海洋猴向科学家展示如何改写湍流定律
内容总结：
海洋“小宠物”揭示湍流能量流向可被操控
上世纪六七十年代，美国纽约Transcience公司曾在漫画书广告中向读者承诺，只要寄出现金或支票，就能收到“满满一碗幸福”——实际上是一只装着冻干卵的小纸包。将这些卵投入盐水中，便会孵化出卤虫，俗称“海猴子”。这种体长约一厘米的小生物倒着游泳，疯狂拍打腿部，拖着细长的腹部如同尾巴。科学家近日发现，这些微小游泳者能做到的远不止移动自身。
长期以来，研究人员认为在湍流系统中，能量只能单向流动——依据系统维度不同，或从大尺度流向小尺度，或反之。但美国匹兹堡大学的科学家在观察这种不起眼的卤虫时意识到，只需微小的调整，能量的流向便可被逆转。他们发现，只要以恰当角度放置一个小障碍物来扰乱二维系统的流动，就能引导能量的级联方向。该研究负责人、匹兹堡大学工程师方磊表示：“几何形状至关重要。”
这项发现基于对力如何相互作用推动能量在系统中传递的一种基础性数学描述。以色列魏茨曼科学研究所物理学家、二维湍流系统研究先驱格雷戈里·法尔科维奇评价道：“这是一项漂亮而巧妙的实验工作。”这些发现可能推广至更大、更混沌的系统，包括三维系统，对流体动力学的理解具有重要意义，并可能在污染控制和药物设计等领域得到应用。
混沌的级联
湍流随处可见：瀑布底部翻腾的泡沫、破碎波浪的波峰、飞机飞行的颠簸、咖啡中牛奶的旋涡，乃至太阳表面的等离子体翻滚。意大利巴里理工大学水动力学专家弗朗切斯卡·德塞里奥说：“我们在生活中处处都能观察到湍流，去海滩或洗手时都会遇到。”
湍流系统复杂，以复杂的力和内部扰动为特征，但其起源可以很简单。例如，流动的流体会因遇到障碍物而改变部分流速，从而产生湍流。在河流中，水因摩擦在岸边减速，速度差产生涡旋。当河流绕过岩石分流时，速度变化形成空隙，水跌落并可能开始旋转。空气也是流体，其湍流由相互竞争的气流和变化的温度产生。
在这种系统中，能量在不同尺度间传递。现代天气预报创始人、英国数学家和物理学家刘易斯·弗赖伊·理查森在研究大气中气体形成的流体系统时发现了这一点：大涡旋的动能逐级传递给越来越小的涡旋，直到黏性力接管，能量最终以热量形式耗散。1922年，理查森用诗句概括了这一概念：“大旋涡有小旋涡，以其速度为食；小旋涡有更小旋涡，如此直至黏性。”
自20世纪40年代初起，苏联数学家安德烈·柯尔莫哥洛夫为湍流研究提供了清晰而严谨的数学基础。但他的工作与理查森一样，主要关注能量从大尺度流向小尺度的三维系统。20世纪60年代末，物理学家罗伯特·克赖奇南和乔治·巴彻勒将研究扩展到二维系统。二维湍流系统包括木星大红斑等现象，其剧烈旋涡压倒了下层大气的任何运动。这类二维湍流系统像三维系统一样在不同尺度间传递能量，但有一个不同之处：二维湍流系统的能量级联方向相反，从小涡旋向大涡旋传递。在木星大红斑中，边缘附近较小的涡旋为大旋涡提供能量。
在这些开创性研究报告了二维系统中的逆能量通量之后的几十年里，物理学家并未深入探究这些流动是否固定不变。2021年前后，当方磊实验室的学生司新宇开始研究卤虫时，二维湍流系统的基本能量机制肯定不在他的考虑之中。
在能量流中游泳
方磊的实验室专注于“活性物质”，这是一个物理学术语，描述能自行运动并向环境注入能量的物体，涵盖细菌等生物网络以及微型机器人等非生命体。在该项目中，司新宇和方磊感兴趣的是研究生物游泳者如何在出现湍流的流体中混合物质。研究人员曾假设，在大型自然系统的流体混合中，微小生物产生的湍流发挥着被低估的作用。毕竟，数以十亿计的微小生物搅动着全球水道。
为了在简单模型中深入研究这一问题，司新宇在水箱中的玻璃表面倒上一层薄盐水，并在下方放置磁铁。当他对导电流体施加电流时，电流与磁铁相互作用，使水产生运动——水沿通道一侧向一个方向流动，沿另一侧向相反方向流动，在中心形成速度梯度。然后他加入卤虫。当司新宇和方磊计算卤虫拍打身体对流动水体的扰动时，他们看到了“非常非常奇怪的东西”，方磊说：卤虫不仅增加了系统的混沌，似乎还改变了能量流动的方向。
