Revisiting Near-Inertial Wind Work: Slab Models, Relative Stress, and Mixed Layer Deepening

The wind generation of near-inertial waves is revisited through use of the Pollard–Rhines–Thompson theory, the Price–Weller–Pinkel (PWP) mixed layer model, and KPP simulations of resonant forcing by Crawford and Large. An Argo mixed layer climatology and 0.6° MERRA-2 reanalysis winds are used to compute global totals and explore hypotheses. First, slab models overestimate wind work by factors of 2–4 when the mixed layer is shallow relative to the scaling H* ≡ u*/(Nf)1/2, but are accurate for deeper mixed layers, giving overestimation of global totals by a factor of 1.23 ± 0.03 compared to PWP. Using wind stress relative to the ocean currents further reduces the wind work by an additional 13 ± 0.3%, for a global total wind work of 0.26 TW. Second, the potential energy increase ΔPE due to wind-driven mixed layer deepening is examined and compared to ΔPE computed from Argo and ERA-Interim heat flux climatology. Argo-derived ΔPE closely matches cooling, confirming that cooling sets the seasonal cycle of mixed layer depth and providing a new constraint on observational estimates of convective buoyancy flux at the mixed layer base. Locally and in fall, wind-driven deepening is comparable in importance to cooling. Globally, wind-driven ΔPE is about 11% of wind work, implying that >50% of wind work goes to turbulence and thus not into propagating inertial motions. The fraction into this “modified wind work” is imperfectly estimated in two ways, but we conclude that more research is needed into mixed layer and transition-layer physics. The power available for propagating near-inertial waves is therefore still uncertain, but appears lower than previously thought.

Nonlinear Dynamics of Swinging Clapper Bells under Arbitrary or Resonant Forcing Functions

Study of swinging clapper bells involves aspects encompassing sound and acoustic engineering, mechanical engineering, and structural engineering. From the musical point of view, clapper bells are directly played idiophone instruments, where the playing device, the clapper, although directly excited, is not explicitly controlled by the bell ringer. The achievement of a clear and optimal sound mainly depends on the acoustic characteristics of the bell and on the regularity of the clapper strokes, which is not only governed by the ringing style and the relevant parameters of clapper and bell but also by the real time corrections to the excitation introduced by trained bell ringers. In fact, despite centuries of experience allowed to optimize the bell performances, standardizing proportions and mounting arrangements, effective sound control requires some fine tuning of the forcing function. Another crucial topic, especially in view of assessing existing structures, regards the evaluation of time histories of the actions transmitted by the bell to the pivots and the study of the interactions between the bell and the supporting structures, belfries, and bell-towers. “Ringability” of swinging bells and bell-structure interactions are usually tackled in the framework of rigid body dynamics, so arriving at an initial value problem, governed by a system of two second order nonlinear ordinary differential equations (ODEs), whose solutions are piecewise-defined functions. In the relevant literature, numerical solutions of the system are commonly sought using built-in algorithms provided in advanced software packages; since the use of such general algorithms is subject to some restrictions, especially regarding the forcing functions, validity of the results is often limited. The present study focuses on an innovative procedure to solve the equations of motion. The method, extremely fast and effective, is based on original numerical explicit-implicit predictor-corrector integration algorithms with constant time step, duly validated reproducing the outcomes of relevant reference case studies. Each time the clapper strikes the bell a new “piece” of the solution is initialized, so avoiding user interventions in the elaboration phase. Independently on the oscillation amplitude and on the duration of the considered time interval, the algorithms can successfully manage undamped oscillations; friction and viscosity damped oscillations; free oscillations in transient and stationary phases; and can be applied also to solve stiff equations. Furthermore, the capability of the proposed methods to deal with arbitrary forcing functions is particularly innovative. The outcomes of relevant case studies, regarding the oscillations of the old tenor bell of the Great St. Mary church in Cambridge, confirm the potentialities of the method, also highlighting some topical issues, involving, for example, the assessment of damping equivalence. Finally, a pioneering feature of the algorithms is their ability to handle and to define “resonant” forcing functions, continuously tuning the frequency of the excitation to the natural frequency of the oscillation, according to the oscillation amplitude.

Forcing Seasonality of influenza-like epidemics with daily Solar resonance

Seasonality of acute viral respiratory diseases is a well-known and yet not fully understood phenomenon. Here we show that such seasonality, as well as the distribution of viral disease’s epidemics with latitude on Earth, can be fully explained by the virucidal properties of UV-B and A Solar photons through a daily, minute-scale, resonant forcing mechanism. Such an induced periodicity can last, virtually unperturbed, from tens to hundreds of cycles, and even in presence of internal dynamics (host’s loss of immunity) much slower than seasonal will, on a long period, generate seasonal oscillations.

