Three-dimensional Wave Structure Research Articles

Short-period planetary-scale waves in a Venus general circulation model: Rotational and divergent component structures and energy conversions

To elucidate the generation and coupling of the short-period waves in the Venus atmosphere, we investigated the three-dimensional wave structure in an AORI (Atmosphere and Ocean Research Institute, University of Tokyo, Japan) Venus general circulation model. The most predominant waves are 7.5-day waves with zonal wavenumber 1 and are slower than observed planetary-scale 5.5-day waves around the cloud bottom (∼50 km), associated with a slower zonal flow in the model. The 7.5-day waves comprise three types: Type I, a Rossby wave in the upper cloud layer; Type II, a Rossby wave around the polar tropopause (∼50 km); and Type III, an equatorial Kelvin-like wave around and below the cloud bottom.Around the cloud top (65–70 km), the Rossby wave (Type I) has a rotational eddy structure and is produced by potential-energy conversion from zonal mean to eddy, suggesting baroclinic instability in the cloud layer. The geopotential of the Rossby wave in the upper cloud layer vertically connects to that of the equatorial Kelvin-like wave (Type III) across the critical line at ∼55 km and 30° latitudes. At the cloud bottom (∼50 km), the Kelvin-like wave and Rossby wave (Type II) are separated at a critical latitude around the cloud bottom, but are horizontally jointed with the stream function and velocity potential at the critical latitude. These two waves are major equatorward momentum transporters and are generated by horizontal shear (or barotropic) and baroclinic instabilities associated with energy conversion at the critical line. For high-latitude Rossby waves around the polar tropopause (Type II), the positive kinetic-energy conversion by vertical momentum transport is predominant, tending to relax the vertical shear of the zonal flow, leading in turn to relaxation of the horizontal temperature gradient under the cyclostrophic thermal wind. In contrast, the negative potential-energy conversion tends to produce the horizontal temperature gradient in the lower atmosphere where the solar insolation is very weak.The equatorial jet core rotating with a 7.5-day period is composed of both divergent and rotational wind components of the equatorial Kelvin-like wave at the cloud bottom. Above the critical level of the Kelvin-like wave, the equatorial Rossby wave (downward and equatorward flank of the Type I wave) appears at around 54 km and is produced by the barotropic energy conversion.

Experimental study of the three-dimensional interfacial wave structure of freely falling liquid film in a vertical large pipe diameter

Most of the experimental and theoretical studies on the film thickness of falling liquid films are focussed on either small diameter pipes or flat plates. Almost, all these studies provide time series data of the film thickness measured at single positions around the pipe wall or along the pipe section, which might not reflect the real flow structure in both axial and circumferential directions. This paper reports the interfacial structure of freely falling liquid films (liquid Reynolds numbers, ReL=618–1670) in a vertical large diameter pipe (127mm) using advanced Multi-Probes Film Sensor (MPFS). Unlike smaller diameter pipes where the waves are characterised as coherent rings, the waves found in this paper with larger diameter pipe were much localised around the pipe circumference and evolved with time in the axial direction. Skewness and Kurtosis numbers showed two distinct linear trends with two different slopes intersecting at ReL=960. One of the significant contributions of the current paper is that the new experimental reconstructed three-dimensional wave structure data for the falling liquid film in a vertical large pipe diameter will be available in the literature which would be of interest to many modellers who need such data to validate their CFD models.

A metamorphosis of three-dimensional wave structure in transitional and turbulent boundary layers

Abstract

Comparative Study of Elliptic and Round Scramjet Combustors Fueled by RP-3

To explore the combustion performance of nonrectangular supersonic combustors, the flow and combustion characteristics in the round and round-to-elliptic shape-transition scramjet combustors were compared, based on the measurements and the improved delayed detached-eddy simulation modelings. The global equivalence ratio was kept at 0.8, whereas two inlet Mach numbers of 2.5 and 3.0 were tested. To reduce the computational cost, four versions of skeletal mechanisms (respectively, , , , and ) have been developed for China RP-3 kerosene; and the latest one was used. The predicted static pressure profiles along the streamwise direction were first validated against the measurements. Then, the aerodynamic fields were analyzed for the two combustors to compare their flow, mixing, and combustion performances. The three-dimensional wave structures inside the nonaxisymmetric elliptic combustor were revealed for the first time to show the influence of shape transition. Specifically, the time evolution of the flame structures was analyzed, and dominant modes were extracted by the aid of proper orthogonal decomposition.

