Introduction to Long Wave Equations in Civil Engineering

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What is the purpose of determining the local combined surface and bottom stress coefficient 𝐾𝑠𝑏 𝜏𝑠 + 𝜏𝑏 = 𝐾𝑠𝑏 𝜌𝑊?

To calibrate wind/bottom stress setup calculations (correct)

To calculate wind speed at a specific site

To estimate the setup due to hydrostatic forces

To measure Coriolis forces in nearshore water segments

In which direction is the bottom stress typically drawn in relation to the surface wind stress in the setup calculations?

Same direction (correct)

Vertical direction

Perpendicular direction

Opposite direction

What does Δ𝑆𝑤 represent in the context of the setup calculations mentioned?

Wind speed near the shore

Depth of the water segment

Change in setup due to wind and bottom stresses (correct)

Distance between two hydrostatic forces

How is the component of wind velocity in the 𝑥 direction 𝑊𝑥 utilized when the wind is blowing at an angle 𝜃?

To evaluate wind/bottom stress setup Signup and view all the answers

What does the setup coefficient 𝐾𝑠𝑏 𝜏𝑠 + 𝜏𝑏 = 𝐾𝑠𝑏 𝜌𝑊 act as according to the provided text?

An 'all inclusive' calibration factor Signup and view all the answers

Why is it beneficial to have adequate wind, pressure, and setup data from a previous storm at a specific site?

To calibrate subsequent wind/bottom stress setup calculations Signup and view all the answers

What is the primary purpose of the 𝑆𝑃𝐻 and 𝑃𝑀𝐻?

To predict storm surges and wave patterns Signup and view all the answers

What is the range of the inflow angle typically observed in a hurricane?

10 to 30 degrees Signup and view all the answers

What is required to convert the surface wind speed to a resulting surface stress for the equations of motion?

A wind stress drag coefficient Signup and view all the answers

Who developed the commonly used relationship for wind stress drag coefficient?

Van Dorn Signup and view all the answers

What is the formula for wind-induced shear stress on a surface?

Drag coefficient times air density times wind speed squared Signup and view all the answers

At what elevation is the surface wind field plotted?

10 m Signup and view all the answers

What type of waves are typically modeled using long wave equations?

Shallow water waves Signup and view all the answers

What are the horizontal coordinates considered in the long wave equations?

𝑥 and 𝑦 Signup and view all the answers

What is the effect of Coriolis acceleration on the long wave equations?

It can be neglected in certain situations Signup and view all the answers

What is the significance of the volumetric flow rate per unit width of vertical section (𝑞𝑥 and 𝑞𝑦) in long wave equations?

It is used to consider horizontal flows in terms of average velocity Signup and view all the answers

Which of the following is generally neglected in the long wave equations?

Vertical flow velocities Signup and view all the answers

What assumption is made about the periods and 𝑑/𝐿 values of waves modeled by long wave equations?

They have long periods and low 𝑑/𝐿 values Signup and view all the answers

What is the primary condition for determining the final surface profile and nodal line position?

The setup and setdown water volumes are equal Signup and view all the answers

What is the unit of measurement for the static pressure setup calculated using Eqs.(4) and (8)?

Meters Signup and view all the answers

What is the purpose of assuming a nodal line position in the setup calculations?

To calculate the setup and setdown water volumes Signup and view all the answers

What is the relationship between the setup and setdown water volumes on the leeward and windward ends of the bay?

The setup volume is equal to the setdown volume Signup and view all the answers

What is the unit of measurement for the pressure differential used in the calculation of static pressure setup?

Inches of mercury Signup and view all the answers

What is the purpose of using Eqs.(4) and (8) in the calculation of static pressure setup?

To calculate the static pressure setup Signup and view all the answers

What is the relationship between wind stress and bottom stress in the context of water surface slope calculation?

Wind stress and bottom stress are directly proportional Signup and view all the answers

How can Eq.(7) be used to calculate setup for a shore normal profile on the open coast?

By calculating setup for each segment and summing them Signup and view all the answers

What is the recommended value for 𝐾𝑠𝑏 when no better information is available?

1.1𝐾𝑠 Signup and view all the answers

What is the significance of the water surface slope Δ𝑆𝑤 /Δ𝑥 in the static balance equation?

It is the driving force for the balance Signup and view all the answers

How can Eq.(7) be applied to enclosed bays?

It can be applied with caution Signup and view all the answers

What is the procedure for calculating setup for a shore normal profile on the open coast?

Start from the offshore point and move towards the shore Signup and view all the answers