Compare fetches of different widths. Fetch B covers three times the area of Fetch A. While the same amount of energy is dissipated from the sides of both fetches, the amount lost as a percentage of the fetch's total energy is larger in fetch A.
Therefore a narrower fetch will result in smaller waves. It is important to analyze the width of the fetch area. Imagine a narrow fetch and winds within that area. If the winds turn slightly, one might define a new fetch because the uniformity of the winds has been broken.
However, with a wide fetch the slight turning of the winds is much less significant to the overall uniformity of the area and a single fetch could still be defined. Click here to see the fetch dimensions animation.
When a fetch changes because the wind speed or direction changes, the waves within the fetch stop growing. A new set of waves begins to grow based on the characteristics of the new fetch.
The original waves begin to propagate out of their fetch generation region. But what happens when the wind speed and direction remain the same, but the fetch length increases? Looking at the wave nomogram shows that a 5 ft wave can be created by a 25 kt wind after just 20 n mi. If conditions change and this fetch length is increased by 60 n mi, then the wave can reach a height of 8 ft.
Notice that the change in fetch length has its greatest effect on wave height for small fetches. When a given wind speed has persisted over a long distance, wave height changes due to increases in fetch length are fairly small. If a wind blows over a 10 nautical mile fetch at 21 knots, what would the resulting wave height be? Answers: b , 3 ft. Locate the intersection of the 10 nautical mile fetch on the x-axis and the 21 knot wind speed line on the y-axis.
This gives a wave height of approximately 3 feet. What would cause the larger increase in wave height for this situation: increasing the wind speed by 60 knots or increasing the fetch length by 60 nautical miles? The correct answer is a. Increasing the wind speed by 60 kt would increase the wave height to approximately 15 feet. Increasing the fetch length by 60 n mi would increase the wave height to approximately 6 feet.
Therefore, increasing the wind speed would cause a larger increase in wave height. When storm systems move, waves in the right quadrant, or right of track, may grow larger than expected because the waves are moving in the same direction as the advancing fetch.
The graphic demonstrates a tropical cyclone with a straight storm path and a fetch in the right of track outlined with a dotted white line. The waves in this outlined fetch area are affected by the fetch winds longer, which leads to continued growth. The distance over which the waves actually grow is called the effective or dynamic fetch, shown in the graphic by a purple rectangle. Click here to see the dynamic fetch introduction animation.
The dynamic fetch length may be different than the stationary fetch length measured within an identical stationary storm system.
In addition to the stationary storm factors of wind speed, duration, and fetch, the assessment of dynamic fetch requires knowledge of an additional factor: the translation speed, or storm speed, of the wave-generating cyclone. There is a non-linear relationship between all of these factors, which makes the forecasting of wave heights in dynamic fetch situations a complex problem.
First, let's look at a tool that allows forecasters to estimate the degree of dynamic fetch that will occur for a given set of storm parameters. Then, using this tool, one can determine if dynamic fetch will lead to wave heights that are different than expected. The Meteorological Service of Canada Atlantic Storm Prediction Centre in Dartmouth, Nova Scotia, has developed a tool that allows forecasters to see the potential effects of dynamic fetch in a storm system.
The following is a description of the graphical output of this tool. The user inputs the fetch area wind speed, the wave generation fetch length, and the storm speed. For this chart the user has input 70 knots for the wind speed, 50 nautical miles for the fetch length, and 15 knots for the storm speed, referred to on the chart as "motion.
Notice that the graph is similar to a histogram in that time is on the y-axis while distance is on the x-axis. Unlike the traditional histogram, the time moves forward going up the y-axis. The red box represents the fetch length entered by the user, which stays constant as time increases. The height of the red box has no relevance. The leading edge of the fetch box is on the right and the trailing edge is on the left. One can imagine the wind blowing from left to right across the fetch in the graph, with the distance on the x-axis representing the movement of the fetch area over the time period on the y-axis.
Inside the fetch box, the positions of each wave are represented by a star and are placed at intervals of 10 nautical miles. A line is drawn through the position points of a given wave as it moves in time.
