Single Vertical Mode Research Articles

Boosting the electrical output of cement-based triboelectric nanogenerator by surface treatment technique

Triboelectric nanogenerators have the potential to convert mechanical energy to electric energy through electrostatic induction thus they are promising alternative cleaning energy sources for human beings. The objective of this work is to increase the electrical outputs of cement-based triboelectric nanogenerators (C-TENGs) by using a surface polishing treatment technique. The hand-mixed cement pastes with water-to-cement ratios of 0.3, 0.4, and 0.5 by weight were cast in the molds and cured in saturated lime water. A study was conducted to investigate the electrical output, which included voltage and current, under a single vertical contract-separation mode with a constant force and a frequency of 3 Hz. To improve the electrical generating performance, all samples were subjected to a surface treatment by polishing with sandpaper. After electrical investigations, the electrical outputs were remeasured. The results showed that the modified surface samples have significantly higher electrical outputs than that of the pristine sample due to the increased contact surface area. Moreover, the cement paste with a water-to-cement ratio of 0.3 after a polished-surface treatment exhibits the highest power density for an external resistance of 10 MΩ, improving around 70% higher than the pristine sample. The study successfully presents a low-cost and simple technique for improving the performance of cement-based triboelectric nanogenerators.

Design and Analysis of Si/CaF<sub>2</sub> Near-Infrared (λ∼1.7µm) DFB Quantum Cascade Laser for Silicon Photonics

We have designed a near-infrared wavelength Si/CaF2 DFB quantum cascade laser and investigated the possibility of single-mode laser oscillation by analysis of the propagation mode, gain, scattering time of Si quantum well, and threshold current density. As the waveguide and resonator, a slab-type waveguide structure with a Si/CaF2 active layer sandwiched by SiO2 on a Si (111) substrate and a grating structure in an n-Si conducting layer were assumed. From the results of optical propagation mode analysis, by assuming a λ/4-shifted bragg waveguide structure, it was found that the single vertical and horizontal TM mode propagation is possible at the designed wavelength of 1.70 μm. In addition, a design of the active layer is proposed and its current injection capability is roughly estimated to be 25.1 kA/cm2, which is larger than required threshold current density of 1.4 kA/cm2 calculated by combining analysis results of the scattering time, population inversion, gain of quantum cascade lasers, and coupling theory of a Bragg waveguide. The results strongly indicate the possibility of single-mode laser oscillation.

Multiple increase in the radiative efficiency of 1060-nm laser diodes based on heterostructures with tunnel-coupled injection and a single waveguide mode.

An approach aimed at increasing the radiative efficiency in heterostructures operating in a single vertical mode at 1060 nm has been studied. Two types of heterostructures-the STJH (single tunnel junction heterostructure) and DTJH (double tunnel junction heterostructure)-have been developed to obtain the operation of a single waveguide mode of the first and second order, respectively. A multiple increase in the injection efficiency is realized by using tunnel junctions (TJs) embedded in the wide-gap barriers and placed between the active regions. An internal quantum efficiency of close to 100% and a transparency current density of 78 A/cm2 is demonstrated for both types of heterostructures, while the internal optical loss is 5.2 and 3.8 cm-1 for STJH and DTJH, respectively. The maximum radiative efficiency (for the initial linear part of the light-current curve) and the output optical power (for the current pulse of 1 µs and 9.6 A) reach 1.6 W/A and 7.8 W for STJH and 2.2 W/A and 15.8 W for DTJH.

Beyond the Rigid Lid: Baroclinic Modes in a Structured Atmosphere

Abstract The baroclinic-mode decomposition is a fixture of the tropical-dynamics literature because of its simplicity and apparent usefulness in understanding a wide range of atmospheric phenomena. However, its derivation relies on the assumption that the tropopause is a rigid lid that artificially restricts the vertical propagation of wave energy. This causes tropospheric buoyancy anomalies of a single vertical mode to remain coherent for all time in the absence of dissipation. Here, the authors derive the Green’s functions for these baroclinic modes in a two-dimensional troposphere (or, equivalently, a three-dimensional troposphere with one translational symmetry) that is overlain by a stratosphere. These Green’s functions quantify the propagation and spreading of gravity waves generated by a horizontally localized heating, and they can be used to reconstruct the evolution of any tropospheric heating. For a first-baroclinic two-dimensional right-moving or left-moving gravity wave with a characteristic width of 100 km, its initial horizontal shape becomes unrecognizable after 4 h, at which point its initial amplitude has also been reduced by a factor of 1/π. After this time, the gravity wave assumes a universal shape that widens linearly in time. For gravity waves on a periodic domain the length of Earth’s circumference, it takes only 10 days for the gravity waves to spread their buoyancy throughout the entire domain.

