Wave motion and vortex breakdown.
Vortex breakdown in rotating fluids associated with wave motion along axis of rotation, considering effects of nonzero wave amplitude
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Vortex breakdown in rotating fluids associated with wave motion along axis of rotation, considering effects of nonzero wave amplitude
Adiabatic motion of hydromagnetic fluid behind spherical fast shock wave for Parker solar wind model
Peristaltic motion of viscous incompressible fluid, applying long wave approximation to two dimensional urine flow model
The propagation and instability characteristics of small-signal electro-fluid-mechanical space-charge and polarization waves in nonhomogeneous fluids are developed. Stratified equilibrium configurations with fluid properties and space-charge density constant within planar, cylindrical, and spherical surfaces, are emphasized. Equilibrium electric fields due both to charges in the fluid and to externally imposed potentials are normal to these surfaces. The liquid is modeled as incompressible, inviscid, and perfectly insulating, with domains of sufficiently high frequency or growth rate to validate the last assumption defined in terms of electrical conductivity or mobility. A general set of relations for perturbation field and flow variables on the perturbed surfaces of fluid layers having constant properties and space charge are derived in each of the configurations.
The vibrations of a cylindrical elastic shell filled with fluid and excited by a monopole acoustic source are studied. The modal mobilities of the shell wall at the source plane are examined for different radial locations of the source. The distribution of vibrational energy between the shell and the fluid field is calculated at various axial locations along the shell and for different radial source locations. An interchange of energy of vibration between the shell and the fluid as the wave field propagates along the shell-fluid system is observed.
A cold fluid approach is presented which yields exact double-layer solutions that can be used to model electrostatic S-type shocks. Solutions derived from the two-temperature electron model are presented in order to show the range of amplitudes and scale lengths possible for this plasma model and to examine how shock properties depend on orientation of the shock. The dependence of various double-layer quantities on plasma composition is then considered for the cold electron beam model. Double-layer solutions pertinent to describing electrostatic shocks are pointed out.
A full scale Gravity Probe-B (GP-B) Spacecraft propellant dewar tank subjected to various frequencies of gravity jitter have been investigated. Excitation of slosh waves induced by gravity jitter are simulated. Results show that fluid stress distribution exerted on the walls of the rotating dewar are closely related to the characteristics of slosh waves excited on the liquid-vapor interface in the rotating dewar tank. Slosh wave excitations shift the fluid mass distribution in the dewar tank which impose time dependent variations in GP-B Spacecraft moment of inertia, angular momentum, and torque produced by imbalance fluid stresses. This can provide a set of data leading toward the control of spacecraft imbalance caused by the uneven fluid stress distribution from slosh waves.
The effect of the fluctuating buoyancy force on wave generation in a weakly magnetized plasma is considered. As expected, the efficiency of MHD wave generation is enhanced by including this force. However, it remains true that the observed variation of coronal emission at fixed spectral type cannot be accounted for by a wave generation process of the type discussed here.
The high surface roughness is one of the major challenges encountered in laser metal additive manufacturing (AM) processes, which is closely related to the melt flow behavior. However, how to control the melt flow in laser metal AM processes to improve surface finish is unknown. Here we reveal the effects of nanoparticles on melt flow behavior at every location of melt pool during laser metal AM process for the first time using Al6061 + TiC nanoparticles system and achieve significant improvement of surface finish by using TiC nanoparticles to control the melt flow and damp the surface wave. Based on the in-situ x-ray imaging observation, the surface wave is fully damped after adding TiC nanoparticles, compared with only 56% damping without nanoparticles during LPBF of Al6061. Our in-depth in-situ x-ray imaging analysis and viscosity measurement enable us to identify that nanoparticle-induced increase of viscosity causes the fully damping of the surface wave by (1) increasing the internal fluid friction for more efficient wave amplitude reduction, (2) controlling the melt flow to increase the surface wave number, (3) controlling the melt flow to increase the wave damping time. Furthermore, we also quantified the relative contributions of increasing fluid friction, increasing wave number, and increasing damping time to wave damping, which account for 61%, 25%, and 14%, respectively. Furthermore, our research provides the mechanisms and potential method to address the surface finish challenge in laser metal AM processes.
The wave bearing software suite is a MALTA application that computes bearing properties for user-specified wave bearing conditions, as well as plain journal bearings. Wave bearings are fluid film journal bearings with multi-lobed wave patterns around the circumference of the bearing surface. In this software suite, the dynamic coefficients are outputted in a way for easy implementation in a finite element model used in rotor dynamics analysis. The software has a graphical user interface (GUI) for inputting bearing geometry parameters, and uses MATLAB s structure interface for ease of interpreting data. This innovation was developed to provide the stiffness and damping components of wave bearing impedances. The computational method for computing bearing coefficients was originally designed for plain journal bearings and tilting pad bearings. Modifications to include a wave bearing profile consisted of changing the film thickness profile given by an equation, and writing an algorithm to locate the integration limits for each fluid region. Careful consideration was needed to implement the correct integration limits while computing the dynamic coefficients, depending on the form of the input/output variables specified in the algorithm.