湍流系统可以通过流体因不同流速相互作用而受到拉伸和压缩的程度来描述。例如，当你将彩色纸屑倒入河流，看着它在相互竞争的洋流中形成 sweeping 的线条顺流而下时，这种动力学就会显现。司新宇和方磊反复进行卤虫实验。他们发现，当一只卤虫以与最大拉伸方向小于45度的角度游动时，能量从小尺度流向大尺度，为流动本身提供能量，正如他们对二维系统的预测。但如果卤虫以与最大拉伸方向大于45度的角度游动，能量则反向流动，从流动的大尺度中汲取能量来激发小尺度扰动。
这似乎是一次彻底的方向逆转。每次实验都指向同一结论：卤虫身体的朝向似乎能改变湍流系统的能量通量。科学家们通过一个名为张量几何的数学领域来解释所见现象，这一领域长期以来是研究湍流的物理学家的得力工具。张量是一种数学工具，可帮助测量同时以多种方式变化的事物。方磊和司新宇发现，如果将卤虫的情况视为二维中两个张量的相互作用，就能说得通。一个张量代表剪切——水的大尺度运动——如何影响能量通量；另一个代表游泳者的小尺度运动如何塑造能量通量。游泳者的朝向决定了两个张量的对齐方式，而张量的对齐方式决定了能量的流动方式。正如方磊和司新宇在2024年报告的，卤虫身体与流体力之间的夹角可以改变能量通量的方向。
扭转潮流
司新宇曾将卤虫释放到水箱中，用摄像机对准它们，耐心等待某只卤虫以恰到好处的角度游过测试区域。在实验的下一阶段，司新宇和方磊用厘米长的棒状物阵列替代了卤虫，这更容易测量。他们发现，通过改变棒状物相对于流动的朝向，能够控制能量是向更高尺度还是更低尺度传递。即使司新宇和方磊邀请另外两位科学家——方磊在会议上结识的意大利都灵大学的菲利波·德利洛和圭多·博费塔——进行审查，结果依然成立。在外部专家的数值模拟中，同样的效应清晰显现。“这让我安心多了，”方磊说，“因为操控能量通量是一件非常奇怪的事情。”
带着重拾的信心，研究人员于2025年报告了他们的发现。德塞里奥说：“这很有趣，因为他们说通过对流动进行微小而特定的干预，我们可以……展示尺度间的能量传递。”他们证明，通过微小的操控，二维系统中的能量通量可以被引导得更像（但不完全像）三维系统中的通量，这表明物理学家或许能将一个维度领域的洞见应用于另一个领域。
还有一些令人困惑的问题需要克服。在实验中，司新宇和方磊使用了浅水槽，其摩擦力使湍流难以引发。而且，实验室中弱湍流的二维系统与自然界中更常见的强湍流三维系统之间存在巨大差异。不过，从数学上讲，科学家的观察没有理由不能推广到这些场景。司新宇和方磊正在研究这种可能性，在桌面龙卷风上测试想法。他们还在探索如何影响“输运屏障”，即两种流体混合时的阈值。根据方磊的理论，破坏这一边界——这可能有助于控制污染或为药物开发混合流体——所需的能量不到维持边界完整所需能量的1%。
其他科学家也已开始尝试操控能量通量。巴里理工大学的德塞里奥一直在向装有高黏度湍流旋转流体的大型水箱中喷射强射流。她说：“我被这个想法吸引，即这些（操控）可以应用于真实环境。”2026年3月，她报告了在大型旋转涡旋上进行的实验结果，该涡旋通过向中部喷射小型水平射流进行操控。她观察到逆能量通量的斑块，最初是间歇性爆发，随着旋转增强而变得稳定。她说，这些发现可能指向在现实情境中控制能量路径的实用策略。
司新宇现在是罗切斯特大学的博士后，他说当前工作提出了一个新假设，可在任何湍流发挥作用的环境中检验，从微小的“满满一碗幸福”到地球大气层的巨大尺度。湍流系统可能以难以理解著称，但决定能量流动的或许只是一个简单的几何问题。
中文翻译：
海猴向科学家展示如何改写一条湍流法则
引言
20世纪60年代和70年代，纽约Transcience公司在彩色漫画书上刊登广告，承诺只要寄来现金、支票或汇款单，就会收到“满满一碗快乐”——实际上，那只是一个小纸信封，里面装着冻干的卵。把它们投入盐水中，这些卵就会孵化出卤虫，也就是人们常说的“海猴”。
卤虫体长约一厘米，倒着游动，疯狂地拍打腿部，拖在身后的细长腹部像尾巴一样。科学家最近发现，这些微小的游泳者能做的远不止移动自己。
