Assessment of the Taylor--Lorentz transform for boundary element solutions to wave propagation with mean flow

2017 ◽  
Author(s):  
Simone Mancini ◽  
R. Jeremy Astley ◽  
Gwenael Gabard ◽  
Michel Tournour
Keyword(s):  
Wave Propagation ◽  
Boundary Element ◽  
Mean Flow

scholarly journals Dynamics of Extreme Stratospheric Negative Heat Flux Events in an Idealized Model

2018 ◽  
Vol 75 (10) ◽  
pp. 3521-3540 ◽  
Author(s):  
Etienne Dunn-Sigouin ◽  
Tiffany Shaw
Keyword(s):  
Heat Flux ◽  
Wave Propagation ◽  
Recent Work ◽  
Wave Interaction ◽  
Higher Order ◽  
Negative Events ◽  
Flow Mechanism ◽  
Mean Flow ◽  
Idealized Model

Recent work has shown that extreme stratospheric wave-1 negative heat flux events couple with the troposphere via an anomalous wave-1 signal. Here, a dry dynamical core model is used to investigate the dynamical mechanisms underlying the events. Ensemble spectral nudging experiments are used to isolate the role of specific dynamical components: 1) the wave-1 precursor, 2) the stratospheric zonal-mean flow, and 3) the higher-order wavenumbers. The negative events are partially reproduced when nudging the wave-1 precursor and the zonal-mean flow whereas they are not reproduced when nudging either separately. Nudging the wave-1 precursor and the higher-order wavenumbers reproduces the events, including the evolution of the stratospheric zonal-mean flow. Mechanism denial experiments, whereby one component is fixed to the climatology and others are nudged to the event evolution, suggest higher-order wavenumbers play a role by modifying the zonal-mean flow and through stratospheric wave–wave interaction. Nudging all tropospheric wave precursors (wave-1 and higher-order wavenumbers) confirms they are the source of the stratospheric waves. Nudging all stratospheric waves reproduces the tropospheric wave-1 signal. Taken together, the experiments suggest the events are consistent with downward wave propagation from the stratosphere to the troposphere and highlight the key role of higher-order wavenumbers.

scholarly journals Nonlinear Saturation of Vertically Propagating Rossby Waves

2009 ◽  
Vol 66 (4) ◽  
pp. 915-934 ◽  
Author(s):  
Constantine Giannitsis ◽  
Richard S. Lindzen
Keyword(s):  
Wave Propagation ◽  
Channel Model ◽  
Plane Channel ◽  
Nonlinear Flow ◽  
Computational Domain ◽  
Mean Flow ◽  
Wave Interactions ◽  
Linear Solution ◽  
Wave Growth ◽  
Flow Interactions

Abstract The interaction between vertical Rossby wave propagation and wave breaking is studied in the idealized context of a beta-plane channel model. Considering the problem of propagation through a uniform zonal flow in an exponentially stratified fluid, where linear theory predicts exponential wave growth with height, the question is how wave growth is limited in the nonlinear flow. Using a numerical model, the authors examine the behavior of the flow as the bottom forcing increases through values bound to lead to a breakdown of the linear solution within the computational domain. Focusing on the equilibrium flow obtained for each value of the bottom forcing, an attempt is made to identify the mechanisms involved in limiting wave growth and examine in particular the importance of wave–wave interactions. The authors also examine the case in which forcing is continuously increasing with time so as to enhance effects peculiar to transiency; it does not significantly alter the main results. Wave–mean flow interactions are found to dominate the dynamics even for strong bottom forcing values. Ultimately, it is the modification of the mean flow that is found to limit the vertical penetration of the forced wave, through either increased wave absorption or downward reflection. Linear propagation theory is found to capture the wave structure surprisingly well, even when the total flow is highly deformed. Overall, the numerical results seem to suggest that wave–wave interactions do not have a strong direct effect on the propagating disturbance. Wave–mean flow interactions limit wave growth sufficiently that a strong additional nonlinear enstrophy sink, through downscale cascade, is not necessary. Quantitatively, however, wave–wave interactions, primarily among the lowest wavenumbers, prove important so as to sufficiently accurately determine the basic state and its influence on wave propagation.

