An Examination of the Time Scales Difference Between Momentum and Mass Transports
Date Issued
2010
Date
2010
Author(s)
Huang, Po-Yuan
Abstract
The purpose of this thesis is to examine the time scales relation between the momentum transports and the mass transports, where the selected momentum transports is an co-oscillating flow field, and the selected model of mass transports is the advection-diffusion equation.
For the feasibility in the mathematical analysis and for the representativeness of the investigation results, in the contents we design a mathematical model, which contains 1-D standing wave flow field and 1-D advection-diffusion equation. For 1-D standing wave flow field, we solve it by linear wave theorem. And for 1-D advection-diffusion equation, by using the method of image and finite Fourier sine transform, we can transform the 2nd order variable coefficient partial differential equation (i.e. advection-diffusion equation) to 1st order coupled variable coefficient ordinary differential equations. Next, adopting Runge-Kutta method to proceed numerical evaluations, by which we can obtain the semi-analytical transformed solutions, and get the semi-analytical solution for advection-diffusion equation by inverse finite Fourier sine transform.
Using dimensionless technique for the governing equations for 1-D standing wave flow field and 1-D advection-diffusion phenomenon, and by an approximate estimation procedure, we can obtain an approximate time scales expression. Finally, by the numerical verifications of the semi-analytical solutions, we can confirm the rationality of the time scales expression, and carry out some discussions based on physics and mathematics.
The major contributions of this thesis are as follows: the first one is that we find the semi-analytical solution of advection-diffusion equation under specified conditions; the second one is that we estimate the time scales expression which is suitable for tidal channel problems; the third one is that we find that time scales relation can change with time.
Subjects
time scales
oscillating flow field
advection-diffusion equation
finite Fourier sine transform
Runge-Kutta method
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