About

Leif Ristroph is an Associate Professor of Mathematics at New York University. His research focuses on applied mathematics, with recent work in the Applied Mathematics Laboratory where he and his team have conducted studies on the factors that cause icebergs to capsize. His team’s research, published in Physical Review Fluids, offers insights into how melting occurs primarily along the wetted surface of the ice below the waterline, leading to changes in the iceberg's stability and eventual rotation. This work contributes to understanding the impacts of climate change on Earth's waters. Professor Ristroph's research has been covered by media outlets such as Cosmos and ENN, highlighting its significance in climate science and fluid dynamics.

Research topics

• Engineering
• Computer Science
• Physics
• Geology
• Paleontology
• Electrical engineering
• Mathematics
• Mechanics
• Thermodynamics
• Geometry
• Earth science
• Optoelectronics
• Chemical engineering
• Geomorphology

Selected publications

• Early turbulence and pulsatile flows enhance diodicity of Tesla’s macrofluidic valve

  Nature Communications · 78 citations

  Senior authorCorresponding
  • Computer Science
  • Mechanics
  • Physics

  Abstract Microfluidics has enabled a revolution in the manipulation of small volumes of fluids. Controlling flows at larger scales and faster rates, or macrofluidics, has broad applications but involves the unique complexities of inertial flow physics. We show how such effects are exploited in a device proposed by Nikola Tesla that acts as a diode or valve whose asymmetric internal geometry leads to direction-dependent fluidic resistance. Systematic tests for steady forcing conditions reveal that diodicity turns on abruptly at Reynolds number $${\rm{Re}}\approx 200$$ Re ≈ 200 and is accompanied by nonlinear pressure-flux scaling and flow instabilities, suggesting a laminar-to-turbulent transition that is triggered at unusually low $${\rm{Re}}$$ Re . To assess performance for unsteady forcing, we devise a circuit that functions as an AC-to-DC converter, rectifier, or pump in which diodes transform imposed oscillations into directed flow. Our results confirm Tesla’s conjecture that diodic performance is boosted for pulsatile flows. The connections between diodicity, early turbulence and pulsatility uncovered here can inform applications in fluidic mixing and pumping.

  DOI

• Quasi-steady aerodynamics predicts the dynamics of flapping locomotion

  Journal of Fluid Mechanics · 2026-04-06

  articleOpen accessSenior author

  The propulsion of a flapping wing or foil is emblematic of bird flight and fish swimming. Previous studies have identified hallmarks of the propulsive dynamics that have been attributed to unsteady effects such as the formation and shedding of edge vortices and wing–vortex interactions. Here, we show that several key features of heaving flight are captured by a quasi-steady aerodynamic model that aims to predict stroke-averaged forces from wing motions without explicitly solving for the flows. We address the forward dynamics induced by up-and-down heaving motions of a thin plate with a nonlinear model which involves lift and drag forces that vary with speed and attack angle. Simulations reproduce the well-known transition for increasing Reynolds number from a stationary state to a propulsive state, where the latter is characterised by a Strouhal number that is conserved across broad ranges of parameters. Parametric, sensitivity and stability analyses provide physical interpretations for these results and show the importance of accounting for the flow regimes which are demarcated by Reynolds number and angle of attack. These findings extend the phenomena of unsteady locomotion that can be explained by quasi-steady modelling, and they broaden the conditions and parameter ranges over which such models are applicable.

