Wake Wave Research Articles

Investigation of internal wave wakes generated by a submerged body in a stratified flow

Internal waves in the ocean with stratified structure are essential: natural internal waves for the untangling of physical and environmental processes in oceanography and internal waves generated by a submerged moving body for understanding the near-field flow structures and wave patterns for detection. The latter in a stratified flow with a pycnocline presented are investigated numerically in the present paper. Systematic analyses on the influences of different hydrodynamic parameters, including the Froude number (Fr), the Reynolds number (Re), the thickness of the pycnocline (ΔL), and the relative position of the submerged body (Δd), on internal wave wakes, are performed. A variation trend diagram of wake angle and wave amplitude for different parameters is obtained, showing the order of influence: Fr > ΔL > Δd > Re. For two key parameters, Fr and ΔL, scalings of wake angle variation are found. Wake angle shows a − 1 power-law dependence on Fr and the same order power law on ΔL in a critical range. In addition, vortex structures and turbulent kinetic energy distributions in the wakes are explored by comparing to the homogeneous case.

On the dynamics of the eradication of a warm core mesoscale eddy after the passage of Hurricane Irma (2017)

Mesoscale oceanic eddies are known to influence air-sea interactions during tropical cyclone (TC) passage by either hindering or sustaining air-sea fluxes into the TC core. However, little is known as to how TCs alter the dynamical structure of such eddies during and after TC passage. Through simulations of Hurricane Irma (2017) using the Navy’s Coupled Ocean Atmospheric Mesoscale Prediction Scheme for Tropical Cyclones, it is found that a simulated mesoscale warm core eddy (WCE) located to the right of the model track disappeared shortly after the TC had passed over it. To further explore this phenomena, time series of ocean kinetic energy, available potential energy (APE), a vorticity budget, and a potential vorticity (PV) budget are examined to understand how TC-induced upper ocean currents influenced the eddy disappearance. Time series of APE within the model-simulated eddy show APE reaching a minimum as the circulation of the eddy disappeared in the model field and positive vorticity, dominated by vertical vorticity advection, became a maximum approximately 6 h after TC passage. These results were confirmed by the PV budget. The succession of subsurface vorticity changes suggest that the WCE was eradicated by a near-inertial wave wake that occurred earlier than expected. As found in a prior study, the early-onset of a near-inertial wake occurs when the model simulated TC with a small radius of maximum winds interacts with the subsurface ocean current field. The findings are important with regards to TC forecasting because the accurate representation and placement of eddies in the model field is necessary to correctly predict the coupled air-sea response during TC passage and for subsequent TCs with similar tracks. Such feedbacks from TCs can also have near-term and long-term influence on the prediction of air-sea interaction in the local and regional marine environment.

Free surface effects and the utility of a skim plate for experiments in a water towing tank at steady and unsteady model velocity

A towing tank is utilized to investigate the flow field around a two-dimensional submerged foil model operating near the free surface. Free surface effects are analyzed for steady and unsteady model velocity. The model’s submergence depth and angle of attack are varied. Tests are conducted for the model facing upside-up and upside-down. The surface deflection is recorded and the experimental results are utilized to validate an analytic model that is deployed to predict wake wave patterns at arbitrary model velocity. The flow mechanism leading to load alterations when the foil is in the vicinity of the free surface is explored in detail using experimental and analytic results. The imposed wave-induced velocity perturbations alter the effective angle of attack experienced by the foil. Flow separation is delayed when the model is facing upside-up and promoted when facing upside-down. For test cases with unsteady sinusoidal model velocity, forward traveling waves are generated, leading to a time-varying change in the inflow condition of the submerged foil. Increasing the model’s submergence depth alleviates free surface effects. A skim plate is installed in-between the free surface and model. It shows similar wave alleviating effects as obtained when increasing the model submergence depth by locally blocking wave-induced velocities. The skim plate position is varied in the longitudinal direction to determine its most advantageous position. Surface wave effects at unsteady model velocity are alleviated most effectively when the skim plate protrudes upstream of the model.Graphical abstract

Spectrum characteristics for internal wave signals of a self-propelled model

Internal waves induced by an underwater self-propelled body expose its existence by changing the sea surface roughness. This study employs short-time Fourier transform to perform the time–frequency analysis on the internal wave signal captured in the experiments. Some key characteristics of the underwater self-propelled body are obtained through the spectrum analysis of the internal wave wake signal. Moreover, the influence of the interaction between the momentums induced by the propulsion and drag force is discussed. The results show that the action of the self-propelled body has varying degrees of influence on the symmetry and spatial distribution of the spectrum characteristics of the signal.