Influence of the Barotropic Mean Flow on the Width and the Structure of the Atlantic Equatorial Deep Jets

AbstractA representation of an equatorial basin mode excited in a shallow-water model for a single high-order baroclinic vertical normal mode is used as a simple model for the equatorial deep jets. The model is linearized about both a state of rest and a barotropic mean flow corresponding to the observed Atlantic Equatorial Intermediate Current System. It was found that the eastward mean flow associated with the North and South Intermediate Counter Currents (NICC and SICC, respectively) effectively shields the equator from off-equatorial Rossby waves. The westward propagation of these waves is blocked, and focusing on the equator due to beta dispersion is prevented. This leads to less energetic jets along the equator. On the other hand, the westward barotropic mean flow along the equator reduces the gradient of absolute vorticity and hence widens the cross-equatorial structure of the basin mode. Increasing lateral viscosity predominantly affects the width of the basin modes’ Kelvin wave component in the presence of the mean flow, while the Rossby wave is confined by the flanking NICC and SICC. Independent of the presence of the mean flow, the application of sufficient lateral mixing also hinders the focusing of off-equatorial Rossby waves, which is hence an unlikely feature of a low-frequency basin mode in the real ocean.

Geostrophic adjustment in a closed basin with islands

AbstractWe consider the geostrophic adjustment of a density-stratified fluid in a basin of constant depth on an $f$-plane in the context of linearized theory. For a single vertical mode, the equations are equivalent to those for a linearized shallow-water theory for a homogeneous fluid. Associated with any initial state there is a unique steady geostrophically adjusted component of the flow compatible with the initial conditions. This steady component gives the time average of the flow and is analogous to the adjusted flow in an unbounded domain without islands. The remainder of the response consists of superinertial Poincaré and subinertial Kelvin wave modes and expressions for the energy partition between the modes in arbitrary basins again follow directly from the initial conditions. The solution for an arbitrary initial density distribution released from rest in a circular domain is found in closed form. When the Rossby radius is much smaller than the basin radius, appropriate for the baroclinic modes, the interior adjusted solution is close to that of the initial state, except for small-amplitude trapped Poincaré waves, while Kelvin waves propagate around the boundaries, carrying, without change of form, the deviation of the initial height field from its average.

Implementation of the Quasi‐equilibrium Tropical Circulation Model 2 (QTCM2): Global simulations and convection sensitivity to free tropospheric moisture

The implementation of the Quasi‐equilibrium Tropical Circulation Model 2 (QTCM2), an intermediate level complexity model, is described. Following the approach of Sobel and Neelin (2006), an explicit, prognostic atmospheric boundary layer (ABL) of fixed depth is added to a free troposphere (FT) containing one baroclinic and one barotropic mode. QTCM2 is shown to simulate reasonable climatologies of temperature, moisture, winds, and precipitation, albeit with only modest improvements relative to the predecessor single vertical mode version, QTCM1. The addition of an ABL increases the sharpness of horizontal precipitation and moisture gradients, and the separation of the moisture profile into ABL and FT components allows investigation into the separate roles of these two components in modulating deep convection. Model sensitivity to various convection parameters is explored, with contrasting precipitation responses often seen within the cores of convecting regions and along their margins.

Multiple vertical mode high power 975 nm diode lasers restricted to single vertical mode operation through use of optical facet coatings

A new design approach has been developed for facet coating of high power diode lasers, that is shown to preferentially suppress higher-order guided optical modes, without any degradation in device performance. Repeated optical coating of reference lasers is found to controllably transform the vertical far field from a three-peaked higher-order mode to a single-peaked fundamental mode, in good agreement with simulations. 975 nm devices with such coatings reach power conversion efficiency of 65%.

