Logarithmic Spiral Beaches
Encyclopedia
A logarithmic spiral beach is a type of beach
which develops in the direction under which it is sheltered by a headland, in an area called the shadow zone. It is characterized as a logarithmic spiral
because if you look at it in plan view or aerially, it represents the same shape that is created from the logarithmic spiral
function. These beaches are also commonly referred to as ‘zeta cure bays’, ‘half heart’ or ‘crenulate’ shaped bays, or ‘headland bays’.
r = eθcotα
where:
θ = the angle of rotation, is located between two lines drawn from the origin to any two points on the spiral.
r = the ratio of the lengths between two lines that extend out from the origin. The two lines are given as RO and R.
So r also equals the ratio R/RO.
α = the angle between any line R from the origin and the line tangent to the spiral which is at the point where line R intersects the spiral.
α is a constant for any given logarithmic spiral.
of approaching waves and their diffraction
by an upcoast headland
. The approaching wave front curves as a result of wave diffraction at the headland, which in turn causes the shoreline to bend and yield a log spiral shape. Log spiral beaches are often on swell
-dominated coasts where waves generally approach the shoreline from one main direction at an oblique angle. The oblique approaching waves refract and diffract into the "shadow zone" which can be considered a relatively sheltered hook of beach behind the headland. Increase in sediment
size, wave height, berm
height, and swash
zone gradient from the up coast headland generally characterizes the concave seaward curved part of the beach.
Beach
A beach is a geological landform along the shoreline of an ocean, sea, lake or river. It usually consists of loose particles which are often composed of rock, such as sand, gravel, shingle, pebbles or cobblestones...
which develops in the direction under which it is sheltered by a headland, in an area called the shadow zone. It is characterized as a logarithmic spiral
Logarithmic spiral
A logarithmic spiral, equiangular spiral or growth spiral is a special kind of spiral curve which often appears in nature. The logarithmic spiral was first described by Descartes and later extensively investigated by Jacob Bernoulli, who called it Spira mirabilis, "the marvelous...
because if you look at it in plan view or aerially, it represents the same shape that is created from the logarithmic spiral
Logarithmic spiral
A logarithmic spiral, equiangular spiral or growth spiral is a special kind of spiral curve which often appears in nature. The logarithmic spiral was first described by Descartes and later extensively investigated by Jacob Bernoulli, who called it Spira mirabilis, "the marvelous...
function. These beaches are also commonly referred to as ‘zeta cure bays’, ‘half heart’ or ‘crenulate’ shaped bays, or ‘headland bays’.
Logarithmic spiral function
The logarithmic spiral can be determined using the equation (written in polar coordinates):r = eθcotα
where:
θ = the angle of rotation, is located between two lines drawn from the origin to any two points on the spiral.
r = the ratio of the lengths between two lines that extend out from the origin. The two lines are given as RO and R.
So r also equals the ratio R/RO.
α = the angle between any line R from the origin and the line tangent to the spiral which is at the point where line R intersects the spiral.
α is a constant for any given logarithmic spiral.
Spiral development
This type of beach forms due to the refractionRefraction
Refraction is the change in direction of a wave due to a change in its speed. It is essentially a surface phenomenon . The phenomenon is mainly in governance to the law of conservation of energy. The proper explanation would be that due to change of medium, the phase velocity of the wave is changed...
of approaching waves and their diffraction
Diffraction
Diffraction refers to various phenomena which occur when a wave encounters an obstacle. Italian scientist Francesco Maria Grimaldi coined the word "diffraction" and was the first to record accurate observations of the phenomenon in 1665...
by an upcoast headland
Headland
A headland is a point of land, usually high and often with a sheer drop, that extends out into a body of water.Headland can also refer to:*Headlands and bays*headLand, an Australian television series...
. The approaching wave front curves as a result of wave diffraction at the headland, which in turn causes the shoreline to bend and yield a log spiral shape. Log spiral beaches are often on swell
Swell
Swell may refer to:*Swell , a formation of long wavelength ocean surface waves*Swell , an indie rock band from San Francisco*Swell, Gloucestershire, England*Swell , a term in bookbinding...
-dominated coasts where waves generally approach the shoreline from one main direction at an oblique angle. The oblique approaching waves refract and diffract into the "shadow zone" which can be considered a relatively sheltered hook of beach behind the headland. Increase in sediment
Sediment
Sediment is naturally occurring material that is broken down by processes of weathering and erosion, and is subsequently transported by the action of fluids such as wind, water, or ice, and/or by the force of gravity acting on the particle itself....
size, wave height, berm
Berm
A berm is a level space, shelf, or raised barrier separating two areas. Berm originates in the Middle Dutch and German berme and came into usage in English via French.- History :...
height, and swash
Swash
Swash, in geography, is a turbulent layer of water that washes up on the beach after an incoming wave has broken. The swash action can move beach material up and down on the beach, which results in the cross-shore sediment exchange. The time-scale of swash motion varies from seconds to minutes...
zone gradient from the up coast headland generally characterizes the concave seaward curved part of the beach.
Famous logarithmic spiral beaches
- Birch Bay, WashingtonBirch Bay, Washington-External links:*...
, USA - Restinga Beach, Isla Margarita, Venezuel
- Half Moon Bay, CaliforniaHalf Moon Bay, CaliforniaHalf Moon Bay is a coastal city in San Mateo County, California, USA. Its population was 11,324 as of the 2010 census. Immediately at the north of Half Moon Bay is the Pillar Point Harbor and the unincorporated community of Princeton-by-the-Sea....
, USA - Pearl Beach, New South WalesPearl Beach, New South WalesPearl Beach is a suburb of Gosford City on the Central Coast of New South Wales, Australia. Pearl Beach was assigned 'suburb' status by the Geographical Names Board of NSW on the 25th October 1991.-History:...
, Australia