Integrating a ponderomotive guiding center algorithm into a quasi-static particle-in-cell code based on azimuthal mode decomposition

High fidelity modeling of plasma based acceleration (PBA) requires the use of three dimensional, fully nonlinear, and kinetic descriptions based on the particle-in-cell (PIC) method. In PBA an intense particle beam or laser (driver) propagates through a tenuous plasma whereby it excites a plasma wave wake. Three-dimensional PIC algorithms based on the quasi-static approximation (QSA) have been successfully applied to efficiently model the interaction between relativistic charged particle beams and plasma. In a QSA PIC algorithm, the plasma response to a charged particle beam or laser driver is calculated based on forces from the driver and self-consistent forces from the QSA form of Maxwell's equations. These fields are then used to advance the charged particle beam or laser forward by a large time step. Since the time step is not limited by the regular Courant-Friedrichs-Lewy (CFL) condition that constrains a standard 3D fully electromagnetic PIC code, a 3D QSA PIC code can achieve orders of magnitude speedup in performance. Recently, a new hybrid QSA PIC algorithm that combines another speedup technique known as an azimuthal Fourier decomposition has been proposed and implemented. This hybrid algorithm decomposes the electromagnetic fields, charge and current density into azimuthal harmonics and only the Fourier coefficients need to be updated, which can reduce the algorithmic complexity of a 3D code to that of a 2D code. Modeling the laser-plasma interaction in a full 3D electromagnetic PIC algorithm is very computationally expensive due the enormous disparity of physical scales to be resolved. In the QSA the laser is modeled using the ponderomotive guiding center (PGC) approach. We describe how to implement a PGC algorithm compatible for the QSA PIC algorithms based on the azimuthal mode expansion. This algorithm permits time steps orders of magnitude larger than the cell size and it can be asynchronously parallelized. Details on how this is implemented into the QSA PIC code that utilizes an azimuthal mode expansion, QPAD, are also described. Benchmarks and comparisons between a fully 3D explicit PIC code (OSIRIS), as well as a few examples related to laser wakefield acceleration, are presented.

EXCITATION OF WAKE FIELDS BY A RELATIVISTIC ELECTRON BUNCH IN A POLAR SEMICONDUCTOR WAVEGUIDE

The process of wake fields excitation by a relativistic electron bunch in polar semiconductors is studied. Cylindrical semiconductor waveguide, in which relativistic electron bunch moves along axis, is considered. It is shown that the excited wake field in the terahertz and infrared frequency ranges consists of the field of longitudinal HF and LF hybrid plasmon-phonon oscillations and the field of the HF and LF transverse polaritons, which are a set of eigen electromagnetic waves of the polar semiconductor waveguide. The spatio-temporal structure of the total excited wake field is obtained, the intensity of the excited wake waves is determined.

Experimental study on the flow patterns and acoustic characteristics of surface piercing cylinders

The hydrodynamic characteristics and noise generated from flow around surface-piercing cylinders are a critical issue for many engineering applications. This article presents an experimental study of flow around a surface-piercing cylinder at Froude number 0.87 to 1.73. The bow wave height, wake pattern, air ventilation, and noise generated have been investigated extensively for different cylinders design such as circular and elliptical cylinders. The diameter of the circular and elliptical cylinders is 40 mm, and 53 mm, respectively. An image processing technique is applied to visualize the air entrainment and calculate the air volume fraction underwater. Due to the lack of experimental published data on the noise around the surface-piercing cylinder, a part of the results discussed the acoustic measurements. A hydrophone is used to study acoustic measurements. The result reveals that the wake region and the bow wave increases significantly as the Froude number increase, accompanied by an air cavity and vortex shedding region behind the circular cylinder, while there was less increment in the bow wave height and wake region as well as there was no air cavity for the case of an elliptical cylinder. The processed image indicated that the air volume fraction for the case of a circular cylinder is four-time higher compared to the elliptical cylinder at Froude number 1.73. Moreover, the results observed that the sound pressure level (SPL) increased as the Froude number increased in all frequency ranges. The sound pressure level behind the circular cylinder increased significantly in the frequency range <1000 Hz, while there was no increment in the SPL behind the elliptical cylinder. The major noise source is due to the air-ventilated cavity behind the cylinder. The outcome results of this study are an important reference for submarine mast designers and some other engineering applications.

