MAST667-010 Coastal Oceanography: From Physics to Fish

Spring 2000

Instructor Andreas Münchow

Homework #2 (due Mar. 5, 2001)

I. Assume a tidal current

u(x,t) = u0*cos(w t-kx)

v(x,t) = u0/2 * cos(w t-kx)

w(x,t) = 0.

where w =2p /T with T=12 hours; k=2p /l where l /T=Ö (gH), H=10m; and u0=u0(z)=U(1+z/H), and z is vertically up from the bottom at z=-H to the surface at z=0.

(a, 10 pts) How does the magnitude of the velocity Ö (u2+v2) vary as a function of time at x=z=0 (sketch the graph of the function)? Does the current speed ever go to zero ?

(b, 10 pts) How does the direction of the current atan(v/u) vary as a function of time at x=z=0 (Sketch the graph if the function)?

(c, 10 pts) If u and v are currents to the East and North, respectively, what is the direction of maximum and minimum current?

(d, 10 pts) Can you sketch how the tidal velocities vary at x=z=0 in a (u,v) plane as a set of vectors with (u,v)=(0,0) as the origin? What does the shape of the tips of the vectors represent?

II. Use the same flow field as above and

(a, 20 pts) Compute the local and field accelerations.

(b, 10 pts) What is the vertically averaged velocity as a function of time and space?

III. A density profile is approximated well by a polynominal of second order, e.g.,

r (z) = r 0(a+bz+cz2)

(a, 5 pts) What are the units of a, b, and c if r and r 0 are in kg/m3 and z is in m?

(b, 10 pts) What is the vertically averaged density?

(c, 5 pts) What is the hydrostatic pressure associated for this density field?

(d, 5 pts) What are the horizontal pressure gradients from associated with this density field?

(e, 5 pts) How will the hydrostatic pressure change if a, b, and c were functions of x?