A two-phase flow model for wave–structure interaction using a virtual boundary force method

A three-dimensional two-phase flow model is developed to study wave interaction with structures by using a virtual boundary force (VBF) method. This model solves the Navier–Stokes equations for two-phase flows. The second-order accurate volume-of-fluid (VOF) method is used to track the free surface. In order to satisfy the no-slip condition on the rigid body surface, the virtual boundary forces are applied along the surface of the body in the computation. The model is first validated for wave interaction with a structure with the curved surface. This model is then used to simulate various types of two-dimensional and three-dimensional wave–structure interaction problems, i.e., solitary wave runup and rundown on a sloping beach, nonlinear wave transformation above a submerged breakwater, and wave diffraction around a large circular cylinder. The computational results compare well with available analytical solutions and experimental data. Lastly, as a demonstration, the three-dimensional wave breaking on a floating truncated circular cylinder is simulated and discussed.

Problem of non-uniqueness of steady-state hypersonic flow past bodies with a cylindrical frontal bluntness

The problem of non-uniqueness of steady-state modes of hypersonic flow past bodies with a cylindrical frontal bluntness is investigated using the direct numerical simulation by means of the “FLUENT” software. The principal aim of the study is to confirm the fact that three-dimensional wave structures developed on the frontal surface of bodies in a homogeneous hypersonic stream represent one of the steady-state modes of the solutions of the Navier-Stokes equations and do not result from the calculation grid roughness or the exciting action of the boundary conditions.

Investigations on the porous media equations and resistance coefficients for coastal structures

This paper considers the flow in porous media that occurs in coastal and offshore engineering problems. Over the past decades numerous formulations of flow equations for porous media have been presented. The present work re-examines the porous media equations of the most recent form and corrects some shortcomings which were identified. The applied type of porosity models relies on empirical resistance coefficients which often need to be measured or calibrated. Only few examples of calibration for numerical models which are present in the literature often applied the same experimental results. In this study new calibration cases were introduced to the calibration procedure in order to achieve a better understanding of the variation of the resistance coefficients. Hereby the coefficients were determined with a better description over the entire parameter space for the resistance coefficients than previously found in the literature. Constant values for the resistance coefficients for a broad range of flow conditions were recommended based on the new calibrations. The model was validated for the main physical processes that occur in wave–structure interaction in coastal structures including three-dimensional wave–structure interaction, run-up, run-down and pressure damping, regular and irregular wave conditions and evaluation of overtopping. Simple two and three dimensional uniform caisson structures and breakwater layouts were investigated. The model was implemented in the open source CFD library OpenFOAM® and has been made publicly available to the engineering community as part of the wave generation framework waves2Foam.

Plunging solitary wave and its interaction with a slender cylinder on a sloping beach

Laboratory experiments were performed for solitary waves breaking on a constant slope. In the second set of experiments a vertical cylinder was installed on the slope, which was subject to the impact of a shoaling solitary wave. PIV was used to record the time history of free surface elevations, and temporal and spatial velocity variations in two fields of view (FOVs). A numerical model was also employed to simulate the three-dimensional wave–structure interaction problem. Filtered Navier–Stokes equations are solved numerically. The small scale eddies were modeled by the traditional Smagorinsky LES model and RNG LES model. The data-model comparisons were performed. The agreement is very good for the free surface elevations before breaking occurs. The laboratory wave appears to break slightly sooner than the numerically simulated wave. The comparisons for the normalized horizontal velocity profiles in the water column in both FOVs show excellent agreement. However, the magnitude of depth-averaged horizontal velocities for the numerical wave is roughly 10–15% higher than that of laboratory wave. The numerical model is used to illustrate the runup process of the solitary wave on the cylinder. The time history of wave force is also calculated and correlated to the free surface evolution.

Time-domain simulation of wave–structure interaction based on multi-transmitting formula coupled with damping zone method for radiation boundary condition

Based on the Rankine source, this paper proposed a time-domain method for analyzing the three-dimensional wave–structure interaction problem in irregular wave. A stable integral form of the free-surface boundary condition (IFBC) is employed to update the velocity potential on the free surface. A multi-transmitting formula, with an artificial wave speed, is used to eliminate the wave reflection for radiation condition on the artificial boundary. An effective multi-transmitting formula, coupled with damping zone method, is further used to analyze the irregular wave diffraction at the artificial boundary. We investigate hydrodynamic forces on floating structure and compare our solution to the frequency-domain solution. It is shown that long time simulation can be done with high stability and the numerical results agree well with the solution obtained under the frequency domain. The efficiency of the proposed multi-transmitting formula and the coupled methods for radiation boundary make them promising candidates in studying the irregular water wave problem in time domain.

