scholarly journals A SIMPLE MATHEMATICAL MODEL OP WAVE MOTION ON A RUBBLE MOUND BREAKWATER FRONT

1966 ◽  
Vol 1 (10) ◽  
pp. 56 ◽  
Author(s):  
Anton Brandtzaeg ◽  
Alf Torum
Keyword(s):  
Mathematical Model ◽  
Mexico City ◽  
Linear Relation ◽  
Water Surface ◽  
Wave Motion ◽  
Wave Steepness ◽  
Simple Mathematical Model ◽  
Order Of Magnitude ◽  
Rubble Mound

This paper is a continuation of a paper under the same title, presented at the Vlllth Conference in Mexico City, 1962, where a mathematical model was proposed, intended to give a rough idea of the order of magnitude of velocities and accelerations in the downrushmg wave on a rubble mound breakwater front. Here observations of 85 individual waves of various dimensions are presented and compared with the formulae derived from the model. Considerable scatter is evident, but it is concluded that the model does correspond roughly to the actual displacements of the water surface during downrush, and therefore may be expected to give useful indications also of velocities and accelerations. The importance of the slope of the surface is emphasized, and, within the scope of the tests, this slope seems to stand in linear relation to the wave steepness.

scholarly journals A SIMPLE MATHEMATICAL MODEL OF WAVE MOTION ON A RUBBLE MOUND BREAKWATER SLOPE

2011 ◽  
Vol 1 (8) ◽  
pp. 26
Author(s):  
Anton Brandtzaeg
Keyword(s):  
Mathematical Model ◽  
Wave Motion ◽  
Point Of View ◽  
Glass Panel ◽  
Wave Channel ◽  
First Approximation ◽  
Rubble Mound ◽  
The Stability ◽  
Rubble Mound Breakwaters ◽  
Made In

In the improvement of design criteria for the layer of cover blocks on rubble mound breakwaters important advance has been made in recent years (l), (2), (3). Still, some points seem to require further study, among them the effect of the specific weights of block material and fluid on the stability of the cover. In this respect the magnitude of the fluid accelerations involved, of which little information is available may be of some importance. For evaluation of the acceleratic as well as for other purposes, a roughly approximate mathematic description of the motion of the water rushing up and down the breakwater front may be of some use. This motion certainly is neither steady nor uniform. Visual and photographic observation through the glass panel a wave channel seems to indicate, however, that unsteadiness the more important characteristic of the motion during the up and downrush proper. It seems reasonable, therefore, to att€ a first approximation to a description of the motion by neglecting, to a certain extent, its non-uniformity. Necessarily, the same time also the requirement of continuity must be partly disregarded. In the following a mathematical model based on this point of view is presented for consideration. It is believed that by means of this model values of displacements, velocity and accelerations can be calculated, which may reasonably be considered as useful, although quite rough, approximations t< the actual values. For a few particular cases, experimental evidence is reported. The model has reference only to the up- and downrush proper, that is, to the motion of the water above some limit level, at or somewhat below the Still Water Line (referred t< hereafter as the StflL). The motion below this level, where tl downrush meets the oncoming next wave, could hardly be conee of as being uniform.

scholarly journals A simple mathematical model that describes the growth of the area and the number of total and viable cells in yeast colonies

2014 ◽  
Vol 59 (6) ◽  
pp. 594-603 ◽  
Author(s):  
E.-M. Rivas ◽  
E. Gil de Prado ◽  
P. Wrent ◽  
M.-I. de Silóniz ◽  
P. Barreiro ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Simple Mathematical Model ◽  
Viable Cells
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