How does energy input at planetary scales in the atmosphere and ocean ultimately reach scales small enough to be dissipated efficiently through turbulence? Here we describe advances in understanding the underlying instability and transport processes achieved through observations, theory, and numerical simulations, with a focus inspired in part by a February 2018 interdisciplinary workshop on the subject held at the Banff International Research Station.

A normally-distributed unidirectional wave-field is observed in experiments to become highly skewed and non-Gaussian upon encountering an abrupt change in depth.

A falling jet of a concentrated suspension is found to break abruptly where its diameter becomes a few particles thick. A simple model explains the jet breakup length observed experimentally.

While at least four plane surface gravity waves are required to make a resonant interaction, only three modes are required in a cylindrical container. An experiment is carried out to isolate and characterize such a triad interaction.

Bacteriophage viruses infect and replicate within bacteria. Some phages ride along the flagellar filaments used by bacteria for propulsion. Here we confirm a 40-year old hypothesis and show that infection can be induced by hydrodynamic forces due to rotation of flagellar filaments.

An experimental study of the effects of bacterial motility on its transport in a porous medium is presented. For flow velocity that can exceed 10 times the swimming velocity, the transport is found to be strongly retarded by the particle-grain hydrodynamic interaction. This is not observed in nonmotile bacteria.

We perform high resolution numerical simulations of a bumblebee in turbulent inflow for both tethered and free flight. We find that average aerodynamic forces, moments, and power do not vary with turbulent intensity, but are sensitive to the spectral distribution of turbulent kinetic energy.

We theoretically predict, that, in sphere suspensions, hydrodynamic interaction forces produce a negligible first normal stress difference, while contact forces produce a positive first normal stress difference.

To understand the coupling between mixing and vibrational relaxation, a novel state-specific model is solved inside a direct numerical simulation of a compressible jet. It is found that gas compressibility effects trigger vibrational nonequilibrium, while turbulence affects the states’ population.

A numerical study of the nonlinear torsional solutions of convection in rotating, internally heated, self-gravitating fluid spheres shows a sequence of transitions towards chaos in which heteroclinic chains connecting unstable periodic solutions can be recognized.

Droplets merging on hydrophobic nanocones jump off, and the takeoff speed is found to be maximum at microscale, below and above which viscosity and inertia, respectively, cap this speed. Microdroplets successively experience strong lift off, slow flight, and smooth landing, which impedes bouncing.

Experiments show that Leidenfrost droplets made of water and surfactant undergo a violent explosion. This unexpected behavior is triggered by the formation of a shell during the evaporation. Shortly afterwards, the temperature increases above the boiling point, leading to bubble growth, shell stretching, and explosion.

A study of the breakup of a droplet falling into a miscible solution of lower density shows that a nondimensional parameter determines the breakup number. A mechanism of the mode-selection based on the Rayleigh-Taylor instability for the growing vortex ring is discussed.

This work expands the scope of modern computational tools for predictive modeling of microscopic active systems, and provides insight into the intricate role of hydrodynamic interaction on the onset of collective behavior of living and synthetic active matter.

A novel method for reduced-order modeling of turbulent flows is discussed in the context of fully turbulent Rayleigh-Bénard convection. The method can be used to control the turbulent mean profiles, to discern the spectral properties of turbulent flows, and to improve the data-driven techniques.

Laboratory experiments suggest a larger Shields parameter value requirement to initiate motion on permeable beds than on impermeable ones, which is connected with the lower lift force on a permeable bed.

The stability of a quasigeostrophic mixing layer is revisited from the kernel wave perspective with a focus on individual Rossby waves behavior. We further conduct nonlinear simulations which show how vortex pairing is hindered by introducing an adverse shear or a finite Rossby radius.

An experimental method for investigating hydrodynamic instability combining light and a physical gel is proposed. Our method allows for a detailed study of hydrodynamic instabilities.

A recent claim that a liquid drop sliding on a solid has a transition from static to sliding friction, based on an ingenious but indirect experiment, disagrees with molecular dynamics simulations which directly measure the forces involved.

A liquid jet striking orthogonally a horizontal superhydrophilic surface can produce a circular hydraulic jump. The same jet impinging on a superhydrophobic surface forms a film that breaks up into droplets. The same superhydrophobic surface with a wettable ring causes a different jet impact outcome.

