Ocean bubbles under high wind conditions. Part 1: Bubble distribution and development

The bubbles generated by breaking waves are of considerable scientific interest due to their influence on air-sea gas transfer, aerosol production, and upper ocean optics and acoustics. However, a detailed understanding of the processes creating deeper bubble plumes (extending 2–10 metres below the ocean surface) and their significance for air-sea gas exchange is still lacking. Here, we present bubble measurements from the HiWinGS expedition in the North Atlantic in 2013, collected during several storms with wind speeds of 10–27 m s−1. A suite of instruments was used to measure bubbles from a self-orienting free-floating spar buoy: a specialised bubble camera, acoustical resonators, and an upward-pointing sonar. The focus in this paper is on bubble void fractions and plume structure. The results are consistent with the presence of a heterogeneous shallow bubble layer occupying the top 1–2 m of the ocean which is regularly replenished by breaking waves, and deeper plumes which are only formed from the shallow layer at the convergence zones of Langmuir circulation. These advection events are not directly connected to surface breaking. The void fraction distributions at 2 m depth show a sharp cut-off at a void fraction of 10−4.5 even in the highest winds, implying the existence of mechanisms limiting the void fractions close to the surface. Below wind speeds of 16 m s−1 or RHw = 2 × 106, the probability distribution of void fraction at 2 m depth is very similar in all conditions, but increases significantly above either threshold. Void fractions are significantly different during periods of rising and falling winds, but there is no distinction with wave age. There is a complex near-surface flow structure due to Langmuir circulation, Stokes drift, and wind-induced current shear which influences the spatial distribution of bubbles within the top few metres. We do not see evidence for slow bubble dissolution as bubbles are carried downwards, implying that collapse is the more likely termination process. We conclude that the shallow and deeper bubble layers need to be studied simultaneously to link them to the 3D flow patterns in the top few metres of the ocean. Many open questions remain about the extent to which deep bubble plumes contribute to air-sea gas transfer. A companion paper (Czerski, 2021) addresses the observed bubble size distributions and the processes responsible for them.

Designing vortices in pipe flow with topography-driven Langmuir circulation

We present direct numerical simulation of a mechanism for creating longitudinal vortices in pipe flow, compared with a model theory. By furnishing the pipe wall with a pattern of crossing waves, secondary flow in the form of streamwise vortex pairs is created. The mechanism, ‘CL1’, is kinematic and known from oceanography as a driver of Langmuir circulation. CL1 is strongest when the ‘wall wave’ vectors make an acute angle with the axis, $\varphi =10^{\circ }$ – $20^{\circ }$ , changes sign near $45^{\circ }$ and is weak and of opposite sign beyond this angle. A competing, dynamic mechanism driving secondary flow in the opposite sense is also observed, created by the azimuthally varying friction. Whereas at smaller angles ‘CL1’ prevails, the dynamic effect dominates when $\varphi \gtrsim 45^{\circ }$ , reversing the flow. Curiously, the circulation strength is a faster-than-linearly increasing function of Reynolds number for small $\varphi$ . We explore an analogy with Prandtl's secondary motion of the second kind in turbulence. A transport equation for average streamwise vorticity is derived, and we analyse it for three different crossing angles, $\varphi =18.6^{\circ }, 45^{\circ }$ and $60^{\circ }$ . Mean-vorticity production is organised in a ring-like structure with the two rings contributing to rotating flow in opposite senses. For the larger $\varphi$ , the inner ring decides the main swirling motion, whereas for $\varphi =18.6^{\circ }$ , outer-ring production dominates. For the larger angles, the outer ring is mainly driven by advection of vorticity and the inner by deformation (stretching) whereas, for $\varphi =18.6^{\circ }$ , both contribute approximately equally to production in the outer ring.

Winds, Waves, and Turbulence on a Shallow Continental Shelf during Passage of a Tropical Storm

Measurements of collocated fields of atmospheric forcing, surface waves, and mean and turbulent velocities associated with passage of Tropical Storm (TS) Barry over the U.S. Navy Tower R2 on the Georgia continental shelf are presented. A vertical-beam ADCP enables computation of directional surface wave spectra and hence of directional Stokes functions of depth and time, as well as mean (including tidal) and turbulent velocities throughout the water column. Full-depth turbulent velocity and backscatter structures observed during TS Barry are determined to be Langmuir supercells (LS). The LS appear in the present observations and in similar observations from a shallower site only when a surface growth rate g* exceeds a critical value, providing a means of predicting how deep an unstratified water column must be before LS will not be expected. When observed, LS structures at Tower R2 are less organized than archetypical LS structures: we suggest that this result is due primarily to smaller near-bottom growth rate in the deeper water column. Despite g* values above the critical value, and appropriate values of Langmuir and Rayleigh numbers, full-depth velocity/backscatter structures disappear completely for a time between the two wind maxima associated with the TS, as wind veers rapidly clockwise with eye passage to the west of Tower R2. From the observations, the most likely explanation for this hiatus is decreased wave breaking during the period of wind veering, reducing surface supply of “effective” vertical vorticity that dominates generation of Langmuir circulation (LC). This result has significant implications for LES modeling of LC.

