静态流体中的同步静止云：理论与实验新机遇

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本文主要探讨的是"静态流体中的同步静止云"这一概念，发表在《物理学 letters B》(Physics Letters B, Vol. 786, Issue 442-447, 2018)上，属于开放获取资源。作者 Carolina L. Benonea、Luís C. B. Crispino、Carlos A. R. Herdeiro 和 Maurício Richartz 等人来自巴西帕拉联邦大学、葡萄牙阿维罗大学、里斯本理工学院等机构，他们共同研究了在两个同心圆柱体之间的水动力学系统。研究的核心是静态流体环境下，当内部圆柱体以恒定角速度 Ω 旋转时，发现了一种特殊的动态现象——同步静止云。这种云的存在并非随机，而是与圆柱体的旋转同步，即云的角速度与圆柱体的旋转速率相匹配。这种同步状态对于维持云的无限长寿命至关重要，因为它能够减小流体间的能量耗散，类似于黑洞旋转周围存在同步的玻色场。作者通过数学建模和理论分析证明了在静态流体中，声波和表面波都可以形成这种同步静止云。他们的研究不仅理论意义重大，也为未来在实验上观测到这种现象提供了独特的可能性。静态流体中的同步静止云可能是理解更复杂物理系统，如宇宙中的黑洞物理或实验室尺度上的类似效应的基石。文章的历史表明，该研究经历了从提交初稿到修订并接受的过程，最终在2018年10月19日上线。关键词包括"静止云"、"模拟模式"等，反映出研究焦点集中在这些特定的物理现象及其在不同领域的潜在应用。总结来说，这篇论文揭示了一个新颖的物理现象，展示了静态流体中的同步静止云的形成原理和同步条件，对理论物理学家和实验科学家都具有重要的启示作用，促进了对流体力学和引力波模拟等领域更深的理解。

Physics Letters B 786 (2018) 442–447

Contents lists available at ScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Synchronized stationary clouds in a static ﬂuid

Carolina L. Benone

, Luís C.B. Crispino

, Carlos A.R. Herdeiro

b,c

, Maurício Richartz

d,∗

Faculdade de Física, Universidade Federal do Pará, 66075-110, Belém, Pará, Brazil

Departamento de Física da Universidade de Aveiro and Center for Research and Development in Mathematics and Applications (CIDMA), Campus de Santiago,

3810-183 Aveiro, Portugal

Centro de Astrofísica e Gravitação -CENTRA, Departamento de Física, Instituto Superior Técnico - IST, Universidade de Lisboa -UL, Avenida Rovisco Pais 1,

1049-001, Portugal

Centro de Matemática, Computação e Cognição, Universidade Federal do ABC (UFABC), 09210-170 Santo André, São Paulo, Brazil

a r t i c l e i n f o a b s t r a c t

Article history:

Received

14 September 2018

Received

in revised form 8 October 2018

Accepted

15 October 2018

Available

online 19 October 2018

Editor:

M. Cveti

Keywords:

Stationary

clouds

Analogue

models of gravity

Black

holes

The existence of stationary bound states for the hydrodynamic velocity ﬁeld between two concentric

cylinders is established. We argue that rotational motion, together with a trapping mechanism for the

associated ﬁeld, is suﬃcient to mitigate energy dissipation between the cylinders, thus allowing the

existence of inﬁnitely long lived modes, which we dub stationary clouds. We demonstrate the existence of

such stationary clouds for sound and surface waves when the ﬂuid is static and the internal cylinder

rotates with constant angular velocity . These setups provide a unique opportunity for the ﬁrst

experimental observation of synchronized stationary clouds. As in the case of bosonic ﬁelds around

rotating black holes and black hole analogues, the existence of these clouds relies on a synchronization

condition between  and the angular phase velocity of the cloud.

(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP

1. Introduction

With a few notable exceptions, like in superconductivity, dis-

sipation

plays an important and decisive role in Physics. Due to

dissipation, the oscillations of any perturbed system (for instance

a ringing bell) will die away with the passing of time. In gen-

eral,

waves propagating in realistic (hence dissipative) media will

lose energy and hence decrease their amplitude in time. Black hole

(BH) absorption in a scattering process and BH response to pertur-

bations

(quasinormal modes), for example, can be interpreted as

manifestations of dissipation: the event horizon acts as a one-way

membrane which extracts energy from the BH exterior, dissipating

any external perturbation [1–4].

Linear

perturbations of a dissipative system will generically de-

cay

in time according to exp(−iωt), where ω is a complex fre-

quency.

Combined with rotational motion, however, dissipation can

be mitigated and unexpected phenomena arise. One such exam-

ple

is superradiance, a scattering process in which low-frequency

modes are ampliﬁed by a rotating object [5–8]. This ampliﬁcation

Corresponding author.

E-mail

addresses: lben.carol@gmail.com (C.L. Benone), crispino@ufpa.br

(L.C.B. Crispino),

herdeiro@ua.pt (C.A.R. Herdeiro), mauricio.richartz@ufabc.edu.br

(M. Richartz).

effect can be understood as the dissipation of negative energies

(with respect to the rest frame of the rotating object), meaning

that low-frequency waves can lower the energy of the rotating

system. In other words, while in the laboratory frame the ﬂux of

dissipated energy is proportional to the oscillation frequency ω of

the waves, in the rotating frame the energy ﬂux is proportional

to the effective frequency

ω = ω −m, where m is the azimuthal

number of the wave and  is the angular velocity of the scatterer.

Therefore, suﬃciently low-frequency waves satisfying

ω < 0will

reverse the energy ﬂux direction, thus extracting energy from the

rotating object.

If,

besides rotational motion, an additional trapping mechanism

is present in the system, a feedback process, in which successive

superradiant ampliﬁcations occur, is triggered. As a result, the sys-

tem

will exhibit superradiant instabilities which, at the linear level,

grow exponentially in time. Such unstable modes have Im(ω) > 0.

At the threshold between stable and unstable modes, stationary

bound

states, characterized by Im(ω) = 0, exist. Such bound states,

dubbed stationary clouds, are generic features of rotating, dissipa-

tive

systems. Nevertheless, they have never been experimentally

observed.

Stationary

clouds have played a key role, for instance, in re-

cent

developments in BHs physics. They appear when a scalar

wave is synchronized with a rotating BH, meaning that the wave’s

angular phase velocity, ω/m, matches the angular velocity  of

https://doi.org/10.1016/j.physletb.2018.10.030

0370-2693/

SCOAP

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