Resonant Forcing of the Climate System in Subharmonic Modes

During recent decades observation of climate archives has raised several questions. Concerning the mid-Pleistocene transition problem, conflicting sets of hypotheses highlight either the role of ice sheets or atmospheric carbon dioxide in causing the increase in duration and severity of ice age cycles. The role of the solar irradiance modulations in climate variability is frequently referenced but the underlying physical justifications remain most mysterious. Here, we extend the key mechanisms involving the oceanic Rossby waves in climate variability, to very long-period, multi-frequency Rossby waves winding around the subtropical gyres. Our study demonstrates that the climate system responds resonantly to solar and orbital forcing in eleven subharmonic modes. We advocate new hypotheses on the evolution of the past climate, implicating the deviation between forcing periods and natural periods according to the subharmonic modes, and the polar ice caps while challenging the role of the thermohaline circulation.

The Dynamics of Shelf Forcing in Greenlandic Fjords

The fjords that connect Greenland’s glaciers to the ocean are gateways for importing heat to melt ice and for exporting meltwater into the ocean. The transport of heat and meltwater can be modulated by various drivers of fjord circulation, including freshwater, local winds, and shelf variability. Shelf-forced flows (also known as the intermediary circulation) are the dominant mode of variability in two major fjords of east Greenland, but we lack a dynamical understanding of the fjord’s response to shelf forcing. Building on observations from east Greenland, we use numerical simulations and analytical models to explore the dynamics of shelf-driven flows. For the parameter space of Greenlandic fjords, we find that the fjord’s response is primarily a function of three nondimensional parameters: the fjord width over the deformation radius (W/Rd), the forcing time scale over the fjord adjustment time scale, and the forcing amplitude (shelf pycnocline displacements) over the upper-layer thickness. The shelf-forced flows in both the numerical simulations and the observations can largely be explained by a simple analytical model for Kelvin waves propagating around the fjord. For fjords with W/Rd > 0.5 (most Greenlandic fjords), 3D dynamics are integral to understanding shelf forcing—the fjord dynamics cannot be approximated with 2D models that neglect cross-fjord structure. The volume flux exchanged between the fjord and shelf increases for narrow fjords and peaks around the resonant forcing frequency, dropping off significantly at higher- and lower-frequency forcing.

Resonant sloshing in an upright annular tank

Resonant sloshing in an upright annular tank is studied by using a new nonlinear modal theory, which is complete within the framework of the Narimanov–Moiseev asymptotics. The applicability is justified for a fairly deep liquid (the liquid-depth-to-outer-tank-radius ratio $1.5\lesssim h=\bar{h}/\bar{r}_{2}$) and away from the non-dimensional inner radii $r_{1}=\bar{r}_{1}/\bar{r}_{2}=0.08546$, 0.17618, 0.27826, 0.31323, 0.31855, 0.43444, 0.46015, 0.48434, 0.68655, 0.70118. The theory is used to describe steady-state (stable and unstable) resonant waves due to a harmonic excitation with the forcing frequency close to the lowest natural sloshing frequency. We show that the surge-sway-pitch-roll excitation is always of either longitudinal or elliptic type. Existing experimental results on the horizontally excited steady-state wave regimes in an upright circular tank ($r_{1}=0$) are utilised for validation. Inserting an inner pole with the radii $r_{1}\approx 0.25$ and 0.35 ($1.5\lesssim h$) causes that no stable swirling and/or irregular waves exist. The response curves for an elliptic-type excitation are examined versus the minor-axis forcing-amplitude component. Stable swirling is then expected being co- and counter-directed to the angular forcing direction. Passage to the rotary (circular) excitation keeps the co-directed swirling stable for all resonant forcing frequencies but the stable counter-directed swirling disappears.

Low-Frequency Seiche in a Large Bay

Short-term observations of sea surface elevations η along the 10-m isobath and long-term observations inside and outside of a large bay (Monterey Bay, CA) were obtained to describe the nodal structure of the modes 0–3 seiches within the bay and the low-frequency (<346 cpd) seiche forcing mechanism. The measured nodal pattern validates previous numerical estimates associated with a northern amplitude bias, though variability exists across the modal frequency band, particularly for modes 0 and 1. Low-frequency oceanic η white noise within seiche frequency bands (24–69 cpd) provides a continuous resonant forcing of the bay seiche with a η2 (variance) amplification of 16–40 for the different modes. The temporal variation of the oceanic η white noise is significantly correlated (R2 = 0.86) at the 95% confidence interval with the bay seiche η that varies seasonally. The oceanic η white noise is hypothesized as being from low-frequency, free, infragravity waves that are forced by short waves.