The instability of liquid and gas interface can be induced by the pressure of longitudinal and lateral accelerations, vehicle vibration, and rotational fields of spacecraft in a microgravity environment. Characteristics of slosh waves excited by the restoring force field of gravity jitters have been investigated. Results show that lower frequency gravity jitters excite slosh waves with higher ratio of maximum amplitude to wave length than that of the slosh waves generated by the higher frequency gravity jitters.
As intense, initially sinusoidal waves propagate in fluids, shocks form and excess attenuation of the wave occurs. Data are presented indicating that shock formation is not necessary for the occurrence of excess attenuation in nonlinear, lossy media, i.e., air-saturated, porous materials. An empirical equation is used to describe the excess attenuation of intense sinusoids in porous materials. The acoustic nonlinearity of and the excess attenuation in porous materials may be predicted directly from dc flow resistivity data. An empirical relationship is used to relate an acoustic nonlinearity parameter to the fundamental frequency and relative dc nonlinearity of two structurally different materials.
The manipulation and control of drops of liquid and gas bubbles is achieved using high intensity acoustics in the form of and/or acoustic radiation pressure and acoustic streaming. generated by a controlled wave emission from a transducer. Acoustic radiation pressure is used to deploy or dispense drops into a liquid or a gas or bubbles into a liquid at zero or near zero velocity from the discharge end of a needle such as a syringe needle. Acoustic streaming is useful in manipulating the drop or bubble during or after deployment. Deployment and discharge is achieved by focusing the acoustic radiation pressure on the discharge end of the needle, and passing the acoustic waves through the fluid in the needle. through the needle will itself, or coaxially through the fluid medium surrounding the needle. Alternatively, the acoustic waves can be counter-deployed by focusing on the discharge end of the needle from a transducer axially aligned with the needle, but at a position opposite the needle, to prevent premature deployment of the drop or bubble. The acoustic radiation pressure can also be used for detecting the presence or absence of a drop or a bubble at the tip of a needle or for sensing various physical characteristics of the drop or bubble such as size or density.
Acoustic approaches to OLM are based on analyzing changes in various forms of pressure waves propagating in solids, fluids or gases. These pressure waves can vary in frequency content from infrasound (seismic events) to the megahertz region (acoustic emissions). A wide variety of commercially available pressure or stain sensing devices are used to make acoustic measurements. These sensors differ in the transduction mechanism used to convert the pressure or strain signal to an electrical output, the sensitivity, dynamic range, bandwidth, directional characteristics, and physical size. All acoustic sensors must be integrated with signal conditioning electronics to convert the sensors’ analog output to discrete digital signals that can then be further analyzed for OLM. Ultimately, the sensing properties listed above will be a function of the sensor transduction mechanism, the sensor design and the conditioning electronics.
A heuristic approach to the derivation of power spectra of wave motion is described and applied to capillary waves. The case of gravity waves studied earlier is briefly reviewed. In contract to the previous studies, the nonlinearity of the wave motion is not required to be small, and the mean number of resonantly interacting wave harmonics is not limited to a smallest possible number (which is 4 for gravity waves on a deep fluid and 3 for capillary waves). The main external parameter of the problem is the input flux Q of the wave energy related to the mean wind velocity. Depending on its value, wave spectra take various forms---from that corresponding to the weak-turbulence limit to that corresponding to the saturated (Phillips') wave spectra...
The two-fluid plasma equations are used to model the interaction of hydromagnetic waves (HMWs) in a magnetic plasma with lower-hybrid waves (LHWs) propagating perpendicular to the magnetic field. The derivation of the governing equations is given in detail, and numerical results are presented in extensive graphs. It is shown that, when the angle between the HMW and LHW propagation directions is small, the HMWs can be excited, with the energy propagating nearly parallel to the LHW direction. The implications of these findings for the geomagnetic tail are briefly discussed.