A Simple Model of a Convectively Coupled Walker Circulation Using the Weak Temperature Gradient Approximation

An idealized model of a Walker circulation based on the weak temperature gradient (WTG) approximation and a single baroclinic vertical mode for all fields is analyzed. The circulation is forced by a sinusoidal variation of sea surface temperature (SST). A simple feedback of deep convective cloud radiative forcing on tropospheric radiative cooling is included, and a moist convective adjustment is used to interactively specify the location and intensity of deep convection. A goal is to understand how the fraction of the domain undergoing deep convection depends on the SST difference across the domain. The WTG approximation greatly simplifies the calculation of the circulation. For small SST differences, convection occurs everywhere and a fully analytic solution is possible; for larger SST differences, a simple nonlinear algorithm is used to determine the edge of the convective region and the tropospheric temperature. The solution is invariant to changes of domain size. The divergent circulation is independent of the Coriolis parameter as long as the domain is sufficiently narrow so WTG remains accurate. The convective region narrows and intensifies considerably when cloud‐radiation feedbacks are considered. As the SST difference increases, the convective region shrinks and the troposphere warms; simple approximate formulas for these trends in terms of the control parameters are derived. For large SST differences, the convection over the warmest water becomes susceptible to a radiative‐convective instability and there is no steady-state solution.

The Kuroshio East of Taiwan: Moored Transport Observations from the WOCE PCM-1 Array

Observations from the WOCE PCM-1 moored current meter array east of Taiwan for the period September 1994 to May 1996 are used to derive estimates of the Kuroshio transport at the entrance to the East China Sea. Three different methods of calculating the Kuroshio transport are employed and compared. These methods include 1) a “direct” method that uses conventional interpolation of the measured currents and extrapolation to the surface and bottom to estimate the current structure, 2) a “dynamic height” method in which moored temperature measurements from moorings on opposite sides of the channel are used to estimate dynamic height differences across the current and spatially averaged baroclinic transport profiles, and 3) an “adjusted geostrophic” method in which all moored temperature measurements within the array are used to estimate a relative geostrophic velocity field that is referenced and adjusted by the available direct current measurements. The first two methods are largely independent and are shown to produce very similar transport results. The latter two methods are particularly useful in situations where direct current measurements may have marginal resolution for accurate transport estimates. These methods should be generally applicable in other settings and illustrate the benefits of including a dynamic height measuring capability as a backup for conventional direct transport calculations. The mean transport of the Kuroshio over the 20-month duration of the experiment ranges from 20.7 to 22.1 Sv (1 Sv ≡ 106 m3 s−1) for the three methods, or within 1.3 Sv of each other. The overall mean transport for the Kuroshio is estimated to be 21.5 Sv with an uncertainty of 2.5 Sv. All methods show a similar range of variability of ±10 Sv with dominant timescales of several months. Fluctuations in the transport are shown to have a robust vertical structure, with over 90% of the transport variance explained by a single vertical mode. The moored transports are used to determine the relationship between Kuroshio transport and sea-level difference between Taiwan and the southern Ryukyu Islands, allowing for long-term monitoring of the Kuroshio inflow to the East China Sea.

Application of a Reduced-Order Kalman Filter to Initialize a Coupled Atmosphere–Ocean Model: Impact on the Prediction of El Niño

A reduced order Kalman Filter, based on a simplification of the Singular Evolutive Extended Kalman (SEEK) filter equations, is used to assimilate observed fields of the surface wind stress, sea surface temperature and sea level into the nonlinear coupled ocean-atmosphere model. The SEEK filter projects the Kalman Filter equations onto a subspace defined by the eigenvalue decomposition of the error forecast matrix, allowing its application to high dimensional systems. The Zebiak and Cane model couples a linear reduced gravity ocean model with a single vertical mode atmospheric model of Zebiak. The compatibility between the simplified physics of the model and each observed variable is studied separately and together. The results show the ability of the model to represent the simultaneous value of the wind stress, SST and sea level, when the fields are limited to the latitude band 10 deg S - 10 deg N. In this first application of the Kalman Filter to a coupled ocean-atmosphere prediction model, the sea level fields are assimilated in terms of the Kelvin and Rossby modes of the thermocline depth anomaly. An estimation of the error of these modes is derived from the projection of an estimation of the sea level error over such modes. This method gives a value of 12 for the error of the Kelvin amplitude, and 6 m of error for the Rossby component of the thermocline depth. The ability of the method to reconstruct the state of the equatorial Pacific and predict its time evolution is demonstrated. The method is shown to be quite robust for predictions I up to six months, and able to predict the onset of the 1997 warm event fifteen months before its occurrence.

