2. Sketch the streamlines for the flow u = ax, v = -ay, w = 0, where a is a positive constant. Next, let the concentration of some pollutant in the fluid be: с(х, у, t) %3D Вx?уе, for y>0, where B is a constant. Does the pollutant concentration for any particular fluid element change with time? An alternative way of describing any flow is to specify the position x of each fluid element at time t in terms of the position X of that element at t= 0. For the above flow this Lagrangian' description is x = Xeat, y = Yeat z= Z. Verify by direct calculation that əx Du = u, Dt in this particular case. Why are these results true in general?

2. Sketch the streamlines for the flow u = ax, v = -ay, w = 0, where a is a positive constant. Next, let the concentration of some pollutant in the fluid be: с(х, у, t) %3D Вx?уе, for y>0, where B is a constant. Does the pollutant concentration for any particular fluid element change with time? An alternative way of describing any flow is to specify the position x of each fluid element at time t in terms of the position X of that element at t= 0. For the above flow this Lagrangian' description is x = Xeat, y = Yeat z= Z. Verify by direct calculation that əx Du = u, Dt in this particular case. Why are these results true in general?

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 69EQ: Let x=x(t) be a twice-differentiable function and consider the second order differential equation...

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