长期以来，研究人员认为，在像水流这样的湍流系统中，能量只沿一个方向流动——要么从大尺度流向小尺度，要么反之，取决于系统的维度。但在观察不起眼的卤虫时，匹兹堡大学的科学家意识到，只需一个微小的调整，能量的流动方向就可以被逆转。
科学家发现，他们可以通过用一个很小的障碍物扰乱系统流动，来引导二维系统中的能量级联——只要角度恰到好处。“几何形状很关键，”领导这项新研究的匹兹堡工程师方磊说。
自然图片图书馆/Alamy
魏茨曼科学研究所物理学家、二维湍流系统研究的先驱格雷戈里·法尔科维奇说，这一发现建立在对力如何相互作用以推动能量在系统中流动的一个基本却常被忽视的数学描述之上。“这是一项漂亮而精巧的实验工作。”
这些发现可能推广到更大、更混沌的系统，包括三维系统。这项工作对我们理解流体动力学具有重要意义，并可能在污染控制和药物设计等领域得到应用。
混沌的级联
湍流无处不在。它搅动瀑布底部喧闹的泡沫，塑造破碎波浪的浪尖。它是飞机颠簸、咖啡杯中牛奶旋涡以及太阳表面等离子体翻涌背后的原因。“我们在生活中到处都能观察到湍流，去海滩或洗手时都会遇到，”意大利巴里理工大学土木工程师、流体动力学专家弗朗切斯卡·德塞里奥说。
湍流系统很复杂，特征是错综复杂的力和内部骚动。但它的起因可以很简单。例如，当流动的流体遇到改变部分流速的障碍物时，湍流就产生了。在河流中，水因摩擦在岸边减速，速度不匹配会产生涡旋或涡流。当河流分流绕过石头时，速度改变，空隙形成；水叠落而下，可能开始旋转。空气也是流体，其湍流由相互竞争的气流和变化的温度产生。
在这样的系统中，能量在不同尺度之间转移。英国数学家和物理学家、现代天气预报的奠基人刘易斯·弗莱·理查森在研究大气中气体形成的流体系统时发现了这一点。他发现，大涡流的动能逐级供给越来越小的涡流，直到达到黏性——即抵抗运动的力——接管的尺度。能量最终以热的形式耗散。1922年，理查森用诗句概括了这一概念：
大旋涡有小旋涡，
以小旋涡的速度为食，
小旋涡又有更小的旋涡，
如此递降，直至黏性。
从20世纪40年代初开始，苏联数学家安德烈·柯尔莫哥洛夫为湍流研究提供了清晰而严谨的数学基础。但他的工作与理查森一样，主要聚焦于能量从大尺度流向小尺度的三维系统。
20世纪60年代末，物理学家罗伯特·克赖奇南和乔治·巴彻勒将研究扩展到二维系统。二维湍流系统包括木星大红斑等现象，其旋转之剧烈，压倒了大气层更深处的一切运动。这类二维湍流系统像三维系统一样在不同尺度之间转移能量，但有一个不同之处：二维湍流系统的能量级联方向相反，从小涡流向大涡流。在木星大红斑中，边缘附近较小的涡流和旋涡为中央的巨大漩涡提供能量。
在这些开创性研究报道了二维系统中的逆能量通量之后的几十年里，物理学家并未深入追问这些流动方向是否固定不变。2021年前后，当辛宇在方磊实验室开始研究卤虫时，二维湍流系统的底层能量机制肯定不在他的考虑之中。
游在能量流中
方磊的实验室专注于“活性物质”，这是物理学中描述自行运动并向环境注入能量的物体的术语。这个标签足够宽泛，既包括细菌等生物网络，也包括微型机器人等非生命体。
在这个项目中，辛宇和方磊感兴趣的是研究生物游泳者如何在出现湍流的流体中混合物质。研究人员曾假设，在大型自然系统的流体混合中，微小生物产生的湍流扮演着被低估的角色。毕竟，数十亿微小的生物搅动着世界的水道。
J·亚当·芬斯特/罗切斯特大学
为了在简单模型中仔细研究这一点，辛宇在一个水槽中的玻璃表面倒上一层薄薄的盐水，并在下方放置磁铁。当他向导电流体施加电流时，电流与磁铁相互作用，在水中产生运动——水沿通道一侧向一个方向流动，沿另一侧向相反方向流动。这在中心产生了速度梯度，辛宇将卤虫加入其中。
当辛宇和方磊计算卤虫拍打的身体如何扰动流动的水时，他们看到了“非常非常奇怪的东西”，方磊说：卤虫不仅为系统的混沌做出贡献，它们似乎还改变了能量流动的方向。
湍流系统可以通过流体内部被拉伸和压缩的程度来描述，这是由不同速度的流体相互作用造成的。例如，当你把彩色纸屑倒入河中，看着它在下游相互竞争的水流中排列成 sweeping 的线条时，这些动力学就会显现出来。