Study on influencing factors of trailing edge flow characteristics of transonic micro turbine rotor

In order to meet the needs of the development of high-performance micro-engine, the micro-turbine is faced with the technical challenge of high-load and transonic flow. At present, the flow characteristics and loss mechanism of high-load micro-impeller are not clear. In this paper, the flow characteristics of high-load micro-turbine rotor are studied. The results show that the loss in rotor trailing edge is the main factor that affect the operation of the micro transonic turbine, and the key to reduce the loss is to reduce the wake diffusion range and the Mach number in front of the extended shock wave. By adjusting the local curvature of the front in front of the incident point of the back-extension wave in the throat of the suction surface, the convergent-divergent ratio is in the range of 1.04 ~ 1.08. Meanwhile, the Mach number of wave front can be reduced by 3.4% and the reflection of trailing edge inward extension can be effectively suppressed, and the total rotor pressure loss coefficient can be reduced by 14.1% at most. The thickness has an important effect on the wave strength and wake loss in the trailing edge. When the relative thickness of the trailing edge decreases by 50%, the maximum Mach number on the suction surface decreases by 7.8%, the turbine stage efficiency increases by 1.92%, and the relative thickness of trailing edge is 0.124~0.185, the studied micro-transonic turbine performs better.

Investigation of the Way of Phase Synchronization of a Self-Injected Bunch and an Accelerating Wakefield in Solid-State Plasma

The electron acceleration, in a laser wakefield accelerator, controlled through plasma density inhomogeneity is studied on a basis of 2.5-dimensional particle-in-cell simulation. The acceleration requires a concordance of the density scale length and shift of the accelerated electron bunch relative to wake bubble during electron acceleration. This paper considers the excitation of a wakefield in plasma with a density equal to the density of free electrons in metals, solid-state plasma (the original idea of Prof. T. Tajima), in the context of studying the wakefield process. As is known in the wake process, as the wake bubble moves through the plasma, the self-injected electron bunch shifts along the wake bubble. Then, the self-injected bunch falls into the phase of deceleration of the wake wave. In this paper, support of the acceleration process by maintaining the position of the self-injected electron bunch using an inhomogeneous plasma is proposed. It is confirmed that the method of maintaining phase synchronization proposed in the article by using a nonuniform plasma leads to an increase in the accelerating gradient and energy of the accelerated electron bunch in comparison with the case of self-injection and acceleration in a homogeneous plasma.

Wake waves of a planing boat: An experimental model

The wake waves generated by the steady movement of a planing hull are analyzed by means of towing tank tests. Two sets of waves, including divergent and transverse waves, are identified and then analyzed. The wave period of the divergent waves is seen to decrease by the increase in speed of the vessel. These waves are seen to damp temporally. The mechanisms that lead to damping of the divergent wave were found to depend on the wave orbital Reynolds number in semi-planing regime, though that of in-planing regime is a function of the Reynolds number of the boat. The wake angle is seen to decrease with the increase in Froude number, the rate of which becomes relatively large in-planing regime. Transverse waves are captured through measurements, and it is shown that while their period is longer than those of the divergent waves, they are not noticeably damped. Throughout the spectral analysis, it is demonstrated that divergent waves reach a higher level of nonlinearity by the increase in Froude number and, hence, the wave energy is distributed over a boarder range of frequency. The height of the transverse wave is observed to become lower by the increase in speed, but as the towing speed increases, the probability density function curves of surface elevation deviate more and more from the Gaussian distribution.

WAKE WASH OF A FAST SMALL BOAT IN RESTRICTED WATERS: MODEL TESTS AND FULL-SCALE MEASUREMENTS

This paper presents the model testing of an 8.23m boat with hard chine planning hull generated waves at the Kilim recreational park. Wake is considered one of the main causes of riverbank erosion due to the energy carried by waves hitting the riverbank. Initially, ship particulars were measured from actual boats to generate a hull form using MAXSURF software. A lines plan was then generated to fabricate the model using fibreglass. Experiments were conducted in the National Hydraulic Research Institute of Malaysia (NAHRIM) at various speeds at a constant operating draft. The wave patterns generated by the modelled boats at different speeds were recorded for analysis. Wave attenuation for deep water conditions was studied and it was found that the wave exponent, n ranged from -0.36 to -0.75 for all depth Froude number (Fnh) condition. Wave decay analysis was used to estimate wave height for defined water depth. For 11 people with an average mass of 65 kg on board, the produced wave height was greater than the permissible wave wake height of 75 mm. The generated energy exceeded 60 Joules/m for nearly all measured speeds. A boat speed of less than 5 knots was suggested for boats loaded with the maximum passenger limit of 11 people. Other recommendations were made to minimize the wave wake height produced by the modelled boat.