  PublisherDOI

• Flow interactions and forward flight dynamics of tandem flapping wings

  Journal of Fluid Mechanics · 2026-05-08

  preprintOpen access

  We examine theoretically the flow interactions and forward flight dynamics of tandem or in-line flapping wings. Two wings are driven vertically with prescribed heaving motions, and the horizontal propulsion speeds and positions are dynamically selected through aero- or hydro-dynamic interactions. Our simulations employ an improved vortex-sheet method to solve for the locomotion of the pair within the collective flow field, and we identify ‘schooling states’ in which the wings travel together with nearly constant separation. Multiple terminal configurations are achieved by varying the initial conditions, and the emergent separations are approximately integer multiples of the wavelength traced out by each wing. We explain the stability of these states by perturbing the follower and mapping out an effective potential for its position in the leader’s wake. Each equilibrium position is stabilised since smaller separations are associated with in-phase follower-wake motions that constructively reinforce the flow but lead to decreased thrust on the follower; larger separations are associated with antagonistic follower-wake motions, increased thrust and a weakened collective wake. The equilibria and their stability are also corroborated by a linearised theory for the motion of the leader, the wake it produces and its effect on the follower. We also consider a weakly flapping follower driven with lower heaving amplitude than the leader. We identify ‘keep-up’ conditions for which the wings may still ‘school’ together despite their dissimilar kinematics, with the ‘freeloading’ follower passively assuming a favourable position within the wake that permits it to travel significantly faster than it would in isolation.

  PublisherDOI

• Aerodynamic equilibria and flight stability of plates at intermediate Reynolds numbers

  Journal of Fluid Mechanics · 2025-07-03 · 1 citations

  articleOpen accessSenior authorCorresponding

  The passive flight of a thin wing or plate is an archetypal problem in flow–structure interactions at intermediate Reynolds numbers. This seemingly simple aerodynamic system displays an impressive variety of steady and unsteady motions that are familiar from fluttering leaves, tumbling seeds and gliding paper planes. Here, we explore the space of flight behaviours using a nonlinear dynamical model rooted in a quasisteady description of the fluid forces. Efficient characterisation is achieved by identification of the key dimensionless parameters, assessment of the steady equilibrium states and linear analysis of their stability. The structure and organisation of the stable and unstable flight equilibria proves to be complex, and seemingly related factors such as mass and buoyancy-corrected weight play distinct roles in determining the eventual flight patterns. The nonlinear model successfully reproduces previously documented unsteady states such as fluttering and tumbling while also predicting new types of motions, and the linear analysis accurately accounts for the stability of steady states such as gliding and diving. While the conditions for dynamic stability seem to lack tidy formulae that apply universally, we identify relations that hold in certain regimes and which offer mechanistic interpretations. The generality of the model and the richness of its solution space suggest implications for small-scale aerodynamics and related applications in biological and robotic flight.

  PublisherOA PDFDOI

• BPS2025 - The effect of microgravity on the organization and dynamics of the human genome

  Biophysical Journal · 2025-02-01 · 1 citations

  article
  PublisherDOI

• Poster: Fluidic gears and pulleys: Hydrodynamic spin-coupling of rotors

  2025-11-23

  articleOpen access
  PublisherDOI

• Modeling flying formations as flow-mediated matter

  ArXiv.org · 2025-06-16

  preprintOpen accessSenior author

  Collective locomotion of swimming and flying animals is fascinating in terms of individual-level fluid mechanics and group-level structure and dynamics. Here we bridge and relate these scales through a model of formation flight that views the collective as a material whose properties arise from the flow-mediated interactions among its members. We build on and revise an aerodynamic model describing how flapping flyers produce vortex wakes and how they are forced by others' wakes. While simplistic, the model faithfully reproduces a series of physical experiments carried out over the last decade on pairwise interactions of flapping foils. By studying longer in-line arrays, we show that the group behaves as a soft "crystal" with regularly spaced member "atoms" whose positioning is, however, susceptible to deformations and dynamical instabilities. Poking or wiggling a member excites longitudinal waves (flow-mediated phonons, or "flonons") that pass down the group while growing in amplitude, and indeed the internal excitation from flapping is sufficient to trigger instabilities. Linear analysis of the model explains the aerodynamic origin of the lattice spacing, the springiness of the "bonds" between flyers, and the tendency for disturbances to resonantly amplify. Other properties such as the timescales for instability growth and wave propagation seem to involve the full nonlinear behavior. These findings suggest intriguing analogies with physical materials that could be generally useful for understanding and analyzing animal groups. Several properties displayed by our system seem particularly relevant to biological collectives, namely group cohesion and organization, sensitive detection of and response to perturbations, and transmission of information through traveling waves.