This helps the user see how many of the waves remain growing within the fetch region and how their relative position within the fetch is changing over time. The wave position number is shown when the wave falls outside of the fetch region. From 0 to 1 hour, the fetch box has moved 15 nautical miles, corresponding to the input storm speed of 15 knots. The wind speed is used to determine the change in wave height and period, and hence the corresponding wave speed, as well as distance traveled in this one hour span.
Notice that both the fetch box and the waves have moved to the right, but the position of the waves within the fetch box has also changed. At one hour the wave in position 6 has moved outside of the fetch region and is no longer growing.
The remaining five waves are still in the fetch area but their positions have moved toward the trailing edge of the fetch. In essence, the fetch is moving faster than the waves it is generating. As time increases the wave positions continue to change until they all are either outrun by the fetch or move ahead of the fetch.
In this case, the waves that initially started at positions 5 and 6 have been outrun by the fetch region, while those that started in positions 1 through 4 have sped up and moved out ahead of the fetch area. Remember that we are looking at only one set of waves that have started at time zero, while in the real world waves are constantly being generated throughout the entire time period. In order to assess wave growth in a dynamic fetch event, the forecaster must determine how long the waves will remain in the fetch area that is moving parallel to the track of the cyclone.
In some instances the storm speed will be faster than the wave speed, and the waves will not remain in the fetch area for a long period of time. Such fast-moving systems may quickly outrun the waves they generate even if the dynamic fetch length is less than the stationary fetch length. Examine this graph where the cyclone is moving at 25 knots and has a 65 knot wind speed over a 60 nautical mile fetch.
After just 5 hours, all of the waves have fallen behind the quickly moving cyclone. Examining the distance that the waves traveled before being outrun by the system reveals that the wave in position 1 is the only wave to have stayed in the fetch area for the entire 60 nautical miles.
Because waves in positions 2 through 7 are effectively influenced by a shorter fetch length, their resulting wave heights are less than if the storm system were stationary. In other words, their resulting wave heights are less than what the Bretschneider wave nomogram would predict. Similarly, a slow-moving system may be outstripped by the waves it creates.
The graph shows the same cyclone with a much slower storm speed of 5 knots. In this case waves starting in positions 5 through 7 remain in the fetch area for a longer time compared to a stationary storm system with the same fetch length and wind speed. Therefore, the cyclone and these generated waves are said to be "resonant" to some degree.
This resonance between storm speed and wave speed leads to wave heights that are greater than the Bretschneider wave nomogram would predict. However, waves starting in positions 1 through 4 will have wave heights that are equal to or less than that determined from the wave nomogram. These waves move ahead of the cyclone fairly quickly and propagate away as swell before the entire 60 nautical mile fetch can act on them.
When there is less wave growth than for a comparable stationary fetch, the cyclone and the generated waves are said to be "dissonant. When the cyclone and waves move at speeds that are resonant, the dynamic fetch can be considerably larger than its stationary counterpart.
Many forecasters make the mistake of assuming that wave speed and storm speed must increase at the same rate in order for dynamic fetch to occur. In reality, only small subsets of storms move this way. Examine the animation below to see why this is true. Optimal dynamic fetch situations result from waves originating at the leading edge of the storm, then losing ground to the more quickly advancing system, then speeding up before the trailing edge of the fetch passes them by, and finally accelerating back through the fetch to the leading edge once again.
The dynamic fetch length of the leading edge wave is again represented by the purple rectangle. If the storm motion remains constant, then this scenario reaches a steady state of high fast-moving waves at the storm's leading edge. Notice that the wave at the leading edge has the largest height and is outrunning the stationary fetch area shown by the dotted white rectangle.
Click here to see the dynamic fetch animation. Dynamic fetch wave growth can be illustrated by taking the cyclone from the previous example and setting the storm speed to 20 knots. Notice that all of the waves are outrun by the cyclone except for the wave starting closest to the leading edge of the fetch. This wave grows as its position in the fetch lags toward the trailing edge.
As the wind continues to influence this wave, its height and period increase. Remember that in deep water the wave speed is dependent on the wave length, and hence the period. Therefore, as the period increases, the wave speed increases as well.
At some point between 11 and 13 hours the wave and fetch have nearly the same speed and continued growth causes the wave to accelerate forward through the fetch area and out the leading edge. To best illustrate how optimal dynamic fetch occurs, it's helpful to look at the conceptual animation and the graph side by side. Each image shows the same seven waves that start in the fetch area.