Three-Dimensional Structure of Thermohaline Circulation Steered by Bottom Topography

An investigation based on the expansion in terms of diffusive vertical modes is made on the effect of an isolated seamount on the three-dimensional structure of thermohaline circulation driven by an inflow of deep water. While the circulation has a relatively simple structure dominated by the first baroclinic mode in a flat ocean, it becomes rather complicated in an ocean with a seamount. Nevertheless its three-dimensional structure is reconstructed and understood well by analyzing the dynamics of the vertical modes. It is shown that the vertical modes respond to the topography-induced stretching in a similar way irrespective of the mode number. When synthesized in the deep layer, therefore, the vertical modes interfere constructively to yield the same pattern of circulation as a single vertical mode or the diffusive reduced-gravity model. It is thus confirmed that the abyssal circulation certainly has the features predicted by the diffusive reduced-gravity model such as cyclonic circulation over the mountain or downwelling in the geostrophic island, in which geostrophic contours close on themselves. Close to the surface, however, different modes of different vertical structures interfere destructively so that the horizontal distribution of topography-induced circulation in the deep layer decays, upward shifting its center westward.

The salt finger amplitude in unbounded T-S gradient layers

Finite amplitude numerical calculations are made for a completely unbounded salt e nger domain whose overall vertical ‘ ‘ property’ ’ gradients ( Tz andSz) are uniform and remain unaltered in time. For diffusivity ratio t 5 k S/k T 5 O(1), Prandtl number n /k T ae 1, and density ratio R 5 Tz/Sz . 1 this regime corresponds to a ‘ ‘ double gradient’ ’ sugar ( S) 2 salt (T) experiment. Two-dimensional pseudo-spectral calculations are made in the vicinity of the minimum critical condition for salt e nger instability, viz., small e ; (Rt ) 2 1 2 1 . 0; the allowed spectrumincludes the fastest growing wave of linear theory. When the vertical wavelength of the fundamental Fourier component is systematically increased the solution changes from a single steady vertical mode to a multi-modal statistically steady chaotic state. Each of the long vertical modes can be amplie ed by the (unchanging overall) gradient Sz, and can be stabilized by the induced vertical T, S gradients on the same scale as the modes; nonlinear triad interactions in the T 2 S equations can also lead to amplitude equilibration even though e , k T/n , and the Reynolds number are extremely small. When subharmonics of the horizonal wavelength of maximum growth are introduced into the numerical calculations the new wave amplie es (via Sz) and produces a quantitative change in the time average e uxes. Experimentally testable values of heat e ux and rms horizontal T-e uctuations are computed in the range2.8 . R . 1.6 for t 5 1 A3.Asymptotic similarity laws e ® 0 are also presented.

Application of the mode vector parabolic equation to the 3‐dimensional wedge problem

The MVPE [Abawi et al., this session] is applied to the problem of propagation of waves in a 3‐dimensional coastal wedge and the results are compared with those when horizontal coupling is neglected and with the results obtained from conventional 3‐dimensional methods. The components of the solution vector are the amplitudes of the vertical modes which are coupled in both range and azimuth. The coupling matrices for both range and azimuth are precomputed by the method summarized in [McDonald et al., 2357 (1994)]. In the absence of mode coupling, the solution reduces to the solution of the adiabatic mode parabolic equation [M. D. Collins, 2269 (1993)]. The system of equations are numerically solved by the Crank–Nicholson finite difference method. For a single vertical mode, this system of equations closely resembles a system of discretized parabolic equation in range and azimuth. For multiple modes, the matrices involved are band diagonal with the coupling matrices appearing in their diagonal. The size of these matrices are thus equal to the number of points in azimuth times the number of vertical modes. When the physics of the problem is contained in a subset of coupled modes, this method offers additional advantages in numerical computation over the conventional 3‐dimensional methods.

Horizontal wave propagation in the equatorial waveguide

The dispersive (i.e. non-Kelvin) linear wave field on the equatorial β-plane, in a single vertical mode, is fully described by a single potential φ. Long Rossby waves, which are weakly dispersive, are represented in this field. This description is free from the problem of the ‘spurious solution’ encountered when working with an evolution equation for the meridional velocity; addition of this unwanted solution represents a gauge transformation that leaves the physical fields unaltered.The general solution of the ray equations is found, including trajectories, and the amplitudes and phase fields. This solution is asymptotically valid for either high or low frequencies. The ray paths are identical in both limits, but the phase field is not, reflecting the isotropy of Poincaré waves, in one case, and the zonal anisotropy of Rossby waves, in the other.Two examples are studied by ray theory: meridional normal modes and wave radiation from a point source in the equator. In the first case, the exact dispersion relation is obtained. In the second one, northern and southern caustics bend towards the equator, meeting there at focal points. The full solution is the superposition of many leaves and has a structure that would be hard to find in a normal modes expansion.

