In part 1 we looked at shoaling and how it can amplify waves. In this part, we will look at how unique features of the ocean floor can amplify and shape waves.
Spot 2: Secret Ridge—The Wildcard#
Secret Ridge is a more dynamic break, influenced by an underwater ridge that amplifies and shapes the swell. This spot has a reputation for producing hollow, punchy waves when the period and direction align. Let’s see if today’s conditions will light it up.
The Numbers for Secret Ridge#
Secret Ridge offers a unique surfing experience shaped by its steep underwater ridge. Waves here are amplified, better aligned, and steeper compared to more typical sandy-bottom breaks like Main Beach. Let’s break down how amplification, refraction, and wave shape interact to create these exceptional waves.
Amplification via Shoaling and Focusing#
The ridge increases wave height through two key mechanisms:
- Shoaling: As waves enter shallower water, they slow down and grow taller to conserve energy. This process occurs at all breaks.
- Focusing: The steep slope of the ridge funnels wave energy into a narrower area. This compression causes additional amplification, much like a magnifying glass concentrating light.
Applying the Amplification Factor#
The total amplification at Secret Ridge is a combination of shoaling and focusing:
- Shoaling: As waves move into shallower water, their speed decreases, and their height increases to conserve energy. This effect can be quantified using the shoaling factor \(K_s\), which depends on the change in group velocity between deep and shallow water. We have already calculated this in part 1, so this will be a review.
- Focusing: The steep slope of Secret Ridge compresses wave energy into a narrower area, amplifying wave height beyond what shoaling alone achieves. This effect is represented by the focusing factor \(K_f\), which depends on the ridge’s steepness and the alignment of the swell.
The total amplification factor combines these effects:
$$ K_{\text{total}} = K_s \cdot K_f $$
Calculating Shoaling Factor#
For Secret Ridge, we calculate the shoaling factor \(K_s\) using the group velocities in deep and shallow water: For more information on how this is calculated, see part 1.
Group Velocity in Deep Water:
With a wave period \(T = 13 , \text{s}\) and wavelength \(L = 1.56 \cdot T^2\): $$ L = 1.56 \cdot 13^2 = 263.64 , \text{m} $$ $$ C_g = 0.5 \cdot \frac{L}{T} = 0.5 \cdot \frac{263.64}{13} \approx 10.14 , \text{m/s} $$Group Velocity in Shallow Water:
For a shallow water depth of \(h = 7 , \text{m}\): $$ C_{g,\text{shallow}} = \sqrt{g \cdot h} = \sqrt{9.8 \cdot 7} \approx 8.3 , \text{m/s} $$Shoaling Factor:
$$ K_s = \sqrt{\frac{C_g}{C_{g,\text{shallow}}}} = \sqrt{\frac{10.14}{8.3}} \approx 1.11 $$
Adding the Focusing Factor#
The steep ridge enhances wave amplification by focusing energy into a narrower zone. This effect, known as wavefront focusing, depends on the steepness of the ridge and the alignment of the incoming swell. By compressing the wavefront laterally, the ridge increases wave height beyond what shoaling alone would achieve.
The focusing factor \(K_f\) quantifies this effect and can be calculated if the ridge’s slope and bathymetry are known.
Calculating the Focusing Factor for Secret Ridge#
Wave focusing depends on how much the ridge narrows the wavefront as it interacts with the slope. Using the principle of energy conservation, a simplified approach is:
$$ K_f = \sqrt{\frac{W_{\text{deep}}}{W_{\text{focused}}}} $$
Where:
- \(W_{\text{deep}}\): The width of the wavefront in deep water.
- \(W_{\text{focused}}\): The width of the wavefront over the ridge, which depends on the slope steepness.
To calculate \(W_{\text{focused}}\), we determine how the slope compresses the wavefront width using the focusing ratio \(R\):
$$ R = \frac{\Delta x}{\Delta x + \Delta h} $$
Here:
- \(\Delta x\): Horizontal distance across the ridge.
- \(\Delta h\): Change in depth over the ridge.
Then:
$$ W_{\text{focused}} = W_{\text{deep}} \cdot R $$
Substituting \(R\) into the focusing formula gives:
$$ K_f = \sqrt{\frac{1}{R}} = \sqrt{\frac{\Delta x + \Delta h}{\Delta x}} $$
The deep-water wavefront width cancels out because the focusing factor depends only on the relative narrowing caused by the ridge, not the absolute width of the wavefront.