Generation of topologically complex three-dimensional electron beams in a plasma photocathode

Laser-triggered ionization injection is a promising way of generating controllable high-quality electrons in plasma-based acceleration. We show that ionization injection of electrons into a fully nonlinear plasma wave wake using a laser pulse comprising of one or more Laguerre-Gaussian modes with combinations of spin and orbital angular momentum can generate exotic three-dimensional spatial distributions of high-quality relativistic electrons. The phase dependent residual momenta and initial positions of the ionized electrons are encoded into their final phase space distributions, leading to complex spatiotemporal structures. The structures are formed as a result of the transverse (betatron) and longitudinal (phase slippage and energy gain) dynamics of the electrons in the wake immediately after the electrons are injected. Theoretical analysis and three-dimensional simulations verify this mapping process leads to the generation of these complex topological beams. These beams may trigger novel beam-plasma interactions as well as produce coherent radiation with orbital angular momentum when sent through a resonant undulator.

Decoupling wind–wave–wake interactions in a fixed-bottom offshore wind turbine

The interest and benefits of offshore wind energy have also brought along legitimate challenges. In the golden age of renewables, offshore wind-energy holds the most potential for growth, but the burgeoning benefits of offshore energy are also entangled in dynamics not fully understood, such as the dynamic coupling of the atmospheric boundary layer, the wind-turbine generated wake, and the surface waves. This study establishes the first experimental turbulent-interaction between the traditionally distinct fields of airflow-dynamics above the air–sea interface and the characterization of wind-turbine wakes. The study details a non-trivial experimental setup combining a wave tank, wind tunnel, and scaled fixed-bottom wind turbine. Particle image velocimetry (PIV) was performed on three successive image planes to visualize wind–wake, wind–wave, and wave–wake interaction far downstream of the turbine. The wave phase-dependent dynamics of the turbine wake on the passing ocean-wave profile and location are outlined. The velocity and stress profiles showed a horizontal wake-pumping motion along with vertical wake-lifting of the offshore turbulent wake. The data were decomposed into incremental wave-phases revealing localized and predictable velocity maxima, stress maxima, and wake modulation that is normally obscured by a time-averaged mean. The results quantified wake pumping and meandering, as well as the Reynolds stress and wave-induced phase-averaged fluctuations. There is a phase-dependent oscillation in both the horizontal (streamwise) direction, as well as a vertical displacement of the wake. The shear stress and advection terms show this imbalance along the vertical direction of the turbine. The results illustrate a more complete picture of offshore wind-energy dynamics, which have implications for insidious mechanical issues, design optimization and/or control strategies.

SUBCRITICAL WAVE WAKE UNSTEADINESS

Vessel wave wake in deep water is well understood, shallow water less so, specifically the effect of restricted water. This operational zone is highly dynamic and non-linear in nature, thus being worthy of closer examination. The paper reviews the primary mechanisms for unsteadiness in wave wake: starting acceleration and soliton generation. A comprehensive set of experiments was conducted using an NPL catamaran hull form to investigate unsteadiness in both wave height and wave angle. The results show that the unsteadiness was primarily due to soliton generation, and that blockage has a significant effect. As a result, additional metrics, aimed at defining shallow water effects in the transcritical region, are proposed.

VESSEL WAVE WAKE CHARACTERISATION USING WAVELET ANALYSIS

&#x0D; &#x0D; &#x0D; This work focuses on characterising vessel wave wake (wash) using wavelet analysis when a vessel is operating in the sub-critical and critical zone. Such characterisation complements other wash characteristics: Froude depth number, bow wave angle, solitons and decay coefficient. The examination of experimental results indicates that differences in characteristics with respect to water depth, Froude depth number, vessel displacement, hull form and soliton generation can be identified through wavelet analysis. The results demonstrate “proof of concept” that wavelet analysis is a powerful tool for characterising vessel wash and captures the effects of key operational and vessel changes.&#x0D; &#x0D; &#x0D;

ACCELERATING OF THE ELECTRONS OF ELECTRON BUNCHES IN A WAVEGUIDE LOADED DIELECTRIC STRUCTURE

The paper presents some results of experimental studies of the excitation of wake fields and the acceleration of electrons in waveguide-dielectric structures (DS) upon injection of a sequence of electron bunches into them. Exper-iments have shown an increase in the amplitude of the wake wave and the acceleration of a small fraction of elec-trons when the wavelength of the excited field is equal to the doubled bunch length. A simple physical model of the observed phenomenon is given. Also, the paper proposes a method for accelerating a part of each electron bunch in the steady-state mode of the resonator dielectric structure. Some of the electrons are “cut out” by the collimator and enter the accelerating phase of the previously excited wake wave. The wave is displaced due to the difference in the distances traveled by the wave and the accelerated part of the electrons.