辛宇和方磊反复进行卤虫实验。他们发现，当一只卤虫以小于45度的角度相对于最大拉伸方向游动时，能量从小尺度流向大尺度，为流动本身提供能量，正如他们对二维系统的预测。但如果卤虫以大于45度的角度相对于最大拉伸方向游动，能量则反向流动，从流动的大尺度中汲取能量来激发更小的扰动。
这似乎是一个干净利落的逆转。每个实验都指向同一个结论：卤虫身体的朝向似乎改变了湍流系统的能量通量。
科学家找到了一种方法，通过一个名为张量几何的数学领域来解释他们所看到的——这个领域长期以来一直是物理学家研究湍流的得力工具。张量是一种数学工具，可以帮助你测量同时以多种方式变化的量。例如，当你按压海绵时，它的侧面会向外鼓起。张量可以描述应力——你手的重量——如何影响应变——海绵的形变。张量为流体动力学研究人员提供了一种强大的方法来建模可以在方向或强度上发生变化的物理现象。
方磊和辛宇发现，如果把他们的卤虫情境看作二维中两个张量的相互作用，就说得通了。一个张量代表剪切——水的大尺度运动——如何影响能量通量。另一个代表能量通量如何被游泳者的小尺度运动所塑造。
游泳者的朝向决定了两张量的对齐方式，而张量的对齐方式决定了能量的流动方式。正如方磊和辛宇在2024年报道的那样，卤虫身体与流体作用力之间的角度可以改变能量通量的方向。
扭转潮流
辛宇一直把卤虫放入水槽，用摄像机对着它们，耐心等待直到有一只以恰到好处的角度游过测试区域。在下一轮实验中，辛宇和方磊用一组厘米长的棒状物替代了卤虫，结果更容易测量。他们发现，通过改变棒状物相对于流动的朝向，他们能够控制能量是向更高尺度还是更低尺度转移。
即使辛宇和方磊邀请另外两位科学家——意大利都灵大学的菲利波·德利洛和圭多·博费塔——进行审查，这些发现依然成立。方磊在会议上结识了他们。在外部专家的数值模拟中，同样的效应清晰地显现出来。“这让我安心多了，”方磊说，“因为操纵能量通量是一件非常奇怪的事情。”
带着 renewed 的信心，研究人员在2025年报告了他们的发现。“这很有趣，因为他们在说，通过对流动进行微小而特定的干预，我们可以……展示尺度之间的能量转移，”德塞里奥说。他们证明了，用最小的操纵，二维系统中的能量通量可以被引导得更像（但不完全像）三维系统中的通量，这表明物理学家或许能将一个维度领域的洞见应用到另一个维度。
还有一些棘手的问题需要克服。在实验中，辛宇和方磊使用了一个浅水槽，其摩擦使湍流难以产生。而且，像他们实验室中那种弱湍流二维系统与自然界中更常见的强湍流三维系统之间存在巨大差异。
不过，从数学上讲，科学家的观察没有理由不能推广到这类场景。辛宇和方磊正在研究这种可能性，在桌面龙卷风上测试想法。
他们还在探索如何影响“输运屏障”，即两种流体混合时的边界阈值。根据方磊的理论，破坏这个边界——这在控制污染或为药物开发混合流体时可能有用——所需的能量不到维持边界完整所需能量的1%。
其他科学家也已开始尝试操纵能量通量。巴里理工大学的德塞里奥一直在向装有高黏度湍流旋转流体的大型水槽中发射强力射流。“我被这个想法吸引了——这些（操纵）可以应用于真实情境，”她说。2026年3月，她报告了在一个大型旋转涡流上进行的实验结果，该涡流用小型水平射流射入其中部进行操纵。她观察到逆能量通量的斑块，最初是间歇性爆发，但随着旋转增强而变得稳定。她说，这些发现可能指向在现实情境中控制能量路径的实用策略。
辛宇现在是罗切斯特大学的博士后，他说当前的工作提出了一个新假说，可以在任何湍流发挥作用的环境中检验——从微小的“满满一碗快乐”到地球大气的巨大尺度。湍流系统可能出了名地难以理解，但决定能量流动的，可能只是一个简单的几何问题。
英文来源：
Sea Monkeys Show Scientists How To Rewrite a Rule of Turbulence
Introduction