The fetch box on the graph is highlighted to show the corresponding time within the animation. Notice how quickly waves 3 through 7 are outrun by the storm system. Wave 2 experiences a small degree of dynamic fetch, but it is wave 1 that eventually equals the speed of the system by the time it reaches the trailing edge of the fetch.
It then continues to grow as it accelerates back through the fetch and out the front edge. Click here to see the optimal storm speed animation. If a forecaster's criteria for the occurrence of optimal dynamic fetch is that storm speed and wave speed be equal, they will actually be focusing on storms that move too quickly. In fact, the storm and waves are often dissonant in such cases, resulting in wave heights being smaller than anticipated. Dynamic fetch frequently affects the offshore waters of Canada when a tropical storm curves to the northeast and moves along the U.
Atlantic seaboard. Examine the image presented here. The fetch to the right of the storm path is highlighted. Initially, as the storm curves, groups of wind waves are shown developing in this fetch. These waves have varying paths due to the curving motion of the storm and will impact different parts of the U. East Coast. As the storm path straightens, wave growth from dynamic fetch begins to occur.
For this illustration there are four groups of waves inserted consecutively just after the tropical cyclone begins moving in a straight path. Remember that waves are constantly being generated in all areas of a real tropical storm as it moves, but for illustration purposes most are not shown here. As the storm moves most of the waves lag behind the quickly moving system.
Eventually, the waves from each of the four initial groups can be seen moving back through the fetch area and then ahead of the system. Keep in mind that dynamic fetch waves are moving faster than the other waves generated by the storm and are preceded by comparatively smaller waves, giving little warning of impending arrival of the larger dynamic fetch waves.
This is shown by the sharp gradient in wave height that occurs ahead of the system and the rather weak gradient in the wake of the system. To see if dynamic fetch could occur with various combinations of wind speeds, fetch lengths, and storm speeds, use the Dynamic Fetch link below. Assessing the sensitive thresholds for these parameters within tropical cyclones can be complex.
In addition to the manual dynamic fetch tool just discussed, the Canadian Hurricane Centre has developed a dynamic, or trapped, fetch wave model which uses data from a parametric hurricane wind model. The trapped-fetch model runs quickly because it works on the assumption that only one spectral mode exists in dynamic fetch situations and simple wave growth formulations are sufficient.
Changes in forecast track and intensity can be re-input to the trapped-fetch wave model with new output available in a matter of seconds. Forecasters need to be able to identify when a fetch is moving with the wind and parent storm system. When fetch movement, wind direction, and storm movement are in line, greater than expected wave growth will result. Using the plot of various mid latitude and tropical storms, identify which paths are most likely to develop dynamic fetch generated waves.
The correct answers are B, C, D, and F. However, this graphic does not depict the wind strength and storm speed associated with each choice. These two factors as well as the fetch length all need to be in harmony to some degree for dynamic fetch to occur. Comparing Fig. Ratio values that are unreasonably large also have large error bars and therefore can be ignored. For the selected long- and short-fetch periods, the error bar is small, and hence the ratio values are significant.
Typical maps of surface currents under the long- and short-fetch conditions are shown in Figs. The currents at the southern end of the mapped area behave uniformly and appear to respond mainly to the wind. At the northern end of the map, the currents are complex and appear to respond to the flow into and out of Port Phillip Bay. For the middle area, the currents follow the bathymetry lines. This is reasonable, because the bathymetry gradients around the m bathymetry line are large and variable; areas with bottoms shallower than 60 m have larger bathymetry gradients.
As depth increases, the gradients become smaller. Therefore, for areas near the coast with bathymetry shallower than 60 m, the currents are steered along the bathymetry contours.
Therefore, only 10 points, as highlighted in Fig. As shown in Fig. Comparing Figs. Because the current map shows the current only at a particular time, the difference in direction relation might not be representative of other times. Therefore, the direction relation averaged over the 10 selected grid points is shown in Fig. The errors of current direction and wind direction are calculated in the same way as for current speed and wind speed in Fig. For the short-fetch period, the angle ranges from To explain these differences, we need to understand that wind generates surface currents as a result of momentum transfer through both wind stress acting directly on the ocean surface and Stokes drift induced by the nonlinearity of waves.
