ERTH 430:Fluid Dynamics in Earth Systems |
Pre-class Quiz #3:
Background Preparation for Lab #3: Numerical Modeling of 1-D Shallow Water Waves in a Wave Tank |

This is a "preview" version of Pre-class Quiz #3. The
preview version is suitable for printing and leisurely inspection before you
submit your answers to the interactive or "live" version—that
is, the real thing. When you feel ready to submit your answers, go to iLearn's
ERTH 430 "Pre-class Quizzes" section, select the interactive
version, and follow its instructions.

(*Responses must be submitted via iLearn by 9:00 a.m. on Friday, Dec.
8*.

**Description:** The questions below are
based on the background and instructions for Lab #3: Numerical Modeling of 1-D Shallow Water Waves in a Wave Tank.

**Questions:**

**(1) Multiple Choice. Variables in the 1-D Shallow Water Wave Equations. **Lab #3 is about the one-dimensional (1-D) shallow water wave equations, which are a pair of coupled, partial differential equations describing how two properties of a layer of water change. What are the two variables? *(Pick the one best answer.)*

- Tendencies and pressure-gradient forces/mass.
- Tendencies and advection.
- Position along the wave tank (
*x*) and time (*t*). - The along-tank component of water velocity (
*u*) and the depth of water in the tank (*h*).

**(2) Multiple Choice. Direct Origins of the 1-D Shallow Water Wave Equations**. The two 1-D shallow water wave equations are scaled and mathematically manipulated versions of the governing equations. Which of the governing equations do they come from most directly?* (Pick the one correct answer.)*

- The
*u*- and*w*-component velocity tendency equations. - The
*u*-component velocity tendency equation and the continuity (or density tendency) equation. - The horizontal velocity tendency equations.
- The temperature tendency equation and the continuity (or density tendency) equation.

**(3) Multiple Choice. Indirect Contribution to the 1-D Shallow Water Wave Equations from the Governing Equations. **The two 1-D shallow water wave equations also contain information indirectly from a third governing equation (via substitution to eliminate one of the variables constrained and described by the governing equations). Which governing equation is it? *(Pick the one correct answer.)*

- The
*w*-component velocity tendency equation (in hydrostatic form). - The temperature tendency equation.
- The continuity (density tendency) equation.
- The equation of state.

**(4) Multiple Choice. Horizontal Pressure-Gradient Force/Mass in the 1-D Shallow Water Wave Equations. **Why does it make sense that the horizontal pressure-gradient force/mass in the water should be related to the horizontal gradient of the depth of the water (that is, the slope of the water surface)? *(Pick the one correct answer.)*

- Under the hydrostatic approximation, pressure in the water at any particular level in the tank is proportional to the depth of the water above that level.
- The horizontal pressure-gradient force/mass depends on the water density.
- The water density depends on the water depth.
- The slope of the water surface depends on convergence of water below that level.

**(5) Multiple Answer. Assumptions Underlying the 1-D Shallow Water Wave Equations. **On what assumptions (supported by scaling) are the 1-D shallow water wave equations based? *(Select all that are correct. There might be more than one.)*

- Friction is negligible.
- The pressure field in the water is approximately hydrostatic.
- The water is essentially incompressible.
- There are no significant variations in the water velocity either horizontally across the tank or vertically—just in the horizontal direction along the tank.
- The density is spatially uniform.

**(6) Multiple Choice. Lab #3 Experiments and Simulations.** Lab #3 asks you to compare observations of waves in the tank to numerical computer model simulations based on the 1-D shallow water wave equations, in two different wave situations (experiment). What distinguishes the two experimental situations?* (Pick the one correct answer.)*

- The depth of the water differs by a factor of two.
- The frequency of the forcing by the wave generator differs by a factor of two.
- The boundary condition at one end of the tank is dissipative in one case, reflective in the other.
- The bottom of the tank is smooth and flat in one case, and in the other case has an obstacle half the depth of the water placed on the bottom.

**(7) Multiple Answer. 1-D Shallow Water Wave Speed. **In 1-D shallow water waves, the waves (as distinct from bits of water) travel at a certain speed. What can we say about that speed? *(Pick all answers that are correct. There might be more than one.)*

- It is proportional to the square root of the average water depth.
- It equals the ratio of the wavelength to the wave period.
- It is inversely proportional to the square root of the density of the water.
- It is proportional to the amplitude of the waves.

**(8) Multiple Answer. Lab #3 1-D Shallow Water Wave Model Input.** When you run the numerical 1-D shallow water wave model using MATLAB, it will prompt you for information that it needs to perform a simulation. For what information will it prompt you? *(Pick all answers that are correct. There might be more than one.)*

- Average depth of water in the tank.
- Length of the wave tank.
- Period of forcing by the wave generator.
- Half-amplitude of the wave generator.
- Boundary condition at the far end of the tank from the wave generator.
- Your name and ID number.
- Density of the water.