Electromagnetic Scattering Model for Far Wakes of Ship with Wind Waves on Sea Surface

A comprehensive electromagnetic scattering model for ship wakes on the sea surface is proposed to study the synthetic aperture radar (SAR) imagery for ship wakes. Our model considers a coupling of various wave systems, including Kelvin wake, turbulent wake, and the ocean ambient waves induced by the local wind. The fluid–structure coupling between the ship and the water surface is considered using the Reynolds–averaged Navier–Stokes (RANS) equation, and the wave–current effect between the ship wake and wind waves is considered using the wave modulation model. The scattering model can better describe the interaction of the ship wakes on sea surface and illustrates well the features of the ship wakes with local wind waves in SAR images.

Huygens' Principle geometric derivation and elimination of the wake and backward wave

Huygens' Principle (1678) implies that every point on a wave front serves as a source of secondary wavelets, and the new wave front is the tangential surface to all the secondary wavelets. But two problems arise: portions of wavelets that exist outside of the new wave front combine to form a wake. Also there are two tangential surfaces so wave fronts are propagated in both the forward and backward directions. These problems have not previously been resolved by using a geometrical theory with impulsive wavelets that are in harmony with Huygens' geometrical description. Doing so would provide deeper understanding of and greater intuition into wave propagation, in addition to providing a new model for wave propagation analysis. The interpretation, developed here, of Huygens' geometrical construction shows Huygens' Principle to be correct: as for the wake, the Huygens' wavelets disappear when combined except where they contact their common tangent surfaces, the new propagating wave fronts. As for the backward wave, a source propagates both a forward wave and a backward wave when it is stationary, but it propagates only the forward wave front when it is advancing with a speed equal to the propagation speed of the wave fronts.

The propagation and decay of a coastal vortex on a shelf

A coastal eddy is modelled as a barotropic vortex propagating along a coastal shelf. If the vortex speed matches the phase speed of any coastal trapped shelf wave modes, a shelf wave wake is generated leading to a flux of energy from the vortex into the wave field. Using a simple shelf geometry, we determine analytic expressions for the wave wake and the leading-order flux of wave energy. By considering the balance of energy between the vortex and wave field, this energy flux is then used to make analytic predictions for the evolution of the vortex speed and radius under the assumption that the vortex structure remains self-similar. These predictions are examined in the asymptotic limit of small rotation rate and shelf slope and tested against numerical simulations. If the vortex speed does not match the phase speed of any shelf wave, steady vortex solutions are expected to exist. We present a numerical approach for finding these nonlinear solutions and examine the parameter dependence of their structure.

Stopping-power enhancement from discrete particle-wake correlations in high-energy-density plasmas.

Three-dimensional (3D) simulations of electron beams propagating in high-energy-density plasmas using the quasistatic Particle-in-Cell (PIC) code QuickPIC demonstrate a significant increase in stopping power when beam electrons mutually interact via their wakes. Each beam electron excites a plasma wave wake of wavelength ∼2πc/ω_{pe}, where c is the speed of light and ω_{pe} is the background plasma frequency. We show that a discrete collection of electrons undergoes a beam-plasma-like instability caused by mutual particle-wake interactions that causes electrons to bunch in the beam, even for beam densities n_{b} for which fluid theory breaks down. This bunching enhances the beam's stopping power, which we call "correlated stopping," and the effect increases with the "correlation number" N_{b}≡n_{b}(c/ω_{pe})^{3}. For example, a beam of monoenergetic 9.7 MeV electrons with N_{b}=1/8, in a cold background plasma with n_{e}=10^{26}cm^{-3} (450 g cm^{-3} DT), has a stopping power of 2.28±0.04 times the single-electron value, which increases to 1220±5 for N_{b}=64. The beam also experiences transverse filamentation, which eventually limits the stopping enhancement.