Applying Secret Ridge’s Bathymetry#
For Secret Ridge:
- \(\Delta x = 20 , \text{m}\): Horizontal distance across the ridge.
- \(\Delta h = 10 , \text{m}\): Change in depth over the ridge.
- \(W_{\text{deep}} = 372.5 , \text{m}\): Wavefront width in deep water (example estimate).
Note: For this example we estimated the wavefront width. The deep-water wavefront width (\(W_{\text{deep}}\)) represents the lateral spread of wave energy before it interacts with features like underwater ridges. While not directly available from buoy data, it can be estimated using the distance from the swell source (\(D\)) and the directional spread of the swell (\(\Delta \theta\)), which is often provided by buoys or models. The formula for estimating \(W_{\text{deep}}\) is \(W_{\text{deep}} = D \cdot \tan\left(\frac{\Delta \theta}{2}\right)\), where \(D\) is in meters and \(\Delta \theta\) is the swell’s angular spread in radians. For example, if a swell originates 500 km away and has a directional spread of 10°, the wavefront width can be calculated as approximately 43,500 meters. This value helps us understand how wave energy is distributed across the ocean before narrowing due to features like Secret Ridge. We will look into this in more detail in future posts.
Focusing Ratio \(R\): $$ R = \frac{\Delta x}{\Delta x + \Delta h} = \frac{20}{20 + 10} = \frac{20}{30} \approx 0.67 $$
Focusing Factor \(K_f\): $$ K_f = \sqrt{\frac{1}{R}} = \sqrt{\frac{1}{0.67}} = \sqrt{1.49} \approx 1.22 $$
Adjusting for Swell Alignment#
In addition to ridge steepness, swell alignment further enhances focusing. Secret Ridge’s NW-SE orientation is well-aligned with the 225° SW swell, providing an additional boost to the focusing effect. We apply a correction factor for alignment, increasing \(K_f\) by approximately 30%, yielding:
Empirical Observations#
Studies of wave behavior around underwater features show that alignment improvements can increase focusing by 20–40%, depending on factors such as swell angle, ridge steepness, and bathymetry. A 30% adjustment is a practical estimate for cases where the alignment is strong but slightly imperfect.
Directional Correction#
The degree of swell alignment with the ridge significantly impacts focusing:
- Perfectly aligned swell (0° offset): Maximum focusing effect.
- Moderately misaligned swell (e.g., 20° offset): Reduced focusing, typically less than a 30% boost.
- Significant misalignment (e.g., 90° offset): Minimal or no focusing enhancement.
$$ K_f = 1.22 \cdot 1.3 \approx 1.59 $$
Rounding to one decimal place gives the focusing factor:
$$ K_f \approx 1.6 $$
Why Focusing Matters#
By deriving \(K_f\) based on the ridge’s slope and swell alignment, we capture the key physical processes driving amplification:
- Steepness: A sharp ridge compresses wavefronts more effectively, resulting in higher \(K_f\).
- Alignment: When the swell direction matches the ridge’s orientation, focusing is maximized.
This calculation explains why the focusing factor for Secret Ridge is \(K_f = 1.6\), significantly amplifying wave height when combined with shoaling effects.
Total Amplification Factor#
Combining shoaling and focusing:
$$ K_{\text{total}} = K_s \cdot K_f = 1.11 \cdot 1.6 \approx 1.78 $$
Calculating Amplified Wave Height#
With an offshore wave height \(H_{deep} = 2.5 , \text{m}\), the amplified wave height is:
$$ H_{\text{ridge}} = H_{deep} \cdot K_{\text{total}} = 2.5 \cdot 1.78 \approx 4.45 , \text{m (peak-to-trough)} $$
Why Shoaling and Focusing Matter#
This calculation explicitly shows how shoaling and focusing amplify wave height at Secret Ridge:
- Shoaling (\(K_s\)) accounts for the gradual increase in wave height as waves slow down in shallow water.
- Focusing (\(K_f\)) adds an extra boost due to the ridge’s steep slope concentrating energy into a smaller area.
These combined effects create waves at Secret Ridge that are significantly larger and more powerful than those at Main Beach.
In this section, we have looked at how unique features of the ocean floor can amplify and shape waves. In the next section, we will look at how refraction can align waves with the surf spot.