In the 1960s and ’70s, colorful comic book advertisements from the Transcience Corporation in New York City promised to mail anyone who sent cash, check, or money order a “bowlfull of happiness” — in reality, a small paper envelope of freeze-dried eggs. Dropped into salt water, the eggs would produce brine shrimp, also known as sea monkeys.
Brine shrimp are about a centimeter long and swim upside down, beating their legs madly and trailing their elongated abdomens behind them like tails. As scientists recently learned, these tiny swimmers can do more than just move themselves.
Researchers have long thought that in a turbulent system like a current of water, energy flows in only one direction, from larger scales to smaller ones, or vice versa, depending on the system’s dimensions. But in observing the humble brine shrimp, scientists at the University of Pittsburgh realized that — with just a tiny adjustment — the flow of energy could be reversed.
The scientists discovered that they could direct the cascade of energy in a two-dimensional system by disrupting the system’s flow with a small obstacle, as long as it was angled just right. “The geometry matters,” said Lei Fang, the Pittsburgh engineer who led the new study.
Nature Picture Library/Alamy
The discovery capitalized on a fundamental, if often unrecognized, mathematical description of how forces interact to push energy through a system, said Gregory Falkovich, a physicist at the Weizmann Institute of Science and a pioneer in the study of turbulent two-dimensional systems. “This is a beautiful and skillful experimental work.”
These findings could extend to larger, more chaotic systems, including those in three dimensions. The work has implications for our understanding of fluid dynamics and may have applications in areas such as pollution control and drug design.