  PublisherOA PDFDOI

• Poster: Secret swirls give sprinklers a whirl

  2024-11-21

  articleOpen access1st authorCorresponding
  PublisherDOI

• Geometrically modulated contact forces enable hula hoop levitation

  Proceedings of the National Academy of Sciences · 2024-12-30 · 1 citations

  articleOpen accessSenior authorCorresponding

  Mechanical systems with moving points of contact-including rolling, sliding, and impacts-are common in engineering applications and everyday experiences. The challenges in analyzing such systems are compounded when an object dynamically explores the complex surface shape of a moving structure, as arises in familiar but poorly understood contexts such as hula hooping. We study this activity as a unique form of mechanical levitation against gravity and identify the conditions required for the stable suspension of an object rolling around a gyrating body. We combine robotic experiments involving hoops twirling on surfaces of various geometries and a model that links the motions and shape to the contact forces generated. The in-plane motions of the hoop involve synchronization to the body gyration that is shown to require damping and sufficiently high launching speed. Further, vertical equilibrium is achieved only for bodies with "hips" or a critical slope of the surface, while stability requires an hourglass shape with a "waist" and whose curvature exceeds a critical value. Analysis of the model reveals dimensionless factors that successfully organize and unify observations across a wide range of geometries and kinematics. By revealing and explaining the mechanics of hula hoop levitation, these results motivate strategies for motion control via geometry-dependent contact forces and for accurately predicting the resulting equilibria and their stability.

  PublisherOA PDFDOI

• Yardangs sculpted by erosion of heterogeneous material

  Proceedings of the National Academy of Sciences · 2024-06-23 · 2 citations

  articleOpen accessSenior authorCorresponding

  The recognizable shapes of landforms arise from processes such as erosion by wind or water currents. However, explaining the physical origin of natural structures is challenging due to the coupled evolution of complex flow fields and three-dimensional (3D) topographies. We investigate these issues in a laboratory setting inspired by yardangs, which are raised, elongate formations whose characteristic shape suggests erosion of heterogeneous material by directional flows. We combine experiments and simulations to test an origin hypothesis involving a harder or less erodible inclusion embedded in an outcropping of softer material. Optical scans of clay objects fixed within flowing water reveal a transformation from a featureless mound to a yardang-like form resembling a lion in repose. Phase-field simulations reproduce similar shape dynamics and show their dependence on the erodibility contrast and flow strength. Through visualizations of the flow fields and analysis of the local erosion rate, we identify effects associated with flow funneling and the turbulent wake that are responsible for carving the unique geometrical features. This highly 3D scouring process produces complex shapes from simple and commonplace starting conditions and is thus a candidate explanation for natural yardangs. The methods introduced here should be generally useful for geomorphological problems and especially those for which material heterogeneity is a primary factor.

  PublisherOA PDFDOI

Recent grants

• PostDoctoral Research Fellowship

  NSF · $135k · 2011–2015

• Shape dynamics of melting ice: Experiments, simulations, modeling and analysis

  NSF · $632k · 2022–2026

• Interactions of shapeable boundaries with flowing fluids:Experiments and mathematical modeling

  NSF · $320k · 2018–2022

• CAREER: Mathematical Modeling, Physical Experiments, and Biological Data for Understanding Flow Interactions in Collective Locomotion

  NSF · $400k · 2019–2025

Frequent coauthors

• Michael Shelley

  106 shared

• Stephen Childress

  48 shared

• Jun Zhang

  Changchun Institute of Applied Chemistry

  38 shared

• Jun Zhang

  University of Chinese Academy of Sciences

  32 shared

• Scott Weady

  Flatiron Health (United States)

  28 shared

• Joel W. Newbolt

  Courant Institute of Mathematical Sciences

  26 shared

• Jun Zhang

  Chinese PLA General Hospital

  24 shared

• Jinzi Mac Huang

  21 shared

Labs

• Applied Mathematics LaboratoryPI