2.1.2 Calculating internal wave velocity

The distance between two wave packets Using distance to calculate velocity

LESSON 2

Internal
Waves I

References:
References for Lesson 2

Images in this lesson:
(Resizable pop-ups)

ASA_WSM_1P~ 20030306~.N1

Bathymetric map of the Mozambique study area
(17K)

Useful information:
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Solitons: Solitary internal waves (Theory and equations)

Identification of internal wave trains and their direction of propagation

Internal wave mean propagation speed

You will now calculate the mean velocity of the two wave packets shown in orange on the bathymetric map of the study area (17K), assuming that IW generation occurs every tidal cycle at approximately the same phase of the tide, as explained in 'Internal wave mean propagation speed'

Make sure the 'Extract' box is checked and the 'Minimize' box unchecked when you open the next image, an ASAR WSM 1P image from 6 March 2003 off Mozambique ( ASA_WSM_1CNPDK20030306_~.N1 ).
Select Bands and open proc data by double-clicking on its icon.
In the Extract dialogue set the sampling interval to 6 in both the x and y dimensions; this will give an overview of the whole image.
In the Redisplay dialogue set the null value to 0 and apply a Gaussian stretch.

This image contains both land and sea areas. In general land has more irregular features and than sea areas. You should be able to identify which areas are land, and which sea, and where the coast is. If in doubt, consult the bathymetric map.

You should also be able to identify two internal wave packets. You will probably need a zoom of 100% for this. (Right-click on the image and select Zoom). Use the scroll bars ( figure (11K) ) to move around the image until you find the wave packets. Again, if you are unsure, the bathymetric map. will show you where to look.


Question 1.
a)	In which direction are these internal waves propagating?
b)	Based on the propagation direction, which of the two was generated first?

Having found the area of interest, you now need to open it in full resolution. A quick way to find an 'Extract window' that covers exactly the area you want is through use of the 'Go-to' dialogue.

On the toolbar choose box selection ( figure (1K) ) and draw a rectangle that contains both wave packets.
Open the 'Go-to' dialogue ( [CTRL+G] ), uncheck 'Coords' and make a note of the top left position ( [x,y]) coordinates and the size of the selection window.
Use the coordinates and window size to calculate the first coordinates you need in order to open the selected area at full resolution/

Question 2
What are the first and last column (X) of the area of interest in the full resolution image? What are the first and last row (Y)?

Close the subsampled image, and use your answer from Question 1 to open the selected area in full resolution. ( Extract dialogue (5K) )

The distance between two wave packets

To calculate the velocity you will first need to calculate the distance, d, between two consecutive internal wave trains, using the formula:

d = square root

where DX is the distance in the x-dimension between the leading crest of the first wave packet and the leading crest of the second wave packet, and DY is the distance in the y-dimension.

The simplest way to find d is to draw a transect across the the two wave packets. However, before you do this, it best to apply a mean filter as described in L2.1.1. ( [CTRL+A] > Image > Filter > Mean, setting the filter window to 5 x 5.)

Find a section where the leading crest of the first wave packet is clearly defined, and where the leading crests of the two wave packets look reasonably parallel.
Starting just ahead of the leading crest of the first wave packet, draw the line perpendicularly across this crest and continue to the second wave packet, finishing the line just behind the leading crest. Ideally the line should now be perpendicular to both wave crests.
Open a new transect document based on this line, making sure the 'Apply stretches' box is unchecked ( [CTRL+N] > TRANSECT ).
With the new transect active, open the 'View' menu and uncheck 'Coords'
Place the cursor on the first wave crest and note its position ( [x,y] ) from the status bar. The last two figures on the status bar give the pixel values (the actual data and the grey-scale stretch value). You can use this feature to find the exact peak. (To move the cursor by one pixel use [CTRL + ] or [CTRL + ] ).
Place the cursor on the last peak in the transect (the leading crest of the second wave packet) and note the ( [x,y] ) position from the status bar.

Question 3
Based on your transect what is the distance between the two wave packets?

Using distance to calculate velocity

Answers:
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Back up to:
Q1 Q2 Q3

Knowing the distance between two tidally generated wave packets makes it possible to calculate their mean propagation speed. The calculations assume that IW generation occurs every tidal cycle at the approximately the same phase of the tide, as explained in Identification of internal wave trains and their direction of propagation. This means that at any time when you are able to observe two such wave trains, the first of these has been travelling away from the propagation area for one tidal cycle longer than the second wave train, and the distance between them is the distance travelled during the time, T , which is the period of the tidal cycle.

Question 4
Use the distance from your answer to question 4 to calculate the mean wave velocity of the first wave train across the stretch of water represented by the transect. The tidal period for this area is T = 12.42 hours.

As internal waves propagate along the continental shelf they enter increasing shallow water and become refracted. This tends to align the wave crests with the shape of the isobaths. Such refraction can be observed for the first internal wave train (on the right side of the leading waves of the first IW packet closest to land, at about 33°42' E, 25°12' S. The wave crests in this area curve round and become more parallell to the coast, as expected when a wave is shoaling (entering increasingly shallow water).

Next: Internal waves in the South China Sea