Resonant Generation and Energetics of Wind-Forced Near-Inertial Motions in a Geostrophic Flow

A slab mixed layer model and two-dimensional numerical simulations are used to study the generation and energetics of near-inertial oscillations in a unidirectional, laterally sheared geostrophic current forced by oscillatory winds. The vertical vorticity of the current ζg modifies the effective Coriolis frequency , which is equivalent to the local resonant forcing frequency. In addition, the resonant oscillatory velocity response is elliptical, not circular, because the oscillation periodically exchanges energy with the geostrophic flow via shear production. With damping, this energy exchange becomes permanent, but its magnitude and sign depend strongly on the angle of the oscillatory wind vector relative to the geostrophic flow. However, for a current forced by an isotropic distribution of wind directions, the response averaged over all wind angles results in a net extraction of energy from the geostrophic flow that scales as the wind work on the inertial motions times (ζg/f)2 for ζg ≪ f. For ζg ~ f, this sink of geostrophic kinetic energy preferentially damps flows with anticyclonic vorticity and thus could contribute toward shaping the positively skewed vorticity distribution observed in the upper ocean.

Phase-bistable pattern formation in oscillatory systems via rocking: application to nonlinear optical systems

We present a review, together with new results, of a universal forcing of oscillatory systems, termed ‘rocking’, which leads to the emergence of a phase bistability and to the kind of pattern formation associated with it, characterized by the presence of phase domains, phase spatial solitons and phase-bistable extended patterns. The effects of rocking are thus similar to those observed in the classic 2 : 1 resonance (the parametric resonance) of spatially extended systems of oscillators, which occurs under a spatially uniform, time-periodic forcing at twice the oscillations' frequency. The rocking, however, has a frequency close to that of the oscillations (it is a 1 : 1 resonant forcing) and hence is a good alternative to the parametric forcing when the latter is inefficient (e.g. in optics). The key ingredient is that the rocking amplitude is modulated either in time or in space, such that its sign alternates (exhibits π -phase jumps). We present new results concerning a paradigmatic nonlinear optical system (the two-level laser) and show that phase domains and dark-ring (phase) solitons replace the ubiquitous vortices that characterize the emission of free-running, broad area lasers.

Nonlinear transient growth in a vortex column

Growth of optimal transient perturbations to an Oseen vortex column into the nonlinear regime is studied via direct numerical simulation (DNS) for Reynolds number, Re (≡ circulation/viscosity), up to 10000. An optimal bending-wave transient mode is obtained from linear analysis and used as the initial condition. (DNS of a vortex column embedded in finer-scale turbulence reveals that optimal modes are preferentially excited during vortex–turbulence interaction.) Tilting of the optimal mode's radial vorticity perturbation into the azimuthal direction and its concomitant stretching by the column's strain field produces positive Reynolds stress, hence kinetic energy growth. Modes experiencing the largest growth are those with initial vorticity localized at a ‘critical radius’ outside the core, such that this perturbation vorticity resonantly induces core waves. Resonant forcing leads to growth of perturbation energy concentrated within the core. Moderate-amplitude (~5%) perturbations cause significant distortion of the core and generate secondary filament-like spiral structures (‘threads’) outside the core. As the mode evolves into the nonlinear regime, radially outward self-advection of thread dipoles accelerates growth arrest by removing the perturbation from the critical radius and disrupting resonant forcing. With increasing Re, the evolving vorticity patterns become more chaotic, more turbulent-like (finer scaled, contorted vorticity), and persist longer. This suggests that at typical Re (~106), nonlinear transient growth may indeed be able to break up, hence induce rapid decay of, column vortices – highly relevant for addressing the aircraft wake hazard crisis and the looming air traffic capacity crisis. In addition, we discover a regenerative transient growth scenario in which threads induce secondary perturbations closer to the vortex column. A parent–offspring regenerative mechanism is postulated and verified by DNS. There is a clear trend towards stronger regenerative growth with increasing Re. These results, showing an important role of transient growth in turbulent vortex decay, are highly relevant to the prediction and control of vortex-dominated flows.