Retrieval of the three-dimensional wave structure of gravity waves from multi-position airglow measurements

The aim of this work is to develop mathematical foundation of a method which can be used to infer the three-dimensional gravity wave characteristics from multi position airglow observations from space. This work derives a one-dimensional Fredholm integral equation of the first kind, which describes the relations between the gravity wave spectrum and spatial structure of wave perturbations registered by a space-based airglow imager. It is shown that the solution of this equation belongs to the central slice through a three-dimensional gravity wave spectrum, whose plane is perpendicular to the optical axis of the airglow imager. Thus, in order to retrieve the three-dimensional gravity wave characteristics from the airglow observations performed from space, it is needed to obtain the set of images of a local emission layer area from different imager positions. Then this data must be processed using the developed mathematical techniques to obtain a set of the central slices of the three-dimensional gravity wave spectrum. Applying the technique, for a superposition of three individual waves, amplitude and wave vector can be determined.

Three-dimensional divergent waves on a model viscoelastic coating in a potential incompressible fluid flow

Generation of three-dimensional nonlinear waves on a model viscoelastic coating in a potential flow of an incompressible fluid is studied. Periodic nonlinear waves enhanced by the development of quasi-static instability (wave divergence) are considered. The coating is modeled by a flexible flat plate supported by a distributed nonlinearly-elastic spring foundation. Plate flexure is described on the basis of the Karman equations of the theory of thin plates. Perturbations of surface pressure in the potential flow are found in the small slope approximation to an accuracy to terms of the second order of smallness. Numerical simulation reveals a jump-like transition from two-dimensional nonlinear waves to three-dimensional wave structures, which are also observed in experiments.

An Analysis of Convectively Coupled Kelvin Waves in 20 WCRP CMIP3 Global Coupled Climate Models

Abstract Output from 20 coupled global climate models is analyzed to determine whether convectively coupled Kelvin waves exist in the models, and, if so, how their horizontal and vertical structures compare to observations. Model data are obtained from the World Climate Research Program’s (WCRP’s) Coupled Model Intercomparison Project phase 3 (CMIP3) multimodel dataset. Ten of the 20 models contain spectral peaks in precipitation in the Kelvin wave band, and, of these 10, only 5 contain wave activity distributions and three-dimensional wave structures that resemble the observations. Thus, the majority (75%) of the global climate models surveyed do not accurately represent convectively coupled Kelvin waves, one of the primary sources of submonthly zonally propagating variability in the tropics. The primary feature common to the five successful models is the convective parameterization. Three of the five models use the Tiedtke–Nordeng convective scheme, while the other two utilize the Pan and Randall scheme. The 15 models with less success at generating Kelvin waves predominantly contain convective schemes that are based on the concept of convective adjustment, although it appears that those schemes can be improved by the addition of convective “trigger” functions. Three-dimensional Kelvin wave structures in the five successful models resemble observations to a large degree, with vertically tilted temperature, specific humidity, and zonal wind anomalies. However, no model completely captures the observed signal, with most of the models being deficient in lower-tropospheric temperature and humidity signals near the location of maximum precipitation. These results suggest the need for improvements in the representations of shallow convection and convective downdrafts in global models.

Shock wave propagation into a surface depression

An aircraft travelling at supersonic speeds close to the ground generates a bow wave which is reflected off the ground surface. If a valley is traversed a complex reflection pattern will be generated. Similar patterns will evolve with a plane wave traversing a depression on a surface or structure. To simulate the process a planar shock wave, generated in a shock tube, is moved over several notched wedge configurations. Schlieren photographs were produced to assist in identifying the resulting complex three-dimensional wave structures and then verified and extended by three- dimensional computations. The valley geometries investigated are rectangular, triangular, parabolic and conical with a number of valley floor inclinations. The main features are extracted in surface models to demonstrate the complexity of the flow, and in particular in the case where the reflection is regular on the ground plane and Mach reflection in the valley.

Simulations of Three-Dimensional Flow and Augmented Heat Transfer in a Symmetrically Grooved Channel

Navier-Stokes simulations of three-dimensional flow and augmented convection in a channel with symmetric, transverse grooves on two opposite walls were performed for 180⩽Re⩽1600 using the spectral element technique. A series of flow transitions was observed as the Reynolds number was increased, from steady two-dimensional flow, to traveling two and three-dimensional wave structures, and finally to three-dimensional mixing. Three-dimensional simulations exhibited good agreement with local and spatially averaged Nusselt number and friction factor measurements over the range 800⩽Re⩽1600. [S0022-1481(00)00904-X]

Modelling of a plasma column sustained by a travelling circularly polarized electromagnetic wave (m = 1 mode) in the presence of a constant axial magnetic field