The onset of leading-edge stall on stationary, smooth, thin, two-dimensional airfoils with blunter than classical nose shapes at low to moderately high Reynolds number flows is studied. Global stall is delayed to higher angles of attack as nose bluntness is increased.

The timescale of droplet rearrangement in a 2D concentrated emulsion—a microfluidic crystal—displays 3 regimes with 2 transitions with increasing capillary number. The loss of order in the crystal flow corresponds to the second transition involving a solid to liquid-like transition of the emulsion.

High-frequency laser interferometry is used to resolve the motion of an immersed sphere prior to its collision with a wetted textured wall below the bouncing transition. The measurements reveal different sphere dynamics resulting from the texture-induced modification of the lubrication drag force.

A computational study of clean drops rising into a layer of dissolved surfactant, modeling oil drops rising in the ocean, is presented. Drops are first accelerated by surface tension gradients before being slowed by accumulated surfactants on their surface.

Shock interaction with a bed of randomly distributed particles leads to large variation in the drag forces, highlighting the impact of neighboring particles, and indicating a need for point-particle force models that account for this drag variation.

We analyze resolved simulations of up to 2000 spherical particles suspended in an incoming fluid stream with single-particle Reynolds number from 40-110 and volume fraction 9-35%. Diffusivities, pair distributions, and other quantities are found. Tetrads (four particle groups) are also studied.

Starting from the notion that a coherent structure is a set of fluid elements with very similar behavior, the idea of linear neighborhoods is introduced. These kinematic structures also play a role in the flow dynamics, in that the spectral energy transfer inside them is higher than it is outside.

We numerically evaluate permeable heterogeneity effects on gravity-driven miscible porous media flows relevant to underground CO${}_2$ storage. For typical finger widths below correlation length we find largest variation measures among random realizations, and lowest mean due to the resonant effect.

We put forth a model that captures the vertical single- and two-particle dispersion in stably stratified turbulence. The model gives insight into the mixture of linear and nonlinear physics in these flows, and on the different physical processes responsible for vertical turbulent dispersion.

Upper bounds on quantities of interest in Rayleigh-Bénard convection are derived by including a constraint derived from the time evolution equation for advective heat transport. This additional constraint leads to improved bounds on the toroidal dissipation.

Direct numerical simulations of passive scalar transport in turbulent channel flow subject to spanwise rotation are performed with two different scalar boundary conditions. A key finding is that rotation strongly reduces the turbulent Prandtl number, irrespective of the scalar boundary conditions.

Direct numerical simulations reveal the three-dimensional flow structures, sustaining mechanism, and sustainability condition of developed turbulence in precessing spheroids.

The influence of various inlet swirling flow profiles on the manifold of steady axisymmetric states of flows, their domain of attraction, and on flow dynamics in a straight, long circular pipe is investigated.

This study proposes a classification for breaker types when internal solitary waves shoal over a uniform slope. We use an extended data set of extant published experimental data and our own numerical experiments. We find that a single index delineates collapsing and plunging breakers.

High resolution numerical simulations of the evolution and subsequent degeneration of large amplitude internal standing waves are presented. Emphasized are examples of large amplitude wave train formation coexisting with shear instability.

Laboratory experiments demonstrate the generation of internal waves by a short-duration impulsive plume. After the plume descends to a maximum depth, it rebounds to an equilibrium level where the ensuing oscillation results in the generation of a propagating internal wave field.

Surface waves in the presence of floating particles are shown to arrest in finite-time as a consequence of dissipation associated with flow between the particles; implications for wave damping by sea ice are discussed.

The onset and growth of shear instability in internal solitary waves is studied. It is found that there are cases in which the instability occurs spontaneously, cases in which its onset is Reynolds-number dependent, and cases in which it must be triggered by externally imposed noise.

The exact Floquet theory reveals that the waveforms (eigenfunctions) of linear eigenwaves over a variable bed have complex features that are reminiscent of nonlinear waveforms. This is in contrast to the long-standing view that linear time harmonic waves are of permanent sinusoidal form.

We observed in a vibrating rectangular narrow tank a cramped water wave that acts as a sequence of load-carrying beams with one end oscillating and the other end almost pinned to the wall. We find the wave to be composed of just two harmonic waves. Nonlinearities account for this robust structure.

The hydroelastic wake created by a perturbation moving along a thin elastic sheet floating atop water is studied. The waves are characterized as a function of the perturbation speed and sheet thickness. Gravity, bending, and stretching are quantified and all are found to be important.