“Traveling Deformation Waves” – What Is It?

So, “traveling deformation waves” – what is it?
We are sure you have been watching them all your life: by looking at wave motions in the water from a thrown stone, or at creeping caterpillar with bend (i.e., wave) rolling along its body. We, the authors of this site, started research of traveling deformation waves by observing and studying wave motion of such creatures as caterpillar, earthworm, snake, and snail. In this site we will tell you how that has helped us to make some discoveries in different fields of science.
Let’s take a closer look on how these land creatures move, even though they have no legs, but only an elongated, deformable body, able to carry deformation waves.

We will prepare and place video films and computer animations of moving mechanisms of mentioned living creatures.

Let’s focus on these two typical and simple models: long, deformable strips lying on solid base. One of them can bend (“caterpillar”), while another one can stretch (“earthworm”).
If we periodically bend one end section of such a strip (i.e., create a transversal wave) and move it towards another strip’s end, the whole strip will “crawl” along the base – this is a model of caterpillar’s movement.
If we stretch some end fragment of the strip (i.e., create a longitudinal wave) and move it towards another strip’s end, the strip will “crawl” as well – a model of earthworm’s movement.
But do not rush to conclusion that those “well-known” phenomena are simple and trivial. This is what we thought when began studying those methods of locomotion from positions of mechanics. Let’s ask ourselves a question: “Why a caterpillar crawls in the same direction as moving deformation wave on its body, but an earthworm moves in the direction opposite to deformation wave’s motion?” Finding answers led us to understanding that there exist only two kinds of traveling deformation waves:
• wave of surplus of mass (example: bend (transversal) wave on caterpillar’s body);
• wave of shortage of mass (example: elongation (longitudinal) wave on earthworm’s body);

Later we will show that all other traveling deformation waves concerned in this site (traveling deformation waves in all media – solid, liquid and gas, and waves of different scales – up to global atmospheric and geospheric waves) are waves of these two kinds – surplus of mass and shortage of mass.
Let’s go back to our “basic biomechanical examples” of traveling deformation waves we started with – methods of transportation of caterpillar and earthworm. From positions of theoretical mechanics, those mechanisms, invented by Nature itself, have many characteristics that are not achievable in man-made devices.
First, this is an extremely economical method of transportation. Because of having massive body and small power for its move, those creatures managed to move themselves “by parts”. As you can see from our models, at every given moment only the wave part of body is moving, while the rest is motionless (“resting”).
Second, there is no sliding friction. This fact seems improbable. How can any legless creature, crawling on solid surface, avoid friction? However, strict analysis shows that:
• for caterpillar, moving part of its body is raised from the ground, thus avoiding friction;
• for earthworm, moving (i.e. stretched) part of its body is raised from the ground as well, because longitudinal stretching of a deformable body leads to its narrowing, i.e., reduction of cross-section (Poisson’s law).

We call such body’s wave movement method, when some of its particles are moving, while others are resting, “discrete-wave” movement.
Let’s define now a concept of mass content for transversal and longitudinal deformation waves. Considering that wave is moving along x-axis, let’s assume a wave length l as a length of the interval along x-axis containing the wave. If mass of deformable body fragment in the wave interval l is , and mass of regular body fragment (not in wave) of the same length l is m, then the mass contents of the wave is
= – m
Another words, mass content of the wave is a difference of mass of body in the wave fragment and mass of non-wave fragment of the same length.

There are two other important characteristics of waves we will need in chapters to follow.
• Wave mass transfer equals to product of mass content  of wave and its traversed path L:
• Momentum (impulse) of traveling deformation wave equals to product of mass content of wave  and its velocity .

Source: Nacionfarma.com

Estuaries: the Ocean’s Nurseries

Ask anyone and they would tell you that water is one of the most important resources for everybody. So why does nature need water? Fishes need water to swim in and lay eggs, plants need water to grow, and some organisms live solely in water and depend on the moisture to survive. Why do we need water? Water is important to help us live, regulate our body temperatures, and grow sex video.

Often viewed as muddy, smelly, mosquito-filled swamps, estuaries and their associated salt marshes and tidal flats are among the most productive habitats in the world. They are mixing zones, where freshwater, delivered by rivers and streams, flows into water from the sea. Animals and plants in this habitat must be able to tolerate wide ranges of salinity and temperature, as well as fluctuating water levels. Nutrient-rich estuaries protect and nurture a variety of shrimp, oysters, crabs, and fishes. Over 490 species of birds live in or migrate through the Coastal Bend of Texas, and many use the estuaries to feed, rest, and find shelter.