Langmuir circulation due to shear flow over wavy topography

<p>Langmuir circulations (LC) in their traditional form are large rolling fluid flow pattern created by the interplay of surface waves and a near-surface shear current, typically both created by the wind. A celebrated theory by Craik and Leibovich (1976) describes two kinematic mechanisms which cause instabilities which grow into Langmuir rolls, both involving only the shear of the flow and the kinematic driving of flow undulations by a wavy surface, but containing no direct reference to the wind as a driving force. The same kinematic processes are present also in boundary layer flow over a wavy bottom topography in almost perfect analogy.</p><p>We present a theory of Langmuir-like circulations created by boundary layer flow over a topography in the form of a regular pattern of two monochromatic waves crossing at an oblique angle. Thus, the Craik-Leibovich instability sometimes referred to as CL1 is triggered and the close analogy with surface waves allows us to follow the general procedure of Craik (1970).</p><p>A flow of arbitrary shear profile is assumed over the bottom topography. In the opposite limits of transient inviscid flow and steady-state viscous flow simple equations for the stream function in cross-current plane can be derived and easily solved numerically. For the special case of a power-law velocity profile, explicit leading-order solutions are available. This allows us to quickly map out the circulation response to different parameters: wavelength, crossing angle and wave amplitude. The study is supplemented with direct numerical simulations which verify the manifestation of Langmuir-like circulations over wavy geometries with a no-slip boundary condition.</p><p><strong>References<br></strong>Craik, A.D.D., A wave-interaction model for the generation of windrows. J. Fluid Mech. (1970) <strong>41</strong>, 801-821.<br>Craik, A.D.D. & Leibovich, S. A rational model for Langmuir circulations. J. Fluid Mech. (1976) <strong>73</strong>, 401-426.</p>

Large Eddy Simulation Coupling Model For Small-scale Air-sea Interaction

<p>Atmosphere and ocean are two important factors that affect the earth's climate system, and their interaction is an important topic in the study. In view of the lack of turbulence scale analysis in the traditional large-scale air-sea coupling model, this paper uses the Parallelized Large-Eddy Simulation Model (PALM) to explore the effect of Langmuir circulation on air-sea flux and turbulent kinetic energy budget at a small scale, and conducts air-sea coupled simulation for atmospheric boundary layer (ABL) and ocean mixed layer (OML). The results show that the distribution of air-sea flux near the surface is greatly influenced by the Langmuir circulation, thus strengthening the ocean mixing. The pressure term in the turbulent kinetic energy budget of the ocean is greatly affected by the Langmuir circulation near the sea surface and weakens rapidly as the depth deepens. This study shows the application of the small-scale air-sea coupling model in the study of air-sea flux, which has certain significance for the study of small-scale air-sea interaction.</p>

On Langmuir circulation in 1 : 2 and 1 : 3 resonance

This paper is concerned with the nonlinear dynamics of spanwise periodic longitudinal vortex modes (Langmuir circulation (LC)) that arise through the instability of two-dimensional periodic flows (waves) in a non-stratified uniformly sheared layer of finite depth. Of particular interest is the excitation of the vortex modes either in the absence of interaction or in resonance, as described by nonlinear amplitude equations built upon the mean field Craik–Leibovich (CL) equations. Since Y-junctions in the surface footprints of Langmuir circulation indicate sporadic increases (doubling) in spacing as they evolve to the scale of sports stadiums, interest is focused on bifurcations that instigate such changes. To that end, surface patterns arising from the linear and nonlinear excitation of the vortex modes are explored, subject to two parameters: a Rayleigh number ${\mathcal{R}}$ present in the CL equations and a symmetry breaking parameter $\unicode[STIX]{x1D6FE}$ in the mixed free surface boundary conditions that relax to those at the layer bottom where $\unicode[STIX]{x1D6FE}=0$. Looking first to linear instability, it is found as $\unicode[STIX]{x1D6FE}$ increases from zero to unity, that the neutral curves evolve from asymmetric near onset to almost symmetric. The nonlinear dynamics of single modes is then studied via an amplitude equation of Ginzburg–Landau type. While typically of cubic order when the bifurcation is supercritical (as it is here) and the neutral curves are parabolic, the Ginzburg–Landau equation must instead here be of quartic order to recover the asymmetry in the neutral curves. This equation is then subjected to an Eckhaus instability analysis, which indicates that linearly unstable subharmonics mostly reside outside the Eckhaus boundary, thereby excluding them as candidates for excitation. The surface pattern is then largely unchanged from its linear counterpart, although the character of the pattern does change when $\unicode[STIX]{x1D6FE}\ll 1$ as a result of symmetry breaking. Attention is then turned to strong resonance between the least stable linear mode and a sub-harmonic of it, as described by coupled nonlinear amplitude equations of Stuart-Landau type. Both 1 : 2 and 1 : 3 resonant interactions are considered. Phase plots and bifurcation diagrams are employed to reveal classes of solution that can occur. Dominant over much of the ${\mathcal{R}}$-$\unicode[STIX]{x1D6FE}$ range considered are non-travelling pure- and mixed-mode equilibrium solutions that act singly or together. To wit, pure modes solutions alone act to realise windrows with spacings in accord with linear theory, while bistability can realise Y-junctions and, depending upon initial conditions, double or even triple the dominant spacing of LC.