As the wave spectrum develops with fetch, the magnitude of Stokes drift also varies with fetch. The response of surface current to wind is composed of both Ekman-type currents generated by wind stress and the Stokes drift. The former is governed by Ekman theory and the latter is governed by Stokes mass transport theory. These findings suggest that at relatively high wind speed, the drag coefficient increases with the wind speed.
Using 5 , we calculate the ratio of standard deviation of C D versus the mean of C D for the long- and short-fetch periods.
The ratio is 4. Therefore, C D is regarded as relatively constant over the selected fetch periods, and thus 3 suggests that a quadratic relation between V E and U 10 is a good approximation for the relation between the wind-generated current speed and the wind speed. Because contributions to the Stokes drift current come mainly from wave components at the spectral peak, the surface mass transport calculated from the average characteristic of dominant waves provides a reliable approximation to that calculated from the wave spectrum Wu Therefore, we consider only the wave component at the spectral peak when calculating the Stokes drift.
To calculate Stokes drift, wave parameters need to be known. Much work has been done to establish the empirical functions of wave parameters versus nondimensional fetch Dobson et al. All of these expressions are obtained under different circumstances: some are obtained from lakes, others are from the ocean; some are of stable stratification, and others are of unstable conditions. For short fetches, when the wave is in fast growth, many different fetch-limited formulas for wave parameters have been suggested.
Excluding formulas derived from unstable conditions, we have the following list:. The above fetch-limited Eqs. Despite their differences, there is a common form that nondimensional wave energy and frequency are power functions of nondimensional fetch; it is only the coefficient and the exponent that vary between the different models.
All of the above expressions of wave parameters are in agreement, with the expectation that as nondimensional fetch increases, wave energy increases and the peak frequency decreases. Between the short fetch with a stable wave growth rate and the long fetch, where waves cease to grow, there is a transition region where the growth rate gradually slows down. For this transition region, the above-mentioned fetch-limited wave growth formulas do not apply, because these empirical formulas are derived from fitting to the data only in the short-fetch region.
Nondimensional variance of wave energy and nondimensional peak frequency in 17 and 19 are plotted in Fig. It can be seen that the transition region is from about 10 4 to about 10 5 in nondimensional fetch. Hence, the long-fetch condition in our study with a nondimensional fetch of 54 belongs to the transition region in the fetch-limited wave growth regime. Therefore, for calculating the wave parameter in this region, it is better to use 19 , which includes the transition region, because it is derived from fitting to both long and short nondimensional fetches.
The short-fetch condition with a nondimensional fetch of belongs to the short-fetch regime where the wave spectrum is in fast development. Wave parameters in this regime can be calculated using 14 — For the short-fetch section, the wave growth will be duration limited for the first 3.
Hence, for long fetches, the influence of duration on wave growth cannot be ignored. Because the long-fetch wind starts around h in the time series, we choose — h to be the section for our long-fetch case, in order to exclude the effect of duration on wave development.
To ascertain the role V E and V S each play under different conditions, the least squares fitting process is applied to 23 to minimize the mean square speed residual.
The least squares fitting process was conducted on each of the 10 chosen points separately, with a set of a 1 and a 2 values obtained for each grid point Table 1. The result of the fitting for 1 of the 10 grid points is shown in Fig. The real current data and the model result derived from the value of a 1 and a 2 at that point are shown for the short- and long-fetch periods.
Figure 12 also shows the current produced separately by wind stress and Stokes mass transport. It can be clearly seen that under the long-fetch condition, Stokes drift is dominant in generating the surface current, while under the short-fetch condition, Stokes drift is equally important as wind stress in generating the surface current.
Table 1 shows the least squares fitting results of coefficients a 1 and a 2 for the 10 grid points during the long- and short-fetch periods, as well as the average fitting error dc between the observed current and the model results.
The modeling process here is done for each grid point in order to evaluate the generality of the value of coefficient a 1 and a 2 so as to verify the influence of fetch on the values. The average coefficient value of these different points can be used for current prediction under the corresponding environmental condition.