Most computational fluid dynamics (CFD) schemes are not adequately accurate for solving aeroacoustics problems, which have wave amplitudes several orders of magnitude smaller yet with frequencies larger than the flow field variations generating the sound. Hence, a computational aeroacoustics (CAA) algorithm should have minimal dispersion and dissipation features. A dispersion relation preserving (DRP) scheme is, therefore, applied to solve the linearized Euler equations in order to simulate the propagation of three types of waves, namely: acoustic, vorticity, and entropy waves. The scheme is derived using an optimization procedure to ensure that the numerical derivatives preserve the wave number and angular frequency of the partial differential equations being discretized. Consequently, simulated waves propagate with the correct wave speeds and exhibit their appropriate properties. A set of radiation and outflow boundary conditions, compatible with the DRP scheme and derived from the asymptotic solutions of the governing equations, are also implemented. Numerical simulations are performed to test the effectiveness of the DRP scheme and its boundary conditions. The computed solutions are shown to agree favorably with the exact solutions. The major restriction appears to be that the dispersion relations can be preserved only for waves with wave lengths longer than four or five spacings. The boundary conditions are found to be transparent to the outgoing disturbances. However, when the disturbance source is placed closer to a boundary, small acoustic reflections start appearing. CAA generates enormous amounts of temporal data which needs to be reduced to understand the physical problem being simulated. Spectral analysis is one approach that helps us in extracting information which often can not be easily interpreted in the time domain. Thus, three different methods for the spectral analysis of numerically generated aeroacoustic data are studied. First, the capabilities of two traditional methods for spectral analysis, namely, the Blackman-Tukey method and periodogram method, are compared in estimating the spectra of a simple-periodic process. The periodogram is then applied to analyze transitory-deterministic processes. Finally, these two methods are compared with a more recent method, referred as the Weighted-Overlapped-Segment-Averaging (WOSA) method, in estimating the spectra of a chaotic (random-like) process. From the demonstrative case for the spectral analyses of data generated by simple-periodic process, the periodogram method is found to give a better estimate of the steep-sloped spectra than the Blackman-Tukey method. Also, for this problem, the Hanning window is found to perform better with the periodogram method than with the Blackman-Tukey method. Finally, for the spectral analysis of data generated by the chaotic process, the periodogram method does not perform well, whereas, the WOSA and Blackman-Tukey methods give equivalently good results.
Terrestrial laboratory experiments studying various fluid dynamical processes are constrained, by being in an Earth laboratory, to have a gravitational body force which is uniform and unidirectional. Therefore fluid free-surfaces are horizontal and flat. Such free surfaces must have a vertical solid boundary to keep the fluid from spreading horizontally along a gravitational potential surface. In atmospheric, oceanic, or stellar fluid flows that have a horizontal scale of about one-tenth the body radius or larger, sphericity is important in the dynamics. Further, fluids in spherical geometry can cover an entire domain without any sidewall effects, i.e. have truly periodic boundary conditions. We describe spherical body-force laboratory experiments using ferrofluid. Ferrofluids are dilute suspensions of magnetic dipoles, for example magnetite particles of order 10 nm diameter, suspended in a carrier fluid. Ferrofluids are subject to an additional body force in the presence of an applied magnetic field gradient. We use this body force to conduct laboratory experiments in spherical geometry. The present study is a laboratory technique improvement. The apparatus is cylindrically axisymmetric. A cylindrical ceramic magnet is embedded in a smooth, solid, spherical PVC ball. The geopotential field and its gradient, the body force, were made nearly spherical by careful choice of magnet height-to-diameter ratio and magnet size relative to the PVC ball size. Terrestrial gravity is eliminated from the dynamics by immersing the "planet" and its ferrofluid "ocean" in an immiscible silicone oil/freon mixture of the same density. Thus the earth gravity is removed from the dynamics of the ferrofluid/oil interface and the only dynamically active force there is the radial magnetic gravity. The entire apparatus can rotate, and waves are forced on the ferrofluid surface by exterior magnets. The biggest improvement in technique is in the wave visualization. Fluorescing dye is added to the oil/freon mixture and an argon ion laser generates a horizontal light that can be scanned vertically. Viewed from above, the experiment is a black circle with wave deformations surrounded by a light background. A contour of the image intensity at any light sheet position gives the surface of the ferrofluid "ocean" at that "latitude". Radial displacements of the waves as a function of longitude are obtained by subtracting the contour line positions from a no-motion contour at that laser sheet latitude. The experiments are run by traversing the forcing magnet with the laser sheet height fixed and images are frame grabbed to obtain a time-series at one latitude. The experiment is then re-run with another laser-sheet height to generate a full picture of the three-dimensional wave structure in the upper hemisphere of the ball as a function of time. We concentrate here on results of laboratory studies of waves that are important in Earth's atmosphere and especially the ocean. To get oceanic scaling in the laboratory, the experiment must rotate rapidly (4-second rotation period) so that the wave speed is slow compared to the planetary rotation speed as in the ocean. In the Pacific Ocean, eastward propagating Kelvin waves eventually run into the South American coast. Theory predicts that some of the wave energy should scatter into coastal-trapped Kelvin waves that propagate north and south along the coast. Some of this coastal wave energy might then scatter into mid-latitude Rossby waves that propagate back westward. Satellite observations of the Pacific Ocean sea-surface temperature and height seem to show signatures of westward propagating mid-latitude Rossby waves, 5 to 10 years after the 1982-83 El Nino. The observational data is difficult to interpret unambiguously owing to the large range of motions that fill the ocean at shorter timescales. This series of reflections giving eastward, north- ward, and then westward traveling waves is observed cleanly in the laboratory experiments, confirming the theoretical expectations.