We present a set of equations modelling a low-pressure plasma column sustained by a travelling electromagnetic wave in the dipolar mode in the presence of a constant external magnetic field. It is shown that, from a practical point of view, only the m = 1 mode (the right-hand-polarized wave) can sustain plasma columns in a wide region of gas-discharge conditions: plasma radius R, wave frequency ωo, magnetic field Bo and low pressures, irrespective of the nature of the gas. We have examined two gas-discharge regimes: freefall/diffusion and recombination respectively. For a given gas-discharge regime the axial column structure and wave-field characteristics are specified by two numerical parameters: σ = ωR/c and ω = ωc/ω, where c is the speed of light and ωc the electron-cyclotron frequency. The main result of our study is that the magnetic field-makes it possible to sustain a plasma column for values of σ smaller than σcr = 0.3726, below which, in the absence of a magnetic field, the dipolar wave cannot produce a plasma. Moreover, at a fixed wave power, the magnetic field – in contrast with the case of plasma columns sustained by azimuthally symmetric waves – increases the plasma density and its axial gradient. The limit of an infinite external magnetic field (Ω → ∞) is also considered. A three-dimensional wave structure is obtained, and it indicates that the wave can be a generalized surface mode, a pure surface or a pseudosurface one.

Modeling of a plasma column produced and sustained by a traveling electromagnetic wave in the presence of a constant axial magnetic field.

We present the basic equations for modeling a plasma column produced and sustained by a traveling electromagnetic wave in the presence of a constant external magnetic field. The model consists of two equations---a local-dispersion relationship and a wave-energy-balance equation---and a relation between the absorbed wave power per unit length averaged across the column (proportional to the squared-wave electric field) and the local electron number density. The dispersion relation and the balance equation are derived in explicit forms and depend on two numerical parameters \ensuremath{\sigma}=\ensuremath{\omega}R/c (\ensuremath{\omega} being the wave angular frequency, R the plasma column radius, c speed of light) and \ensuremath{\Omega}=${\mathrm{\ensuremath{\omega}}}_{\mathit{c}}$/\ensuremath{\omega} (${\mathrm{\ensuremath{\omega}}}_{\mathit{c}}$ is the electron cyclotron frequency). The limit of an infinite external magnetic field (\ensuremath{\Omega}\ensuremath{\rightarrow}\ensuremath{\infty}) is also considered. The influence of the two parameters \ensuremath{\Omega} and \ensuremath{\sigma} on the dimensionless axial profiles of the wave characteristics and plasma column density, obtained by numerical solution of the basic equations, has been studied for two different gas-discharge regimes. A three-dimensional wave structure has been obtained, and it is shown that the wave can be a generalized surface mode, a pure surface, or a pseudosurface one. The results obtained are in agreement with the available experimental data.

One-to-Two Month Oscillations in the Stratosphere during Southern Winter

Abstract Stratospheric disturbances on the 35–60 day time scale are investigated with particular emphasis on the Southern Hemisphere. The data used are stratospheric brightness temperatures from 90 to 1.5 hPa covering seven 6-month southern winter periods (from April 1980 to March 1987). Global time-lag correlation plots are constructed from which tropical/extratropical connections, three-dimensional wave structure, and propagation characteristics are studied. Horizontal correlation patterns at 90 hPa reveal a strong connection between the Indonesian tropics and the winter extratropics. Vertical correlation patterns in the southern winter extratropics reveal westward tilt with height and vertical propagation of 35–60 day zonal wavenumber 1 perturbations, from tropospheric regions up to great heights, at least as high as the stratopause region. Disturbances are found to propagate from 90 hPa to 1.5 hPa in generally 6 to 9 days. In contrast, the vertical correlation plots in the tropics indicate little or n...

Study of three-dimensional wave structure of nonstationary gas outflow from a planar sonic nozzle

Results are reported of an experimental study of the three-dimensional structure of nonstationary gas outflow from a planar nozzle. Outflow of a heated shock wave in a nitrogen tube at different moments of time from the start of outflow (0–1 msec) in two mutually perpendicular directions is considered. A scheme for reconstructing the flow at different outflow stages is proposed. The dimensions of the Riemann wave are found to oscillate.

Effect of waves at a gas—liquid interface on a turbulent air flow

Air flowing over a liquid surface encounters an increased resistance if waves are present. The relation of this increased resistance to the properties of the waves has been studied. Air and a liquid flowed co-currently in an enclosed channel which is 12 in. wide and 1 in. high and which is long enough so that flow in the air and the liquid and the interfacial structure are fully developed. The drag on interfaces with three-dimensional wave structures was found to increase with the square of the gas velocity and to depend more on the height of the waves than on other parameters characterizing the interface. The ratio of the equivalent sand roughness to the root-mean-square of the fluctuations in the height of the liquid film is approximately equal to 3 √2. The velocity profiles in the gas were found to be different from what has been reported for flows over sand roughened surfaces.