Results show that the value of the coefficient a 2 for Stokes drift is much smaller under the short- than long-fetch conditions. This suggests that under long-fetch conditions, resulting from more mature wave development, the influence of Stokes drift is much stronger than under short-fetch conditions. In contrast, the similarity of the value of the coefficient a 1 under these two fetch conditions suggests that fetch condition does not have much influence on the wind stress—generated surface current V E.
As indicated by Eq. The dependence of drag coefficient C D on sea state has been a contentious issue; recently, some studies show that there is lack of evidence of this dependence Janssen ; Yelland et al. In our study, a conclusion on whether the drag coefficient C D depends on sea state might be too early without further information of the variation of eddy viscosity A z with fetch.
For the transition zone which applies to the long-fetch condition , only 19 applies for the wave parameters, thus Stokes drift can be calculated from Therefore, the result of our analysis for surface currents induced by Stokes drift is in agreement with that calculated from the empirical wave growth functions. In addition, the curve from 28 in Fig. Data representing large nondimensional fetch conditions are needed to verify this trend. The theoretical approach by Creamer et al.
The results of this paper indicate that the response of the ocean surface current to wind is a result of momentum transfer by both the wind stress and the Stokes mass transport. A quadratic law governs the former, and a linear law governs the latter. Therefore, the surface current is a superposition of components from both quadratic and linear relations. The correlation analysis of tidally filtered surface current data measured by HF radar with the local winds shows that, for most of the study area, wind dominates over other factors in generating surface currents with correlation coefficient higher than 0.
Current maps show that currents tend to follow the bathymetry contours in areas of high-bathymetry gradients. Ten grid points at the southern end where the filtered surface current is highly correlated with the filtered wind were chosen for the fetch analysis.
Two durations in the time series of wind represent the short- and long-fetch conditions. Wind data for these two durations are reasonably constant and strong. Analysis of the data suggests that under the long-fetch condition, Stokes drift dominates the surface current, while under the short-fetch condition, wind stress and Stokes drift are almost equally important in generating surface current.
The long-fetch condition belongs to the transition region in the wave growth regime, while the short-fetch condition belongs to the region with a high wave growth rate. In the open sea, the wind fetch is often long, which is favorable for wave development. Hence, the Stokes drift is expected to dominate the surface drift in the open ocean. This explains why in the open sea, the linear relation between the surface current and the wind dominates over the quadratic relation, as found by Kirwan et al.
However, for areas under short fetch in the wave growth regime, the quadratic law for Ekman-type currents and the linear law for Stokes drift are about equally important in generating surface currents.
These results imply that in the surface current prediction and 3D numerical modeling, varying the relation between current response and the wind according to different fetch condition will improve the outcomes. This is an early result from 1 month of data in which only two periods satisfied the condition of constant wind direction at reasonably high, constant wind speed. It is also worth noting that no wave information was available in our study; otherwise, Stokes drift would have been derived independently from measured wave data.
In the future, a more complete quantitative assessment of these ideas using measured wave directional spectra should be carried out. This work provides some insight into the physics of the momentum transfer from air to sea and shows that HF radar measurements of surface currents include the effect of Stokes drift.
It demonstrates the value of HF ocean surface radar technology for carrying out surface current studies. This work was carried out while Y. The wind data were provided by the Australian Bureau of Meteorology. We wish to thank the Editor Dr. Smith for drawing our attention to Creamer et al. Valuable comments from the anonymous reviewers are also acknowledged. Citation: Journal of Physical Oceanography 38, 5; Search Magicseaweed. Live Data. Log In. Sign Up. Walter Munk, a legendary oceanographer and one of the original pioneers of wave forecasting.
Tony Butt. By Nick Carroll on 6th November We love the Med! First XL Swell of the Yeah, things got kinda spicy. So, what determines how long the wind can blow, uninterrupted, over a body of water? The answer is very simple - it's the length of the water between one obstacle and the next one. That length of open water over which the wind can blow unobstructed is called the Fetch. For a bowl of soup it would be one edge of the bowl to the other, for a lake it's one shore to the opposite one, and for a sea or ocean it's exactly the same idea, but obviously with greater distances.
A very short fetch, like the soup bowl or the width of a small lake just isn't long enough for the amount of energy needed to make big waves to be transferred to the water. You don't get 10m high waves on a 50m wide lake, regardless of how deep it may be!
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