**5. Theoretical study**

The increased concern with riverbank erosion has increased the demand for theoretical models that can predict flow and bed features in a meandering alluvial channel where the flow in such a channel is complex than that in a straight channel in the nature.

In order to plan, design, construct, or maintain bank-erosion control structures and river-basin projects in general, the meander characteristics must be quantified by the point bar and deep pool bed topography near the apex of each bend [1]. The relations for depth and depth-averaged mean velocity are developed using standard flow equations with simplifications in the theory of river plume in sedimentladen rivers.

Clouds, shapes of mountains, clouds, trees, stars and the flood of rivers, river meanders were of the old concerns of human which are interested in searching behind the universe and cosmos, motion of planets, ocean waves, the structure and dynamics of the universe by the scientists. Checking behind the seemingly complex

**89**

*River Plume in Sediment-Laden Rivers*

*DOI: http://dx.doi.org/10.5772/intechopen.90089*

with the behavior of the complex dynamic theories.

and adapt to the surrounding environment of nature.

object that is chaotic in space is called fractal."

**6. Discussion**

and civil engineering.

are complex ones.

algorithmic rules generate the fractal-rich structures.

from Venturis' ideas for architects to fractal in architecture.

and self-organized universe was introduced by mathematicians.

conical, river meanders are not circle and barks are not smooth, etc.

and chaotic nature of universe resulted in the emergence of chaos and complexity sciences. Fractal, chaos, catastrophe, and complexity theories are all concerned

The complex theoretical study of complexity was named edge of chaos that is a middle area between static and chaotic behavior of the natural systems where the complexity science is interested by the dynamic system means that change by time. It is interested in how disorder gives way to order in reality. This theory studies the interaction between elements of complex system and subsystems, which is not about the sum of its agents but the relationship between parts and how they interact

With the difficulty of the complexity theory, the notion of nonlinear, feedback,

Here, the bottoms-up concept of organization replaced the machine-oriented ideas: that structure is designed into the system. This new theory was introduced by the mathematician Benoit Mandelbrot in the 1970s to explain the complexity of the systems, which are explained as follows: clouds are not spherical, mountains are not

When the development of the nonlinear complex system behavior was given, it will take a geometrical mathematical form whose shape is geometrically fractal "an

This new geometry is an extension of the classical geometry; it's a practical geometric middle ground between the extreme order of Euclidean geometry and the geometric chaos of general scientists. Discrete mathematics is the core foundation of fractal and fractal geometry where algorithms create the magic and simple

Theory of emergence, self-organization, evolution, and cosmogenesis rejected the concepts of determination, mechanism, reductivism, and materialism whose shift in thought had been reflected on engineers and architectures as well starting

These views of complexity appear to be contradicting and rejecting modernism concepts in civil engineering, which is refused the plainer, clean, white architecture of modernism; instead, his ideas were directed to the indirect engineering meanings, forms, and compositions that satisfy the mind. Chaotic theory makes one think how things are put together; it takes time to be perceived and decoded. What chaotic theory was aiming for in civil engineers was actually found in the characteristics of fractal whose geometry plays an integral role between natures' complexity

In civil engineering, starting from design views in 1960s through the postmodernism movement and till the digital age, engineers have started to design iconic

The modernism perception of ornament is a crime was changed for the sake of nature. Where thoughts of ornaments as expensive decoration and it is a crime for the economy, waste of raw material and manpower. New thoughts were rejected and postmodernists returned to think about nature where they agreed that nature is the regulator morphology of the universe patterns and of the earth's surface occurrences. Nature is the source of patterns and the most which

In the new area with the use of computers, architects tend to create computergenerated natural occurrences and organizational patterns where the natural

cosmo-related works as it is called tending to be esthetically attractive.

#### *River Plume in Sediment-Laden Rivers DOI: http://dx.doi.org/10.5772/intechopen.90089*

*Current Practice in Fluvial Geomorphology - Dynamics and Diversity*

*Both the ht-index and fractal dimensions, characterizing fractals from different perspectives [4].*

**88**

**Figure 5.**

**Figure 4.**

in the nature.

laden rivers.

*Sierpinski triangles and Koch curve [7].*

The increased concern with riverbank erosion has increased the demand for theoretical models that can predict flow and bed features in a meandering alluvial channel where the flow in such a channel is complex than that in a straight channel

In order to plan, design, construct, or maintain bank-erosion control structures and river-basin projects in general, the meander characteristics must be quantified by the point bar and deep pool bed topography near the apex of each bend [1]. The relations for depth and depth-averaged mean velocity are developed using standard flow equations with simplifications in the theory of river plume in sediment-

Clouds, shapes of mountains, clouds, trees, stars and the flood of rivers, river meanders were of the old concerns of human which are interested in searching behind the universe and cosmos, motion of planets, ocean waves, the structure and dynamics of the universe by the scientists. Checking behind the seemingly complex

**5. Theoretical study**

and chaotic nature of universe resulted in the emergence of chaos and complexity sciences. Fractal, chaos, catastrophe, and complexity theories are all concerned with the behavior of the complex dynamic theories.

The complex theoretical study of complexity was named edge of chaos that is a middle area between static and chaotic behavior of the natural systems where the complexity science is interested by the dynamic system means that change by time.

It is interested in how disorder gives way to order in reality. This theory studies the interaction between elements of complex system and subsystems, which is not about the sum of its agents but the relationship between parts and how they interact and adapt to the surrounding environment of nature.

With the difficulty of the complexity theory, the notion of nonlinear, feedback, and self-organized universe was introduced by mathematicians.

Here, the bottoms-up concept of organization replaced the machine-oriented ideas: that structure is designed into the system. This new theory was introduced by the mathematician Benoit Mandelbrot in the 1970s to explain the complexity of the systems, which are explained as follows: clouds are not spherical, mountains are not conical, river meanders are not circle and barks are not smooth, etc.

When the development of the nonlinear complex system behavior was given, it will take a geometrical mathematical form whose shape is geometrically fractal "an object that is chaotic in space is called fractal."

This new geometry is an extension of the classical geometry; it's a practical geometric middle ground between the extreme order of Euclidean geometry and the geometric chaos of general scientists. Discrete mathematics is the core foundation of fractal and fractal geometry where algorithms create the magic and simple algorithmic rules generate the fractal-rich structures.
