asymptotics of the centre mode instability in viscoelastic channel flow: with and without inertia
Asymptotics of the centre mode instability in viscoelastic channel flow: with and without inertia Open
Motivated by the recent numerical results of Khalid et al., Phys. Rev. Lett., 127, 134502 (2021), we consider the large-Weissenberg-number ($W$) asymptotics of the centre mode instability in inertialess viscoelastic channel flow. The insta…
View article: Polymer diffusive instability leading to elastic turbulence in plane Couette flow
Polymer diffusive instability leading to elastic turbulence in plane Couette flow Open
Elastic turbulence is a chaotic flow state observed in dilute polymer solutions in the absence of inertia. It was discovered experimentally in circular geometries and has long been thought to require a finite amplitude perturbation in para…
View article: Exploring the free-energy landscape of a rotating superfluid
Exploring the free-energy landscape of a rotating superfluid Open
The equilibrium state of a superfluid in a rotating cylindrical vessel is a vortex crystal—an array of vortex lines, which is stationary in the rotating frame. Experimental realizations of this behavior typically show a sequence of transie…
View article: Exact coherent structures in two-dimensional turbulence identified with convolutional autoencoders
Exact coherent structures in two-dimensional turbulence identified with convolutional autoencoders Open
Convolutional autoencoders are used to deconstruct the changing dynamics of two-dimensional Kolmogorov flow as $Re$ is increased from weakly chaotic flow at $Re=40$ to a chaotic state dominated by a domain-filling vortex pair at $Re=400$. …
View article: Multistability of elasto-inertial two-dimensional channel flow
Multistability of elasto-inertial two-dimensional channel flow Open
Elasto-inertial turbulence (EIT) is a recently discovered two-dimensional chaotic flow state observed in dilute polymer solutions. It has been hypothesised that the dynamical origins of EIT are linked to a center-mode instability, whose no…
View article: Exploring the free-energy landscape of a rotating superfluid
Exploring the free-energy landscape of a rotating superfluid Open
The equilibrium state of a superfluid in a rotating cylindrical vessel is a vortex crystal -- an array of vortex lines which is stationary in the rotating frame. Experimental realisations of this behaviour typically show a sequence of tran…
View article: Recurrent flow patterns as a basis for turbulence: predicting statistics from structures
Recurrent flow patterns as a basis for turbulence: predicting statistics from structures Open
A dynamical systems approach to turbulence envisions the flow as a trajectory through a high-dimensional state space transiently visiting the neighbourhoods of unstable simple invariant solutions (E. Hopf, Commun. Appl. Maths 1, 303, 1948)…
View article: Finite-amplitude elastic waves in viscoelastic channel flow from large to zero Reynolds number
Finite-amplitude elastic waves in viscoelastic channel flow from large to zero Reynolds number Open
Using branch continuation in the FENE-P model, we show that finite-amplitude travelling waves borne out of the recently discovered linear instability of viscoelastic channel flow (Khalid et al. , J. Fluid Mech. , vol. 915, 2021, A43) are s…
View article: Polymeric diffusive instability leading to elastic turbulence in plane Couette flow
Polymeric diffusive instability leading to elastic turbulence in plane Couette flow Open
Elastic turbulence is a chaotic flow state observed in dilute polymer solutions in the absence of inertia. It was discovered experimentally in circular geometries and has long been thought to require a finite amplitude perturbation in para…
View article: Vorticity amplification in wavy viscoelastic channel flow
Vorticity amplification in wavy viscoelastic channel flow Open
Surface distortions to an otherwise planar channel flow introduce vorticity perturbations. In Newtonian fluids, the vorticity induced by small surface undulations on the lower wall is advected by the background flow and diffuses into the f…
View article: First coherent structure in elasto-inertial turbulence
First coherent structure in elasto-inertial turbulence Open
Two-dimensional channel flow simulations of FENE-P (finitely extensible nonlinear elastic-Peterlin) fluid in the elasto-inertial turbulence (EIT) regime reveal distinct regimes ranging from chaos to a steady traveling wave which takes the …
View article: Weakly nonlinear analysis of the viscoelastic instability in channel flow for finite and vanishing Reynolds numbers
Weakly nonlinear analysis of the viscoelastic instability in channel flow for finite and vanishing Reynolds numbers Open
The recently discovered centre-mode instability of rectilinear viscoelastic shear flow (Garg et al. , Phys. Rev. Lett. , vol. 121, 2018, 024502) has offered an explanation for the origin of elasto-inertial turbulence that occurs at lower W…
View article: Finite-amplitude elastic waves in viscoelastic channel flow from large to zero Reynolds number
Finite-amplitude elastic waves in viscoelastic channel flow from large to zero Reynolds number Open
Using branch continuation in the FENE-P model, we show that finite-amplitude travelling waves borne out of the recently-discovered linear instability of viscoelastic channel flow (Khalid et al. {\em J. Fluid Mech.} {\bf 915}, A43, 2021) ar…
View article: Vorticity amplification in viscoelastic channel flows with long-wave surface distortions
Vorticity amplification in viscoelastic channel flows with long-wave surface distortions Open
Surface distortions to an otherwise planar channel flow introduce vorticity perturbations. We examine this scenario in viscoelastic fluids, and identify new mechanisms by which significant vorticity perturbations can be generated in both i…
View article: Weakly nonlinear analysis of the viscoelastic instability in channel flow for finite and vanishing Reynolds numbers
Weakly nonlinear analysis of the viscoelastic instability in channel flow for finite and vanishing Reynolds numbers Open
The recently-discovered centre-mode instability of rectilinear viscoelastic shear flow (Garg et al. Phy. Rev. Lett. 121, 024502, 2018) has offered an explanation for the origin of elasto-inertial turbulence (EIT) which occurs at lower Weis…