Water Particle Paths Near a Vertical Barrier
Water Particle Paths Near a Vertical Barrier
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In our eReader you can find the full English version of the book. Read Water Particle Paths Near a Vertical Barrier Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Water Particle Paths Near a Vertical Barrier
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Y ^ - Re ne" « ne"*^ cos x 1) <^o = Re -iz /-iz (z « X + iy; Re » Real part of) du + nie •12 ne^ sin x (for large x) To obtain a progressing wave, we set 2) ($(x, yjt) = 4-j^(x, y) sin t + ^^{x. Y) cos t (t represents dimensionless tine, (tT) Therefore, for large x ^(x, y;t) * ne'^[cos x sin t + sin x oos t] = ne^ sin (x + t). The particles of water, [x(t), y(t)], satisfy the following system of differential equations: s) S ' - ^J-'V:^) % ■ - V''-^'*' (the subscript mesining partial differentiation with respect to that variable) together with some initial conditions. x(t ) =» X ^ o' o y(*o) - ^0- ♦ We are employing the appropriate dimensionless lengths x and y where, if we set A = wave length at «, -s— x and ■=-• y represent 2ng tjrue distances (i. E. A = —5^, where g = acceleration due to 6^ itft gravity, tf = frequency of standing waves, (^e ). We have integrated the equations of nation 3) for several ini- tial points and have verified that the following simple description of the particle paths is correct: Any individual particle path is fundamentally elliptical in shape — the "ellipses" are large near the surface because the velocities are large and decrease in size as w© go deeper.
What to read after Water Particle Paths Near a Vertical Barrier?
You can find similar books in the "Read Also" column, or choose other free books by Eugene Isaacson to read online
To quickly assess the difficulty of the text, read a short excerpt:
Y ^ - Re ne" « ne"*^ cos x 1) <^o = Re -iz /-iz (z « X + iy; Re » Real part of) du + nie •12 ne^ sin x (for large x) To obtain a progressing wave, we set 2) ($(x, yjt) = 4-j^(x, y) sin t + ^^{x. Y) cos t (t represents dimensionless tine, (tT) Therefore, for large x ^(x, y;t) * ne'^[cos x sin t + sin x oos t] = ne^ sin (x + t). The particles of water, [x(t), y(t)], satisfy the following system of differential equations: s) S ' - ^J-'V:^) % ■ - V''-^'*' (the subscript mesining partial differentiation with respect to that variable) together with some initial conditions. x(t ) =» X ^ o' o y(*o) - ^0- ♦ We are employing the appropriate dimensionless lengths x and y where, if we set A = wave length at «, -s— x and ■=-• y represent 2ng tjrue distances (i. E. A = —5^, where g = acceleration due to 6^ itft gravity, tf = frequency of standing waves, (^e ). We have integrated the equations of nation 3) for several ini- tial points and have verified that the following simple description of the particle paths is correct: Any individual particle path is fundamentally elliptical in shape — the "ellipses" are large near the surface because the velocities are large and decrease in size as w© go deeper.
What to read after Water Particle Paths Near a Vertical Barrier?
You can find similar books in the "Read Also" column, or choose other free books by Eugene Isaacson to read online
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