Modes of Tropical Variability under Convective Adjustment and the Madden–Julian Oscillation. Part I: Analytical Theory

Abstract The interaction between the collective effects of cumulus convection and large-scale dynamics is examined using the Betts–Miller moist convective adjustment (MCA) parameterization in a linearized primitive equation model on an equatorial β plane. In Part I of this paper, an analytical approach to the eigenvalue problem is taken using perturbation expansions in the cumulus adjustment time, which is short compared to planetary dynamical time scales. The modes of tropical variability that arise under MCA are dominated by the presence of moist processes; some modes act to adjust the system rapidly toward a convectively adjusted state, while others evolve on time scales set by the large-scale dynamics subject to near-adjusted (quasi equilibrium) thermodynamical constraints. Of the latter, a single vertical mode stands out, which obeys special balances implied by the quasi-equilibrium constraints and is the only propagating deep convective mode. The propagation speed is determined by an internally defi...

On Wave-CISK and the Evaporation-Wind Feedback for the Madden-Julian Oscillation

The combined effects of Kelvin wave-CISK and the evaporation-wind (E-W) feedback are proposed as a possible mechanism for the Madden-Julian oscillation. A very simple single vertical mode model has been employed to examine the effects of both these processes on moist Kelvin waves. The effects of wave-induced moisture convergence is parameterized by reducing the moist static stability, and CISK occurs when the moist static stability becomes negative. The E-W feedback in the presence of mean easterlies leads to unstable Kelvin modes. The presence of mean westerlies leads to decaying Kelvin modes. When CISK and the E-W feedback work in concert, an unstable Kelvin mode develops that has phase speeds of propagation between 5 m/s and 10 m/s for a large range of parameter values. On the other hand, the E-W feedback mechanism alone, in the case when CISK is not operating, produces the phase speeds of the observed Madden-Julian oscillation for only a very limited range of parameter values.

A Simple Model of the Climatology and Variability of the Low-Level Wind Field in the Tropics

A simple model of the low-level wind field in the entire tropics is presented. The dynamics are the same as those within the familiar Gill model, i.e., linear, steady state, contained within a single vertical mode and damped by Rayleigh friction. Convective atmospheric heating can occur if a lifted air parcel is buoyant relative to its surroundings, and the heating is computed with reference to the cloud model of Yanai et al. Radiative cooling is represented by a Newtonian cooling to an equilibrium lapse rate. The model is forced by surface temperature and humidity. A qualitatively correct representation of the climatological flow is achieved. The main differences between model and observations relate to the model's inability to reproduce the intensity and limited spatial scale of the convergence zones. Model simulations of anomalous circulations are subject to the same limitations. Problems related to the lack of an explicit boundary layer in the model, the poor representation of radiation, and the cumulus parameterization are discussed, together with suggestions for future work.

Vertical Structure and Interannual Variability of Tropical Zonal Winds

Geographical and seasonal variations of the variance and vertical structure of interannual anomalies of seasonally averaged zonal winds are calculated from rawinsonde records at tropical stations between 80°E and 140°W, the longitudes spanned by the “Walker Circulation.” Wind anomalies are negatively correlated in the upper and lower troposphere only in a latitude band within about 10° of the equator, defining the latitudinal extent of the Walker Circulation; about 70% of the interannual variance of tropospheric zonal winds is accounted for by a single vertical mode within this band. The band shifts seasonally north and south slightly, in conjunction with seasonal shifts in large-scale convection. The level of zonal overturning occurs between 300 and 500 mb, and is highest near the seasonal convective maximum. Other vertical structures, suggestive of interannual variability not associated with thermally forced circulations, are also found near the equator at some longitudes in the boreal winter season.

Modelling intraseasonal and interannual variability in the tropics

A tropical ocean-atmosphere model of intermediate complexity, incorporating a limited set of physical processes, is used to investigate variability up to interannual timescales. The model atmosphere has a single vertical mode and an explicit moisture budget, whereas the ocean has one active upper layer. Basic experiments confined to a Pacific-size closed ocean basin and the overlying atmosphere are described. Eastward-propagating coupled waves with a period of about six years arise for strong coupling, but with weak coupling a steady equilibrium is reached. The model has no internal high-frequency variability, so for some cases a small amount of noise is added to the atmospheric forcing terms. This noise is selectively amplified by moist processes in the atmosphere to generate eastward-propagating intraseasonal waves. It is found that these waves have little effect on the robust interannual coupled wave: rather, the interannual mode imposes large-scale patterns that inhibit the intraseasonal waves.