skip to main content


Title: Onset of energy equipartition among surface and body waves
We derive a radiative transfer equation that accounts for coupling from surface waves to body waves and the other way around. The model is the acoustic wave equation in a two-dimensional waveguide with reflecting boundary. The waveguide has a thin, weakly randomly heterogeneous layer near the top surface, and a thick homogeneous layer beneath it. There are two types of modes that propagate along the axis of the waveguide: those that are almost trapped in the thin layer, and thus model surface waves, and those that penetrate deep in the waveguide, and thus model body waves. The remaining modes are evanescent waves. We introduce a mathematical theory of mode coupling induced by scattering in the thin layer, and derive a radiative transfer equation which quantifies the mean mode power exchange.We study the solution of this equation in the asymptotic limit of infinite width of the waveguide. The main result is a quantification of the rate of convergence of the mean mode powers toward equipartition.  more » « less
Award ID(s):
2010046
NSF-PAR ID:
10281522
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Proceedings of the Royal Society of London
Volume:
477
ISSN:
2053-9150
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. A two‐column radiative–convective equilibrium (RCE) model is used to study the depth of convection that develops in the subsiding branch of a Walker‐like overturning circulation. The model numerically solves for two‐dimensional non‐rotating hydrostatic flow, which is damped by momentum diffusion in the boundary layer and model interior, and by convective momentum transport. Convection, clouds and radiative transfer are parametrized, and the convection scheme does not include explicit freezing or melting.

    While integrating the model towards local RCE, the level of neutral buoyancy (LNB) fluctuates between mid‐ and high levels. Evaporation of detrained moisture at the LNB locally cools the environment, so that the final RCE state has a stable layer at mid‐levels (550 hPa ≈ 50–100 hPa below 0 °C), which is unrelated to melting of ice. Preferred detrainment at mid‐ and high levels leaves the middle‐to‐upper troposphere relatively dry.

    A circulation is introduced by incrementally lowering the sea‐surface temperature in one column, which collapses convection: first to a congestus mode with tops near 550 hPa, below the dry layer created in RCE; then to congestus with tops near 650 hPa; and finally to shallow cumulus with tops near 850 hPa. Critical to stabilizing congestus near 650 hPa is large radiative cooling near moist cumulus tops under a dry upper atmosphere. This congestus mode is very sensitive, and only develops when horizontal temperature gradients created by evaporative and radiative cooling can persist against the work of gravity waves. This only happens in runs with ample momentum diffusion, which are those with convective momentum transport or large domains.

    Compared to the shallow mode, the congestus mode produces a deep moist layer and more precipitation. This reduces radiative cooling in the cloud layer and enhances stability near the cloud base, which weakens the circulation, and leads to less precipitation over the warm ocean.

     
    more » « less
  2. Abstract

    The spontaneous self-aggregation (SA) of convection in idealized model experiments highlights the importance of interactions between tropical convection and the surrounding environment. The authors have shown that SA fundamentally changes with the background rotation in previousf-plane simulations, in terms of both the resulting forms of organized convection and the relative roles of the physical feedbacks driving them. This study considers the dependence of SA on rotation in one large domain on theβplane, introducing an additional layer of complexity. Simulations are performed with uniform thermal forcing and explicit convection. Focuses include statistical and structural analysis of the convective modes, process-oriented diagnostics of how they develop, and resulting mean states. Two regimes of SA emerge within the first 15 days, separated by a critical zone wherefis analogous to 10°–15° latitude. Organized convection at near-equatorial values offprimarily consists of convectively coupled Kelvin waves. Wind speed–surface enthalpy flux feedbacks are the dominant process driving moisture variability early on, then clear-sky shortwave radiative feedbacks are strongest in wave maintenance. In contrast, at higherf, numerous tropical cyclones develop and coexist, dominated by surface flux and longwave processes. Tropical cyclogenesis is most pronounced at intermediatef(analogous to 25°–40°), but are longer-lived at higherf. The resulting modes of SA at lowfdiffer between theseβ-plane simulations (convectively coupled waves) and priorf-plane simulations (weak tropical cyclones or nonrotating clusters). Otherwise, these results provide further evidence for the changing roles of radiative, surface flux, and advective processes in influencing SA asfchanges, as found in our previous study.