A modal boundary element method for axisymmetric acoustic problems in an arbitrary uniform mean flow

2020 ◽  
pp. 1475472X2097838
Author(s):  
Bassem Barhoumi ◽  
Jamel Bessrour
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Singular Integrals ◽  
Acoustic Radiation ◽  
Normal Derivative ◽  
Boundary Integral ◽  
Meridian Plane ◽  
Mean Flow ◽  
Transform Method ◽  
Element Method

This paper presents a new numerical analysis approach based on an improved Modal Boundary Element Method (MBEM) formulation for axisymmetric acoustic radiation and propagation problems in a uniform mean flow of arbitrary direction. It is based on the homogeneous Modal Convected Helmholtz Equation (MCHE) and its convected Green’s kernel using a Fourier transform method. In order to simplify the flow terms, a general modal boundary integral solution is formulated explicitly according to two new operators such as the particular and convected kernels. Through the use of modified operators, the improved MBEM approach with flow takes a convective form of the general MBEM approach and has a similar form of the nonflow MBEM formulation. The reference and reduced Helmholtz Integral Equations (HIEs) are implicitly taken into account a new nonreflecting Sommerfeld condition to solve far field axisymmetric regions in a uniform mean flow. For isolating the singular integrations, the modal convected Green’s kernel and its modified normal derivative are performed partly analytically in terms of Laplace coefficients and partly numerically in terms of Fourier coefficients. These coefficients are computed by recursion schemes and Gauss-Legendre quadrature standard formulae. Specifically, standard forms of the free term and its convected angle resulting from the singular integrals can be expressed only in terms of real angles in meridian plane. To demonstrate the application of the improved MBEM formulation, three exterior acoustic case studies are considered. These verification cases are based on new analytic formulations for axisymmetric acoustic sources, such as axisymmetric monopole, axial and radial dipole sources in the presence of an arbitrary uniform mean flow. Directivity plots obtained using the proposed technique are compared with the analytical results.

scholarly journals Moist Formulations of the Eliassen–Palm Flux and Their Connection to the Surface Westerlies

2017 ◽  
Vol 74 (2) ◽  
pp. 513-530 ◽  
Author(s):  
John G. Dwyer ◽  
Paul A. O’Gorman
Keyword(s):  
Wave Propagation ◽  
Lower Troposphere ◽  
Static Stability ◽  
Reanalysis Data ◽  
Similar Amount ◽  
Mean Flow ◽  
Flux Divergence ◽  
Equivalent Potential ◽  
Subtropical Jet ◽  
Anomalous Region

Abstract The Eliassen–Palm (EP) flux is an important diagnostic for wave propagation and wave–mean flow interaction in the atmosphere. Here, two moist formulations of the EP flux are compared with the traditional dry EP flux, and their links to the surface westerlies are analyzed using reanalysis data and simulations with GCMs. The first moist formulation of the EP flux modifies only the static stability to account for latent heat release by eddies, while the second moist formulation simply replaces all potential temperatures with equivalent potential temperatures. For reanalysis data, the peak upward EP flux in the lower troposphere is farther equatorward and stronger when the moist formulations are used, with greater changes for the second moist formulation. The moist formulations have the advantage of giving a closer relationship over the seasonal cycle between the latitudes of the peak surface westerlies and the peak upward EP flux. In simulations with a comprehensive GCM, the dry and moist upward EP fluxes shift poleward by a similar amount as the climate warms. In simulations over a wider range of climates with an idealized GCM, the surface westerlies can shift both poleward and equatorward with warming, and they are influenced by an anomalous region of dry EP flux divergence near the subtropical jet. Using moist EP fluxes weakens this anomalous divergence in the idealized GCM simulations, and the shifts in the surface westerlies can then be understood through changes in the preference for equatorward or poleward wave propagation.

A theoretical study of viscous effects in peristaltic pumping

1994 ◽  
Vol 279 ◽  
pp. 177-195 ◽  
Author(s):  
Alden M. Provost ◽  
W. H. Schwarz
Keyword(s):  
Wave Propagation ◽  
Pressure Gradient ◽  
Flow Rate ◽  
Mean Flow ◽  
Viscous Effects ◽  
Transverse Waves ◽  
Peristaltic Pumping ◽  
Mean Pressure ◽  
Flow Through ◽  
The Mean

Intuition and previous results suggest that a peristaltic wave tends to drive the mean flow in the direction of wave propagation. New theoretical results indicate that, when the viscosity of the transported fluid is shear-dependent, the direction of mean flow can oppose the direction of wave propagation even in the presence of a zero or favourable mean pressure gradient. The theory is based on an analysis of lubrication-type flow through an infinitely long, axisymmetric tube subjected to a periodic train of transverse waves. Sample calculations for a shear-thinning fluid illustrate that, for a given waveform, the sense of the mean flow can depend on the rheology of the fluid, and that the mean flow rate need not increase monotonically with wave speed and occlusion. We also show that, in the absence of a mean pressure gradient, positive mean flow is assured only for Newtonian fluids; any deviation from Newtonian behaviour allows one to find at least one non-trivial waveform for which the mean flow rate is zero or negative. Introduction of a class of waves dominated by long, straight sections facilitates the proof of this result and provides a simple tool for understanding viscous effects in peristaltic pumping.

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