A Cascade of Chaos
Turbulence is hard to miss. It stirs the raucous foam at the base of a waterfall and shapes the crest of a breaking wave. It’s behind the bumpiness of a flight, the swirls of milk in a cup of coffee, and the roil of plasma on the surface of the sun. “We observe turbulence generally everywhere in our lives, when we go to the beach or wash our hands,” said Francesca De Serio, a civil engineer and expert on hydrodynamics at the Polytechnic University of Bari in Italy.
A turbulent system is complicated, characterized by complex forces and inner turmoil. But it can start simply enough. For example, turbulence arises when a flowing fluid encounters an obstacle that changes the velocity of part of the flow. In a river, water slows down by the bank due to friction, and the velocity mismatches can produce vortices or eddies. When a river divides to move around a rock, speeds change and voids form; water falls over itself and may start to rotate. Air, too, is a fluid, its turbulence produced by competing currents and changing temperatures.
In such a system, energy moves between size scales. English mathematician and physicist Lewis Fry Richardson, the founder of modern weather forecasting, discovered this when he studied the fluid systems formed by gases in the atmosphere. He found that the kinetic energy of a large eddy feeds into smaller and smaller eddies, until it reaches the scale where viscosity, which resists motion, takes over. The energy is ultimately dissipated as heat. In 1922, Richardson captured the concept in verse:
Big whorls have little whorls
Which feed on their velocity,
And little whorls have lesser whorls
And so on to viscosity.
Starting in the early 1940s, the Soviet mathematician Andrey Kolmogorov provided a clear and rigorous mathematical foundation for the study of turbulence. But his work, like Richardson’s, mainly focused on three-dimensional systems in which energy flows from large features to small ones.
In the late 1960s, the physicists Robert Kraichnan and George Batchelor extended the investigation to two-dimensional systems. Two-dimensional turbulent systems include phenomena like Jupiter’s Great Red Spot, which swirls so violently that it overwhelms any motion farther down in the atmosphere. This type of two-dimensional turbulent system transfers energy from one scale to another, like a three-dimensional one, but with a twist: The energy of a two-dimensional turbulent system cascades in the opposite direction, moving from small eddies up to large ones. In Jupiter’s Great Red Spot, smaller eddies and vortices near the perimeter feed the giant maelstrom in the center.
In the decades after those pioneering studies reported an inverse flux in two-dimensional systems, physicists did not deeply interrogate whether those flows were fixed. The underlying energy mechanisms of two-dimensional turbulent systems certainly weren’t on the mind of Xinyu Si around 2021, when he started investigating brine shrimp as a student in Fang’s lab.
Swimming in the Energy Flow
Fang’s lab focuses on “active matter,” a physics term describing things that move by themselves and inject energy into their environments. It’s a label broad enough to include networks of living things, like bacteria, and nonliving things, like tiny robots.
In this project, Si and Fang were interested in investigating how biological swimmers mix materials in fluids where turbulence shows up. The researchers had hypothesized that, in the mixing of fluids in large natural systems, turbulence generated by tiny organisms plays an underappreciated role. Billions of minuscule creatures, after all, agitate the waterways of the world.
J. Adam Fenster/University of Rochester
To closely study this in a simple model, Si poured a thin film of salt water over a glass surface in a tank and positioned magnets underneath. When he applied an electric current to the conductive fluid, it interacted with the magnets and created motion in the water, which flowed in one direction along one side of a channel and in the opposite direction along the other side. This created a gradient of velocities across the center, to which Si added brine shrimp.
When Si and Fang calculated how the shrimp’s flailing bodies disrupted the moving water, they saw “something very, very strange,” Fang said: The shrimp weren’t just contributing to the chaos of the system; they also seemed to be shifting the direction in which energy flowed.
A turbulent system can be described in terms of how much it stretches and compresses the fluids within, due to the interactions of fluids flowing at different velocities. These dynamics show up, for example, when you pour confetti into a river and watch it organize into sweeping lines as it races on competing currents downstream.
