scholarly journals Measurements of the Second‐Harmonic Component of a Plane, Finite‐Amplitude Wave

1963 ◽  
Vol 35 (11) ◽  
pp. 1894-1894
Author(s):  
William W. Lester
Keyword(s):  
Second Harmonic ◽  
Harmonic Component ◽  
Finite Amplitude ◽  
Amplitude Wave

scholarly journals On the stability of the boundary layer at the bottom of propagating surface waves

2021 ◽  
Vol 928 ◽  
Author(s):  
Paolo Blondeaux ◽  
Jan Oscar Pralits ◽  
Giovanna Vittori
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Second Harmonic ◽  
Harmonic Component ◽  
Threshold Value ◽  
Finite Amplitude ◽  
Turbulent Regime ◽  
Laminar Regime ◽  
Steady Streaming ◽  
The Stability

This study contributes to an improved understanding of the stability of the boundary layer generated at the bottom of a propagating surface wave of small but finite amplitude such that both a second harmonic component and a steady streaming component, which are superimposed on the main oscillatory flow, assume significant values. A linear stability analysis of the laminar flow is made to determine the conditions leading to transition and turbulence appearance. The Reynolds number of the phenomenon is assumed to be large and a ‘momentary’ criterion of stability is used. The results show that, at a given location, the laminar regime becomes unstable when the flow close to the bottom reverses its direction from the onshore to the offshore direction and the Reynolds number exceeds a first critical value $R_{\delta ,c1}$ . However, close to the critical condition, the flow is expected to relaminarize during the other phases of the cycle. Only when the Reynolds number is increased does turbulence tend to appear also after the passage of the wave trough when the flow close to the bottom reverses from the offshore to the onshore direction. When the Reynolds number is further increased and becomes larger than a second ‘threshold’ value, the growth rate of the perturbations becomes positive over the entire wave period. The obtained results suggest the existence of four different flow regimes: the laminar regime, the disturbed laminar regime, the intermittently turbulent regime and the fully developed turbulent regime.

Finite-Amplitude Equilibration of Baroclinic Waves on a Jet

2010 ◽  
Vol 67 (2) ◽  
pp. 434-451 ◽  
Author(s):  
Sukyoung Lee
Keyword(s):  
Wave Breaking ◽  
Lower Layer ◽  
Finite Amplitude ◽  
Primary Role ◽  
Ekman Pumping ◽  
Amplitude Wave ◽  
Wave Source ◽  
Model Calculations ◽  
Baroclinic Waves ◽  
Pv Gradient

Abstract A two-layer quasigeostrophic model is used to study the equilibration of baroclinic waves. In this model, if the background flow is relaxed toward a jetlike profile, a finite-amplitude baroclinic wave solution can be realized in both supercritical and subcritical regions of the model’s parameter space. Analyses of the model equations and numerical model calculations indicate that the finite-amplitude wave equilibration hinges on the breaking of Rossby waves before they reach their critical latitude. This “jetward” wave breaking results in an increase in the upper-layer wave generation and a reduction in the vertical phase tilt. This change in the phase tilt has a substantial impact on the Ekman pumping, as it weakens the damping on the lower-layer wave for some parameter settings and enables the Ekman pumping to serve as a source of wave growth at other settings. Together, these processes can account for the O(1)-amplitude wave equilibration. From a potential vorticity (PV) perspective, the wave breaking reduces the meridional scale of the upper-layer eddy PV flux, which destabilizes the mean flow. This is followed by a strengthening of the lower-layer eddy PV flux, which weakens the lower-layer PV gradient and constrains the growth of the lower-layer eddy PV. The same jetward wave breaking focuses the upper-layer PV flux toward the jet center where the upper-layer PV gradient is greatest. This results in an intensification of the upper-layer eddy PV relative to lower-layer eddy PV. Because of this large ratio, the upper-layer eddy PV plays the primary role in inducing the upper- and lower-layer eddy streamfunction fields, decreasing the vertical phase tilt. As a result, the Ekman pumping on the eddies is weakened, and for some parameter settings the Ekman pumping can even act as a wave source, contributing toward O(1)-amplitude wave equilibration. By reducing the horizontal shear of the zonal wind, the same wave breaking process weakens the barotropic decay, which also contributes to the wave amplification.

On resonant over-reflexion of internal gravity waves from a Helmholtz velocity profile

1979 ◽  
Vol 90 (1) ◽  
pp. 161-178 ◽  
Author(s):  
R. H. J. Grimshaw
Keyword(s):  
Velocity Profile ◽  
Gravity Waves ◽  
Second Harmonic ◽  
Phase Speed ◽  
Internal Gravity Waves ◽  
Finite Amplitude ◽  
Weakly Nonlinear ◽  
Velocity Discontinuity ◽  
Interface Displacement ◽  
Boussinesq Fluid

