On resonance of an offshore channel bounded by a reef

1981 ◽  
Vol 32 (6) ◽  
pp. 833 ◽  
Author(s):  
VT Buchwald ◽  
JW Miles
Keyword(s):  
Wave Equations ◽  
Amplification Factor ◽  
Dominant Mode ◽  
Two Dimensional ◽  
Barrier Reef ◽  
Reef Lagoon ◽  
Long Wave ◽  
Frictional Damping ◽  
Linear Friction ◽  
Western Australian

The period and amplification factor for the dominant mode in a channel formed by the shore and a submerged parallel reef (which separates the channel from deeper water) are calculated from the two- dimensional long-wave equations with linear friction. Results are obtained for both narrow and wide reefs and are compared with observed oscillations on the Western Australian coast and on the Barrier Reef. Although the calculated periods might explain the anomalous tides in the Barrier Reef lagoon. it seems that there is sufficient frictional damping to prevent the required amplification.

The two-dimensional flow oscillations of a fluid in a spindle-shaped basin; application to Port Kembla Outer Harbour, N. S. W., Australia

1972 ◽  
Vol 23 (1) ◽  
pp. 1 ◽  
Author(s):  
DJ Clarke ◽  
ND Thomas
Keyword(s):  
Amplification Factor ◽  
Resonant Mode ◽  
Two Dimensional ◽  
Storm Activity ◽  
Long Wave ◽  
Model Study ◽  
Study Results ◽  
Two Dimensional Flow ◽  
History Of ◽  
Flow Oscillations

Port Kembla Outer Harbour has a history of severe ranging during storm activity, and hence a knowledge of its resonant behaviour is a necessary requirement towards understanding the cause of the range action. The Harbour has been shown to be suitably approximated by a spindle shape, which is the name given by Hidaka (1931) to a basin whose surface perimeter is defined as the intersection of two confocal parabolae. In this paper Hidaka's results are enlarged, more basic harmonics being found. These are then applied to the Outer Harbour which is assumed to be excited by a fully formed clapotis with an antinode at the entrance. The two particular harmonics which are most likely to be excited are found to have the same period of 153 sec. Experimental evidence has given long wave periods in the Harbour as 150 and 160 sec. The resonant mode corresponding to a period of 54 sec is found to have a large amplification factor at the entrance to the Inner Harbour, and this may be compared with model study results where at 56-58 sec the range action is greatest.

The influence of two-dimensional temperature modulation on nonlinear Marangoni waves in two-layer films

2018 ◽  
Vol 846 ◽  
pp. 944-965 ◽  
Author(s):  
Alexander A. Nepomnyashchy ◽  
Ilya B. Simanovskii
Keyword(s):  
Nonlinear Dynamics ◽  
Wave Equations ◽  
Flow Regimes ◽  
Solid Substrate ◽  
Temperature Modulation ◽  
Two Dimensional ◽  
Periodic Flows ◽  
Long Wave ◽  
Nonlinear Simulations ◽  
Time Periodic

The nonlinear dynamics of waves generated by the deformational oscillatory Marangoni instability in a two-layer film under the action of a two-dimensional temperature modulation on the solid substrate is considered. A system of long-wave equations governing the deformations of the upper surface and the interface between the liquids is presented. The long-wave approach is applied. The nonlinear simulations reveal the existence of different dynamic regimes, including stationary, time-periodic and quasi-periodic flows. The general diagrams of the flow regimes are constructed.

The Generalisation of Integrable (2+1)-Dimensional Dispersive Long-Wave Equations

1997 ◽  
Vol 66 (5) ◽  
pp. 1288-1290 ◽  
Author(s):  
Thangavel Alagesan ◽  
Ambigapathy Uthayakumar ◽  
Kuppusamy Porsezian
Keyword(s):  
Wave Equations ◽  
Long Wave

scholarly journals Global existence, energy decay and blow-up of solutions for wave equations with time delay and logarithmic source

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Sun-Hye Park
Keyword(s):  
Time Delay ◽  
Global Existence ◽  
Wave Equations ◽  
Blow Up ◽  
Logarithmic Sobolev Inequality ◽  
Decay Rates ◽  
Infinite Time ◽  
Global Existence Of Solutions ◽  
Frictional Damping ◽  
T Tau

AbstractIn this paper, we study the wave equation with frictional damping, time delay in the velocity, and logarithmic source of the form $$ u_{tt}(x,t) - \Delta u (x,t) + \alpha u_{t} (x,t) + \beta u_{t} (x, t- \tau ) = u(x,t) \ln \bigl\vert u(x,t) \bigr\vert ^{\gamma } . $$ u t t ( x , t ) − Δ u ( x , t ) + α u t ( x , t ) + β u t ( x , t − τ ) = u ( x , t ) ln | u ( x , t ) | γ . There is much literature on wave equations with a polynomial nonlinear source, but not much on the equations with logarithmic source. We show the local and global existence of solutions using Faedo–Galerkin’s method and the logarithmic Sobolev inequality. And then we investigate the decay rates and infinite time blow-up for the solutions through the potential well and perturbed energy methods.

Water quality in the inshore Great Barrier Reef lagoon: Implications for long-term monitoring and management

2012 ◽  
Vol 65 (4-9) ◽  
pp. 249-260 ◽  
Author(s):  
Britta Schaffelke ◽  
John Carleton ◽  
Michele Skuza ◽  
Irena Zagorskis ◽  
Miles J. Furnas
Keyword(s):  
Water Quality ◽  
Great Barrier Reef ◽  
Barrier Reef ◽  
Reef Lagoon ◽  
Long Term Monitoring ◽  
Term Monitoring ◽  
Inshore Great Barrier Reef
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