scholarly journals Solution Formula of the Compressible Fluid Motion in Three Dimension Euclidean Space using Fourier Transform

2021 ◽  
Vol 1751 ◽  
pp. 012006
Author(s):  
A H Alif ◽  
S Maryani ◽  
S R Nurshiami
Keyword(s):  
Fourier Transform ◽  
Euclidean Space ◽  
Compressible Fluid ◽  
Fluid Motion ◽  
Three Dimension

scholarly journals Two-dimensional oscillations in divergent jets of compressible fluid

1934 ◽  
Vol 145 (854) ◽  
pp. 52-71 ◽  
Keyword(s):  
Compressible Fluid ◽  
Radial Flow ◽  
Fluid Motion ◽  
Radial Distance ◽  
Two Dimensions ◽  
Common Point ◽  
Compressible Fluids ◽  
Fluid Density ◽  
Straight Lines ◽  
Steady Velocity

1. The problem of determining the possible modes of stationary oscillation for a compressible fluid, moving with a steady velocity which is not constant, usually presents great difficulties. One case which is to some extent amenable to analysis is that of uniform radial flow in two dimensions, where the undisturbed paths of the fluid particles are straight lines radiating from a common point or source. The term “source” is here used somewhat loosely, for in the solution which will be given it is found that the fluid density attains unreal values inside a certain circle having its centre at this common point. It is well known that in radial flow two systems of velocity are possible to a compressible fluid—namely, either (i) zero velocity at r = ∞, and an increasing but limited velocity as the radial distance from the source decreases ( i. e. , a modified “perfect fluid” motion); or (ii) the maximum possible velocity at infinity (corresponding with zero pressure and density), and a decreasing speed—also limited—as r decreases. This type of flow is peculiar to compressible fluids.

LP -bound for the Fourier Transform of Surface-Carried Measures Supported on Hypersurfaces with D∞ Type Singularities

2020 ◽  
pp. 350-359
Author(s):  
Nigina A. Soleeva
Keyword(s):  
Fourier Transform ◽  
Euclidean Space ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Dimensional Euclidean Space ◽  
Convex Surfaces ◽  
The Fourier Transform

Estimate for Fourier transform of surface-carried measures supported on non-convex surfaces of three-dimensional Euclidean space is considered in this paper.The exact convergence exponent was found wherein the Fourier transform of measures is integrable in tree-dimensional space. This result gives an answer to the question posed by Erd¨osh and Salmhofer

Transient response of a compressible fluid in a rapidly rotating circular pipe

2001 ◽  
Vol 427 ◽  
pp. 275-297 ◽  
Author(s):  
JUN SANG PARK ◽  
JAE MIN HYUN
Keyword(s):  
Angular Momentum ◽  
Analytical Solutions ◽  
Compressible Fluid ◽  
Numerical Solutions ◽  
Fluid Motion ◽  
Temperature Fields ◽  
Adjustment Process ◽  
Formal Stability ◽  
Entire Flow ◽  
Heavy Gas

The transient adjustment process of a compressible fluid in a rapidly rotating pipe is studied. The system Ekman number E is small, and the assumptions of small Mach number and the heavy-gas limit (γ = 1.0) are invoked. Fluid motion is generated by imposing a step-change perturbation in the temperature at the pipe wall Tw. Comprehensive analytical solutions are obtained by deploying the matched asymptotic technique with proper timescales O(E−1/2) and O(E−1). These analytical solutions are shown to be consistent with corresponding full numerical solutions. The detailed profiles of major variables are delineated, and evolution of velocity and temperature fields is portrayed. At moderate times, the entire flow field can be divided into two regions. In the inner inviscid region, thermo-acoustic compression takes place, and the process is isothermal–isentropic with the angular momentum being conserved. In the outer viscous region, diffusion of angular momentum occurs. The principal dynamic mechanisms are discussed, and physical rationalizations are offered. The essential differences between the responses of a compressible and an incompressible fluid are highlighted.The issue of stability of the analytically obtained flow is addressed by undertaking a formal stability analysis. It is illustrated that, within the range of parameters of present concern, the flow is stable when ε ∼ O(E).

Landslide Tsunamis Propagating Along a Semi-Plane Beach

2009 ◽  
Author(s):  
Paolo Sammarco ◽  
Emiliano Renzi ◽  
Matthieu Lecouvez
Keyword(s):  
Fourier Transform ◽  
Analytical Model ◽  
Eigenfunction Expansion ◽  
Separation Of Variables ◽  
Three Dimension ◽  
The Fourier Transform ◽  
Sloping Beach ◽  
Landslide Tsunamis

A forced three-dimension analytical model is developed to investigate the main characteristics of landslide tsunamis propagating on a semi-plane beach. The method of separation of variables and the Fourier transform are employed to obtain the solution in the form of an eigenfunction expansion. Parametric discussion and further comparison with the model of a uniformly sloping beach are finally made.

Structure Along Arithmetic Patterns in Sequences of Vectors

2009 ◽  
Vol 18 (6) ◽  
pp. 861-870
Author(s):  
P. CANDELA
Keyword(s):  
Fourier Transform ◽  
Euclidean Space ◽  
Natural Generalization ◽  
Arithmetic Combinatorics ◽  
Vector Valued

We discuss a new direction in which the use of some methods from arithmetic combinatorics can be extended. We consider functions taking values in Euclidean space and supported on subsets of {1, 2, . . ., N}. In this context we present a proof of a natural generalization of Szemerédi's theorem. We also prove a similar generalization of a theorem of Sárkőzy using a vector-valued Fourier transform, adapting an argument of Green and obtaining effective bounds.

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