A discussion of three‐dimensional wave propagation effects

1987 ◽  
Vol 82 (S1) ◽  
pp. S44-S44 ◽  
Author(s):  
Ding Lee ◽  
Paul D. Scully‐Power ◽  
George Botseas ◽  
William L. Siegmann
Keyword(s):  
Wave Propagation ◽  
Three Dimensional ◽  
Propagation Effects ◽  
Dimensional Wave

IS WAVE PROPAGATION COMPUTABLE OR CAN WAVE COMPUTERS BEAT THE TURING MACHINE?

2002 ◽  
Vol 85 (2) ◽  
pp. 312-332 ◽  
Author(s):  
KLAUS WEIHRAUCH ◽  
NING ZHONG
Keyword(s):  
Wave Propagation ◽  
Turing Machine ◽  
Sobolev Spaces ◽  
Three Dimensional ◽  
Subject Classification ◽  
Physical Machine ◽  
The Church ◽  
Dimensional Wave

According to the Church-Turing Thesis a number function is computable by the mathematically defined Turing machine if and only if it is computable by a physical machine. In 1983 Pour-El and Richards defined a three-dimensional wave $u(t,x)$ such that the amplitude $u(0,x)$ at time 0 is computable and the amplitude $u(1,x)$ at time 1 is continuous but not computable. Therefore, there might be some kind of wave computer beating the Turing machine. By applying the framework of Type 2 Theory of Effectivity (TTE), in this paper we analyze computability of wave propagation. In particular, we prove that the wave propagator is computable on continuously differentiable waves, where one derivative is lost, and on waves from Sobolev spaces. Finally, we explain why the Pour-El-Richards result probably does not help to design a wave computer which beats the Turing machine.2000 Mathematical Subject Classification: 03D80, 03F60, 35L05, 68Q05.

scholarly journals A Formulation of Unified Three-Dimensional Wave Activity Flux of Inertia–Gravity Waves and Rossby Waves

2013 ◽  
Vol 70 (6) ◽  
pp. 1603-1615 ◽  
Author(s):  
Takenari Kinoshita ◽  
Kaoru Sato
Keyword(s):  
Wave Propagation ◽  
Gravity Waves ◽  
Rossby Waves ◽  
Three Dimensional ◽  
Wave Activity ◽  
Storm Tracks ◽  
Mean Flow ◽  
Wave Activity Flux ◽  
Inertia Gravity Waves ◽  
Dimensional Wave

Abstract A companion paper formulates the three-dimensional wave activity flux (3D-flux-M) whose divergence corresponds to the wave forcing on the primitive equations. However, unlike the two-dimensional wave activity flux, 3D-flux-M does not accurately describe the magnitude and direction of wave propagation. In this study, the authors formulate a modification of 3D-flux-M (3D-flux-W) to describe this propagation using small-amplitude theory for a slowly varying time-mean flow. A unified dispersion relation for inertia–gravity waves and Rossby waves is also derived and used to relate 3D-flux-W to the group velocity. It is shown that 3D-flux-W and the modified wave activity density agree with those for inertia–gravity waves under the constant Coriolis parameter assumption and those for Rossby waves under the small Rossby number assumption. To compare 3D-flux-M with 3D-flux-W, an analysis of the European Centre for Medium-Range Weather Forecasts (ECMWF) Interim Re-Analysis (ERA-Interim) data is performed focusing on wave disturbances in the storm tracks during April. While the divergence of 3D-flux-M is in good agreement with the meridional component of the 3D residual mean flow associated with disturbances, the 3D-flux-W divergence shows slight differences in the upstream and downstream regions of the storm tracks. Further, the 3D-flux-W magnitude and direction are in good agreement with those derived by R. A. Plumb, who describes Rossby wave propagation. However, 3D-flux-M is different from Plumb’s flux in the vicinity of the storm tracks. These results suggest that different fluxes (both 3D-flux-W and 3D-flux-M) are needed to describe wave propagation and wave–mean flow interaction in the 3D formulation.

Silencer for high-frequency turbocharger compressor noise via an acoustic straightener

2021 ◽  
Vol 263 (5) ◽  
pp. 1744-1755
Author(s):  
Pranav Sriganesh ◽  
Rick Dehner ◽  
Ahmet Selamet
Keyword(s):  
Wave Propagation ◽  
Plane Wave ◽  
High Frequency ◽  
Three Dimensional ◽  
Mean Flow ◽  
Analytical Treatment ◽  
Underlying Assumption ◽  
Wide Range ◽  
Plane Wave Propagation ◽  
Dimensional Wave

Decades of successful research and development on automotive silencers for engine breathing systems have brought about significant reductions in emitted engine noise. A majority of this research has pursued airborne noise at relatively low frequencies, which typically involve plane wave propagation. However, with the increasing demand for downsized turbocharged engines in passenger cars, high-frequency compressor noise has become a challenge in engine induction systems. Elevated frequencies promote multi-dimensional wave propagation rendering at times conventional silencer treatments ineffective due to the underlying assumption of one-dimensional wave propagation in their design. The present work focuses on developing a high-frequency silencer that targets tonal noise at the blade-pass frequency within the compressor inlet duct for a wide range of rotational speeds. The approach features a novel "acoustic straightener" that creates exclusive plane wave propagation near the silencing elements. An analytical treatment is combined with a three-dimensional acoustic finite element method to guide the early design process. The effects of mean flow and nonlinearities on acoustics are then captured by three-dimensional computational fluid dynamics simulations. The configuration developed by the current computational effort will set the stage for further refinement through future experiments.

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