Si and Fang ran the brine shrimp experiment repeatedly. They found that when a solo shrimp swam at an angle of less than 45 degrees to the direction of maximum stretching, the energy flowed from smaller scales to larger ones, feeding the flow itself, as they’d predicted for a 2D system. But if the shrimp swam at an angle of more than 45 degrees to the direction of maximum stretching, the energy went in reverse, pulling from the larger scale of the flow to energize smaller perturbations.
It appeared to be a clean about-face. Every experiment suggested the same conclusion: The orientation of a brine shrimp’s body seemed to change the turbulent system’s energy flux.
The scientists found a way to interpret what they were seeing through a field of mathematics called tensor geometry, which has long been a workhorse for physicists studying turbulence. A tensor is a mathematical tool that can help you measure something that changes in multiple ways at once. For example, when you press down on a sponge, its sides bulge outward. A tensor can describe how stress — the weight of your hand — affects strain — the deformation of the sponge. Tensors give fluid dynamics researchers a powerful way to model physical phenomena that can transform in terms of direction or strength.
Fang and Si found that their brine-shrimp situation made sense if they looked at it as the interaction of two tensors in two dimensions. One tensor represented how shear — the large-scale movement of the water — affected energy flux. The other represented how the energy flux was shaped by small-scale movements from the swimmers.
The orientation of the swimmer determined the alignment of the two tensors, and the alignment of the tensors determined how the energy flowed. As Fang and Si reported in 2024, the angle between the brine shrimp’s body and the forces of the fluid could alter the direction of the energy flux.
Turning the Tide
Si had been releasing brine shrimp into the tank, pointing a camera at them, and patiently waiting until one swam through the test area at just the right angle. In the next iteration of the experiment, Si and Fang replaced the brine shrimp with an array of centimeter-long rods, which proved easier to measure. They found that, by altering the orientation of the rods relative to the flow, they were able to control whether energy transferred to higher or lower scales.
The findings held even when Si and Fang invited the scrutiny of two other scientists: Filippo De Lillo and Guido Boffetta of the University of Turin in Italy, whom Fang met at a conference. In the outside experts’ numerical simulations, the same effect clearly showed up. “That made me much more comfortable,” Fang said, “because it’s a very weird thing to manipulate energy flux.”
With renewed confidence, the researchers reported their findings in 2025. “It was interesting because they were saying that with small, specific interventions in the flow we can … show a transfer of energy between scales,” De Serio said. They demonstrated that with minimal manipulation, the energy flux in a 2D system can be steered to act more like (but not exactly like) the flux in a 3D one, which suggests that physicists might be able to apply insights from one dimensional domain to the other.
There are confounding issues to overcome. In their experiments, Si and Fang used a shallow pool of fluid whose friction made turbulence hard to initiate. And there are big differences between a weakly turbulent two-dimensional system like the one in their lab and the strongly turbulent three-dimensional ones more commonly found in nature.
Mathematically, though, there’s no reason the scientists’ observations shouldn’t extend to such scenarios. Si and Fang are investigating the possibility, testing ideas on tabletop tornadoes.
They’re also exploring how to influence the “transport barrier,” the threshold between two fluids as they mix. According to Fang’s theory, disrupting this boundary — which could be useful in controlling pollution or mixing fluids for drug development — would use less than 1% of the energy required to keep the boundary intact.
Other scientists have also begun experimenting with manipulating energy flux. De Serio, at the Polytechnic University of Bari, has been firing strong jets into large tanks of turbulent, rotating fluids with high viscosity. “I was attracted by this idea that these [manipulations] could be applied in a real context,” she said. In March 2026, she reported results from experiments conducted on a large rotating vortex manipulated with small, horizontal jets firing into the middle. She observed patches of inverse energy flux that started out as intermittent bursts but grew steady with increasing rotation. Those findings, she says, may point to practical strategies for controlling energy pathways in real-world situations.
Si, now a postdoc at the University of Rochester, said that the current work introduces a new hypothesis that’s testable in any setting where turbulence plays a role, from a tiny “bowlfull of happiness” to the enormous scale of Earth’s atmosphere. Turbulent systems may be notoriously difficult to understand, but what dictates the flow of energy may be an issue of simple geometry.