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Flow in an ocean basin An idealized two-dimensional ocean is modeled by the square region R = - x - with boundary C. Consider the stream function (x, y) = 4 cos x cos y defined on R (see figure). yA 3 a. The horizontal (east-west) component of the velocity is u = 4, and the vertical (north-south) component of the veloc- ity is v = -, Sketch a few representative velocity vectors and show that the flow is counterclockwise around the region. b. Is the velocity field source free? Explain. c. Is the velocity field irrotational? Explain. d. Let C be the boundary of R. Find the total outward flux across C. e. Find the circulation on C assuming counterclockwise orientation.

Flow in an ocean basin An idealized two-dimensional ocean is modeled by the square region R = - x - with boundary C. Consider the stream function (x, y) = 4 cos x cos y defined on R (see figure). yA 3 a. The horizontal (east-west) component of the velocity is u = 4, and the vertical (north-south) component of the veloc- ity is v = -, Sketch a few representative velocity vectors and show that the flow is counterclockwise around the region. b. Is the velocity field source free? Explain. c. Is the velocity field irrotational? Explain. d. Let C be the boundary of R. Find the total outward flux across C. e. Find the circulation on C assuming counterclockwise orientation.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Flow in an ocean basin An idealized two-dimensional ocean is modeled by the square region R = - x - with boundary C. Consider the stream function (x, y) = 4 cos x cos y defined on R (see figure). yA 3 a. The horizontal (east-west) component of the velocity is u = 4, and the vertical (north-south) component of the veloc- ity is v = -, Sketch a few representative velocity vectors and show that the flow is counterclockwise around the region. b. Is the velocity field source free? Explain. c. Is the velocity field irrotational? Explain. d. Let C be the boundary of R. Find the total outward flux across C. e. Find the circulation on C assuming counterclockwise orientation.
Transcribed Image Text:Flow in an ocean basin An idealized two-dimensional ocean is modeled by the square region R = - x - with boundary C. Consider the stream function (x, y) = 4 cos x cos y defined on R (see figure). yA 3 a. The horizontal (east-west) component of the velocity is u = 4, and the vertical (north-south) component of the veloc- ity is v = -, Sketch a few representative velocity vectors and show that the flow is counterclockwise around the region. b. Is the velocity field source free? Explain. c. Is the velocity field irrotational? Explain. d. Let C be the boundary of R. Find the total outward flux across C. e. Find the circulation on C assuming counterclockwise orientation.
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