A Helmholtz velocity profile with velocity discontinuity 2U is embedded in an infinite continuously stratified Boussinesq fluid with constant Brunt—Väisälä frequency N. Linear theory shows that this system can support resonant over-reflexion, i.e. the existence of neutral modes consisting of outgoing internal gravity waves, whenever the horizontal wavenumber is less than N/2½U. This paper examines the weakly nonlinear theory of these modes. An equation governing the evolution of the amplitude of the interface displacement is derived. The time scale for this evolution is α−2, where α is a measure of the magnitude of the interface displacement, which is excited by an incident wave of magnitude O(α3). It is shown that the mode which is symmetrical with respect to the interface (and has a horizontal phase speed equal to the mean of the basic velocity discontinuity) remains neutral, with a finite amplitude wave on the interface. However, the other modes, which are not symmetrical with respect to the interface, become unstable owing to the self-interaction of the primary mode with its second harmonic. The interface displacement develops a singularity in a finite time.

scholarly journals Control Strategy Based on Arm-Level Control for Output and Circulating Current of MMC in Stationary Reference Frame

Energies ◽  
2021 ◽  
Vol 14 (14) ◽  
pp. 4160
Author(s):  
Waqar Uddin ◽  
Tiago D. C. Busarello ◽  
Kamran Zeb ◽  
Muhammad Adil Khan ◽  
Anil Kumar Yedluri ◽  
...  
Keyword(s):  
Reference Frame ◽  
Control Method ◽  
Second Harmonic ◽  
Harmonic Component ◽  
Effective Control ◽  
Level Control ◽  
Circulating Current ◽  
Stationary Reference Frame ◽  
Pr Controller ◽  
Dc Component

This paper proposed a control method for output and circulating currents of modular multilevel converter (MMC). The output and circulating current are controlled with the help of arm currents, which contain DC, fundamental frequency, and double frequency components. The arm current is transformed into a stationary reference frame (SRF) to isolate the DC and AC components. The AC component is controlled with a conventional proportional resonant (PR) controller, while the DC component is controlled by a proportional controller. The effective control of the upper arm and lower arm ultimately controls the output current so that it delivers the required power to the grid and circulating current in such a way that the second harmonic component is completely vanished leaving behind only the DC component. Comparative results of leg-level control based on PR controller are included in the paper to show the effectiveness of the proposed control scheme. A three-phase, five-level MMC is developed in MATLAB/Simulink to verify the effectiveness of the proposed control method.

Local Finite-Amplitude Wave Activity as a Diagnostic for Rossby Wave Packets

2018 ◽  
Vol 146 (12) ◽  
pp. 4099-4114 ◽  
Author(s):  
Paolo Ghinassi ◽  
Georgios Fragkoulidis ◽  
Volkmar Wirth
Keyword(s):  
Rossby Wave ◽  
Model Simulation ◽  
Wave Packets ◽  
Meridional Wind ◽  
Finite Amplitude ◽  
Wave Activity ◽  
Amplitude Wave ◽  
High Impact Weather ◽  
Finite Amplitude Wave Activity ◽  
Isentropic Coordinates

AbstractUpper-tropospheric Rossby wave packets (RWPs) are important dynamical features, because they are often associated with weather systems and sometimes act as precursors to high-impact weather. The present work introduces a novel diagnostic to identify RWPs and to quantify their amplitude. It is based on the local finite-amplitude wave activity (LWA) of Huang and Nakamura, which is generalized to the primitive equations in isentropic coordinates. The new diagnostic is applied to a specific episode containing large-amplitude RWPs and compared with a more traditional diagnostic based on the envelope of the meridional wind. In this case, LWA provides a more coherent picture of the RWPs and their zonal propagation. This difference in performance is demonstrated more explicitly in the framework of an idealized barotropic model simulation, where LWA is able to follow an RWP into its fully nonlinear stage, including cutoff formation and wave breaking, while the envelope diagnostic yields reduced amplitudes in such situations.

A more general model equation of nonlinear Rayleigh waves and their quasilinear solutions

2016 ◽  
Vol 30 (08) ◽  
pp. 1650096 ◽  
Author(s):  
Shuzeng Zhang ◽  
Xiongbing Li ◽  
Hyunjo Jeong
Keyword(s):  
Rayleigh Waves ◽  
General Equation ◽  
Wave Motion ◽  
Numerical Solutions ◽  
Second Harmonic ◽  
Approximate Equation ◽  
Finite Amplitude ◽  
Sound Beam ◽  
Quasilinear Theory ◽  
Sound Beams

A more general two-dimensional wave motion equation with consideration of attenuation and nonlinearity is proposed to describe propagating nonlinear Rayleigh waves of finite amplitude. Based on the quasilinear theory, the numerical solutions for the sound beams of fundamental and second harmonic waves are constructed with Green’s function method. Compared with solutions from the parabolic approximate equation, results from the general equation have more accuracy in both the near distance of the propagation direction and the far distance of the transverse direction, as quasiplane waves are used and non-paraxial Green’s functions are obtained. It is more effective to obtain the nonlinear Rayleigh sound beam distributions accurately with the proposed general equation and solutions. Brief consideration is given to the measurement of nonlinear parameter using nonlinear Rayleigh waves.

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