    Significance Statement

    In model simulations, convection often self-organizes due to interactions with its surrounding environment. These interactions are relevant in the real-world organization of rainfall and clouds, and may thus be useful to understand for improved prediction of tropical weather and climate. Previous work using a set of simple model experiments with constant Coriolis force showed that at different latitudes, different processes dominate, and different types of organized convection result. This study verifies that finding using a more complex and realistic model, where the Coriolis force varies within the domain to resemble different latitudes. Specifically, the convection here self-organizes into atmospheric waves (periodic disturbances) at low latitudes, and tropical cyclones at high latitudes.

     
    more » « less
  3. We consider a strongly nonlinear long wave model for large amplitude internal waves in a three-layer flow between two rigid boundaries. The model extends the two-layer Miyata–Choi–Camassa (MCC) model (Miyata, Proceedings of the IUTAM Symposium on Nonlinear Water Waves , eds. H. Horikawa & H. Maruo, 1988, pp. 399–406; Choi & Camassa, J. Fluid Mech. , vol. 396, 1999, pp. 1–36) and is able to describe the propagation of long internal waves of both the first and second baroclinic modes. Solitary-wave solutions of the model are shown to be governed by a Hamiltonian system with two degrees of freedom. Emphasis is given to the solitary waves of the second baroclinic mode (mode 2) and their strongly nonlinear characteristics that fail to be captured by weakly nonlinear models. In certain asymptotic limits relevant to oceanic applications and previous laboratory experiments, it is shown that large amplitude mode-2 waves with single-hump profiles can be described by the solitary-wave solutions of the MCC model, originally developed for mode-1 waves in a two-layer system. In other cases, however, e.g. when the density stratification is weak and the density transition layer is thin, the richness of the dynamical system with two degrees of freedom becomes apparent and new classes of mode-2 solitary-wave solutions of large amplitudes, characterized by multi-humped wave profiles, can be found. In contrast with the classical solitary-wave solutions described by the MCC equation, such multi-humped solutions cannot exist for a continuum set of wave speeds for a given layer configuration. Our analytical predictions based on asymptotic theory are then corroborated by a numerical study of the original Hamiltonian system. 
    more » « less
  4. null (Ed.)
    Variations of vertical atmospheric electric field E z have been attributed mainly to meteorological processes. On the other hand, the theory of electromagnetic waves in the atmosphere, between the bottom ionosphere and earth’s surface, predicts two modes, magnetic H (TE) and electric E (TH) modes, where the E-mode has a vertical electric field component, E z . Past attempts to find signatures of ULF (periods from fractions to tens of minutes) disturbances in E z gave contradictory results. Recently, study of ULF disturbances of atmospheric electric field became feasible thanks to project GLOCAEM, which united stations with 1 sec measurements of potential gradient. These data enable us to address the long-standing problem of the coupling between atmospheric electricity and space weather disturbances at ULF time scales. Also, we have reexamined results of earlier balloon-born electric field and ground magnetic field measurements in Antarctica. Transmission of storm sudden commencement (SSC) impulses to lower latitudes was often interpreted as excitation of the electric TH 0 mode, instantly propagating along the ionosphere–ground waveguide. According to this theoretical estimate, even a weak magnetic signature of the E-mode ∼1 nT must be accompanied by a burst of E z well exceeding the atmospheric potential gradient. We have examined simultaneous records of magnetometers and electric field-mills during >50 SSC events in 2007–2019 in search for signatures of E-mode. However, the observed E z disturbance never exceeded background fluctuations ∼10 V/m, much less than expected for the TH 0 mode. We constructed a model of the electromagnetic ULF response to an oscillating magnetospheric field-aligned current incident onto the realistic ionosphere and atmosphere. The model is based on numerical solution of the full-wave equations in the atmospheric-ionospheric collisional plasma, using parameters that were reconstructed using the IRI model. We have calculated the vertical and horizontal distributions of magnetic and electric fields of both H- and E-modes excited by magnetospheric field-aligned currents. The model predicts that the excitation rate of the E-mode by magnetospheric disturbances is low, so only a weak E z response with a magnitude of ∼several V/m will be produced by ∼100 nT geomagnetic disturbance. However, at balloon heights (∼30 km), electric field of the E-mode becomes dominating. Predicted amplitudes of horizontal electric field in the atmosphere induced by Pc5 pulsations and travelling convection vortices, about tens of mV/m, are in good agreement with balloon electric field and ground magnetometer observations. 
    more » « less
  5. Abstract

    Heat conduction in solids is typically governed by the Fourier’s law describing a diffusion process due to the short wavelength and mean free path for phonons and electrons. Surface phonon polaritons couple thermal photons and optical phonons at the surface of polar dielectrics, possessing much longer wavelength and propagation length, representing an excellent candidate to support extraordinary heat transfer. Here, we realize clear observation of thermal conductivity mediated by surface phonon polaritons in SiO2nanoribbon waveguides of 20-50 nm thick and 1-10 μm wide and also show non-Fourier behavior in over 50-100 μm distance at room and high temperature. This is enabled by rational design of the waveguide to control the mode size of the surface phonon polaritons and its efficient coupling to thermal reservoirs. Our work laid the foundation for manipulating heat conduction beyond the traditional limit via surface phonon polaritons waves in solids.

     
    more » « less