Seagrasses are plants that root, pollinate, and spend their entire lives submerged in shallow waters. Special adaptations allow for their survival in the fluctuating conditions of coastal bays and estuaries. The estuaries in the Coastal Bend of Texas contain 40% of Texas’ total seagrass acreage. Seagrasses provide oxygen, nutrients, anchorage, food, habitat, cover, and places for attachment.


Bay System Seagrass
Meadow Area* Area of
Bay Bottom* Percent Seagrass
Galveston Bay _____ 391 _____143,153 _____ _____
Matagorda Bay _____ 1,096 _____ 101,368 _____ _____
San Antonio Bay _____ 2,743 _____ 54,335 _____ _____
Aransas Bay _____ 2,455 _____ 47,267 _____ _____
Corpus Christi Bay _____ 5,249 _____ 43,550 _____ _____
Upper Laguna Madre _____ 24,900 _____ 33,100 _____ _____
Lower Laguna Madre _____ 48,200 _____ 68,400 _____ _____

* All measurements are in hectares.


The Texas bay systems above are listed in order from north to south. Use the measurements provided to calculate the percent seagrass coverage in each bay.
Rank the measurements in each category. Number one through seven from largest to smallest. Record the rankings in the blanks to the left of each measurement, including percent seagrass coverage.
Examine the rankings. Do you see any relationships between the measurements provided and percent seagrass coverage? How about location north and south? If, so, explain.

Seahorses are among the most unusual-looking animals in the world. Unlike most fishes, they lack the caudal, or tail, fin. Most fish species use the caudal fin to propel themselves through the water. Lacking that, the seahorse uses its dorsal and pectoral fins to propel itself.
The seahorse has a unique tail in that it is prehensile or grasping. Just as monkeys are able to use their prehensile tails to grasp and swing from trees, seahorses are able to use their tails to grasp seagrasses, algae, and other stationary objects.

Humans have thumbs which similarly allow them to grasp objects. This is one adaptation that has contributed to our ability to use tools and manipulate objects easily.


Gather a collection of at least ten tools and objects (screwdriver, hammer, coins, etc.).
Divide a sheet of paper into three long columns. List the tools and objects down the page in the first column. Label the second column “with thumb” and the third column “without thumb.”
Manipulate each tool and lift each object. Rate the effort required to perform each task on a scale of one to ten, with ten being very easy and one being very difficult. Write your rating in the second column.
Fold your thumb across your palm. Using the masking tape, tape your thumb in place.
Re-do each of the tasks that you performed earlier. Rate the difficulty of each task on the one to ten scale.
Compare your ratings with and without the use of your thumb. List other tasks that would be affected by the presence or absence of thumbs

NEAT GIN – North East Atlantic, Greenland-Iceland-Norwegian sea experiment

The NEAT GIN experiment took place during September-October 1989 at the Norwegian shelf edge near 68°N. Seven moorings, five in a closely-spaced cross-slope section, have proved a valuable precursor to the Shelf Edge Study (SES) west of Scotland. The NEAT GIN data analysis has now been completed.
A mean current (0.2-0.3 m/s) north-eastwards along the slope was found to be a predominant feature and is common to many locations around the north-west European shelf edge. The total transport was estimated to be 4 to 9 106m3/s, values at the upper end of the range of estimates from elsewhere around north-west Europe. Measurements near to the bottom showed slight anti-clockwise veering, consistent with the presence of a bottom Ekman layer.
Rotary motion, coherent down to about 300 m, made another large contribution to the total flow. Most energy occurred in periods exceeding 2 days (« day at the top of the slope). Comparisons with hindcast meteorological data showed little evidence of correlation between this rotary flow and the weather. Hence a stochastic source mechanism is suggested, eg. baroclinic instability.
Tidal analysis of the currents showed modest values; the M2 component was largest, about 0.05 m/s at the top of the slope in 200 m water depth, decreasing to about 0.03 m/s in the deeper waters on the slope. In comparison, tidal models of the region do not fully resolve the slope and exaggerate the increase of tidal currents in shallow water. Attempts to represent the diurnal tidal currents as a trapped wave also show this exaggeration. There was little evidence of internal-wave or internal-tide effects.
A significant finding for subsequent shelf-edge studies was a lateral coherence scale of about 10 km for the currents, comparable with the theoretical Rossby radius of deformation scaling eddies and internal features. This scale gives a basis for future array design. In the temperature field, however, smaller scales were evident from satellite imagery and appeared to contribute a large proportion of the variability. Consequently, a transport balance for temperature (heat) could not be constructed, although movements of the thermocline and changing temperature profiles suggested primarily advective contributions.
Fluctuating contributions to heat flux were calculated from the current meter and thermistor chain records. In common with other locations, eg. north-west of Scotland in 1982-83, these showed a principal contribution along the shelf (to the southwest, against the mean flow) and a small component.