Complete phase diagram for coherent vortex formation in a two-dimensional inviscid fluid in an annulus

AbstractWe study the scaling properties and Kraichnan–Leith–Batchelor (KLB) theory of forced inverse cascades in generalized two-dimensional (2D) fluids (${\it\alpha}$-turbulence models) simulated at resolution $8192^{2}$. We consider ${\it\alpha}=1$ (surface quasigeostrophic flow), ${\it\alpha}=2$ (2D Euler flow) and ${\it\alpha}=3$. The forcing scale is well resolved, a direct cascade is present and there is no large-scale dissipation. Coherent vortices spanning a range of sizes, most larger than the forcing scale, are present for both ${\it\alpha}=1$ and ${\it\alpha}=2$. The active scalar field for ${\it\alpha}=3$ contains comparatively few and small vortices. The energy spectral slopes in the inverse cascade are steeper than the KLB prediction $-(7-{\it\alpha})/3$ in all three systems. Since we stop the simulations well before the cascades have reached the domain scale, vortex formation and spectral steepening are not due to condensation effects; nor are they caused by large-scale dissipation, which is absent. One- and two-point p.d.f.s, hyperflatness factors and structure functions indicate that the inverse cascades are intermittent and non-Gaussian over much of the inertial range for ${\it\alpha}=1$ and ${\it\alpha}=2$, while the ${\it\alpha}=3$ inverse cascade is much closer to Gaussian and non-intermittent. For ${\it\alpha}=3$ the steep spectrum is close to that associated with enstrophy equipartition. Continuous wavelet analysis shows approximate KLB scaling $\mathscr{E}(k)\propto k^{-2}~({\it\alpha}=1)$ and $\mathscr{E}(k)\propto k^{-5/3}~({\it\alpha}=2)$ in the interstitial regions between the coherent vortices. Our results demonstrate that coherent vortex formation (${\it\alpha}=1$ and ${\it\alpha}=2$) and non-realizability (${\it\alpha}=3$) cause 2D inverse cascades to deviate from the KLB predictions, but that the flow between the vortices exhibits KLB scaling and non-intermittent statistics for ${\it\alpha}=1$ and ${\it\alpha}=2$.

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Large-Scale Coherent Vortex Formation in Two-Dimensional Turbulence

JETP Letters ◽

10.1134/s0021364018030128 ◽

2017 ◽

Vol 107 (3) ◽

pp. 157-162 ◽

Cited By ~ 3

Author(s):

A. V. Orlov ◽

M. Yu. Brazhnikov ◽

A. A. Levchenko

Keyword(s):

Large Scale ◽

Vortex Formation ◽

Two Dimensional ◽

Coherent Vortex

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The lateral force on a keel and rudder

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100016789 ◽

1937 ◽

Vol 33 (1) ◽

pp. 62-69 ◽

Cited By ~ 3

Author(s):

S. D. Daymond ◽

L. Rosenhead

Keyword(s):

Theoretical Investigation ◽

Lateral Force ◽

Inviscid Fluid ◽

Two Dimensional ◽

Naval Architecture ◽

Dimensional Flow ◽

Two Dimensional Flow ◽

The University

The following theoretical investigation of the two-dimensional flow of an inviscid fluid past a keel and rudder, and of the consequent lateral force, follows experiments performed by Prof. T. B. Abell in the Department of Naval Architecture of the University of Liverpool, and we wish to acknowledge our indebtedness to him for the information given in many discussions.

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COMPLEX BIFURCATION STRUCTURES IN THE HINDMARSH–ROSE NEURON MODEL

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127407018877 ◽

2007 ◽

Vol 17 (09) ◽

pp. 3071-3083 ◽

Cited By ~ 71

Author(s):

J. M. GONZÀLEZ-MIRANDA

Keyword(s):

Phase Diagram ◽

Bifurcation Diagram ◽

Parameter Space ◽

Neuron Model ◽

Two Dimensional ◽

Dimensional Parameter ◽

Rapid Responses ◽

Bifurcation Structures

The results of a study of the bifurcation diagram of the Hindmarsh–Rose neuron model in a two-dimensional parameter space are reported. This diagram shows the existence and extent of complex bifurcation structures that might be useful to understand the mechanisms used by the neurons to encode information and give rapid responses to stimulus. Moreover, the information contained in this phase diagram provides a background to develop our understanding of the dynamics of interacting neurons.

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Universal behavior of the bosonic metallic ground state in a two-dimensional superconductor

npj Quantum Materials ◽

10.1038/s41535-021-00312-x ◽

2021 ◽

Vol 6 (1) ◽

Author(s):

Zhuoyu Chen ◽

Bai Yang Wang ◽

Adrian G. Swartz ◽

Hyeok Yoon ◽

Yasuyuki Hikita ◽

...

Keyword(s):

Magnetic Field ◽

Phase Diagram ◽

Quantum Phase Transitions ◽

Metallic State ◽

Two Dimensional ◽

Metallic Behavior ◽

Universal Behavior ◽

Hall Resistivity ◽

Wide Range ◽

Metal State

AbstractAnomalous metallic behavior, marked by a saturating finite resistivity much lower than the Drude estimate, has been observed in a wide range of two-dimensional superconductors. Utilizing the electrostatically gated LaAlO3/SrTiO3 interface as a versatile platform for superconductor-metal quantum phase transitions, we probe variations in the gate, magnetic field, and temperature to construct a phase diagram crossing from superconductor, anomalous metal, vortex liquid, to the Drude metal state, combining longitudinal and Hall resistivity measurements. We find that the anomalous metal phases induced by gating and magnetic field, although differing in symmetry, are connected in the phase diagram and exhibit similar magnetic field response approaching zero temperature. Namely, within a finite regime of the anomalous metal state, the longitudinal resistivity linearly depends on the field while the Hall resistivity diminishes, indicating an emergent particle-hole symmetry. The universal behavior highlights the uniqueness of the quantum bosonic metallic state, distinct from bosonic insulators and vortex liquids.

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