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JONSWAP Spectrum for Fetch-limited Seas Formula

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Frequency Energy Spectrum refers to a representation of the distribution of energy across different frequencies within a system or environment. Check FAQs

E f = (\frac{α \cdot {[g]}^{2}}{{(2 \cdot π)}^{4} \cdot f^{5}}) \cdot {(\exp (- 1.25 \cdot {(\frac{f}{f p})}^{- 4}) \cdot γ)}^{\exp (- \frac{{((\frac{f}{f p}) - 1)}^{2}}{2 \cdot σ^{2}})}

E_f - Frequency Energy Spectrum?α - Dimensionless Scaling Parameter?f - Wave Frequency?f_p - Frequency at Spectral Peak?γ - Peak Enhancement Factor?σ - Standard Deviation?[g] - Gravitational acceleration on Earth?π - Archimedes' constant?

JONSWAP Spectrum for Fetch-limited Seas Example

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Here is how the JONSWAP Spectrum for Fetch-limited Seas equation looks like with Values.

Here is how the JONSWAP Spectrum for Fetch-limited Seas equation looks like with Units.

Here is how the JONSWAP Spectrum for Fetch-limited Seas equation looks like.

2.9E-22 = (\frac{0.1538 \cdot {9.8066}^{2}}{{(2 \cdot 3.1416)}^{4} \cdot 8^{5}}) \cdot {(\exp (- 1.25 \cdot {(\frac{8}{0.0132})}^{- 4}) \cdot 5)}^{\exp (- \frac{{((\frac{8}{0.0132}) - 1)}^{2}}{2 \cdot {1.33}^{2}})}

2.9E-22 = (\frac{0.1538 \cdot {9.8066m/s²}^{2}}{{(2 \cdot 3.1416)}^{4} \cdot {8kHz}^{5}}) \cdot {(\exp (- 1.25 \cdot {(\frac{8kHz}{0.0132kHz})}^{- 4}) \cdot 5)}^{\exp (- \frac{{((\frac{8kHz}{0.0132kHz}) - 1)}^{2}}{2 \cdot {1.33}^{2}})}

2.9E-22 = (\frac{0.1538 \cdot {9.8066}^{2}}{{(2 \cdot 3.1416)}^{4} \cdot 8^{5}}) \cdot {(\exp (- 1.25 \cdot {(\frac{8}{0.0132})}^{- 4}) \cdot 5)}^{\exp (- \frac{{((\frac{8}{0.0132}) - 1)}^{2}}{2 \cdot {1.33}^{2}})}

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JONSWAP Spectrum for Fetch-limited Seas Solution

Follow our step by step solution on how to calculate JONSWAP Spectrum for Fetch-limited Seas?

FIRST Step Consider the formula

E f = (\frac{α \cdot {[g]}^{2}}{{(2 \cdot π)}^{4} \cdot f^{5}}) \cdot {(\exp (- 1.25 \cdot {(\frac{f}{f p})}^{- 4}) \cdot γ)}^{\exp (- \frac{{((\frac{f}{f p}) - 1)}^{2}}{2 \cdot σ^{2}})}

Next Step Substitute values of Variables

∴

E f = (\frac{0.1538 \cdot {[g]}^{2}}{{(2 \cdot π)}^{4} \cdot {8kHz}^{5}}) \cdot {(\exp (- 1.25 \cdot {(\frac{8kHz}{0.0132kHz})}^{- 4}) \cdot 5)}^{\exp (- \frac{{((\frac{8kHz}{0.0132kHz}) - 1)}^{2}}{2 \cdot {1.33}^{2}})}

Next Step Substitute values of Constants

∴

E f = (\frac{0.1538 \cdot {9.8066m/s²}^{2}}{{(2 \cdot 3.1416)}^{4} \cdot {8kHz}^{5}}) \cdot {(\exp (- 1.25 \cdot {(\frac{8kHz}{0.0132kHz})}^{- 4}) \cdot 5)}^{\exp (- \frac{{((\frac{8kHz}{0.0132kHz}) - 1)}^{2}}{2 \cdot {1.33}^{2}})}

Next Step Convert Units

∴

E f = (\frac{0.1538 \cdot {9.8066m/s²}^{2}}{{(2 \cdot 3.1416)}^{4} \cdot {8000Hz}^{5}}) \cdot {(\exp (- 1.25 \cdot {(\frac{8000Hz}{13.162Hz})}^{- 4}) \cdot 5)}^{\exp (- \frac{{((\frac{8000Hz}{13.162Hz}) - 1)}^{2}}{2 \cdot {1.33}^{2}})}

Next Step Prepare to Evaluate

∴

E f = (\frac{0.1538 \cdot {9.8066}^{2}}{{(2 \cdot 3.1416)}^{4} \cdot 8000^{5}}) \cdot {(\exp (- 1.25 \cdot {(\frac{8000}{13.162})}^{- 4}) \cdot 5)}^{\exp (- \frac{{((\frac{8000}{13.162}) - 1)}^{2}}{2 \cdot {1.33}^{2}})}

Next Step Evaluate

∴

E f = 2.89619819293977E-22

LAST Step Rounding Answer

∴

E f = 2.9E-22

JONSWAP Spectrum for Fetch-limited Seas Formula Elements

Variables

Constants

Functions

Frequency Energy Spectrum

Frequency Energy Spectrum refers to a representation of the distribution of energy across different frequencies within a system or environment.

Symbol: E_f

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Frequency Energy Spectrum

Dimensionless Scaling Parameter

Dimensionless Scaling Parameter is a value used in mathematical or scientific models to scale or normalize variables without units. It is used in the JONSWAP spectrum for fetch-limited seas.

Symbol: α

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Dimensionless Scaling Parameter

Wave Frequency

Wave Frequency is the number of waves that pass a fixed point in a given amount of time.

Symbol: f

Measurement: FrequencyUnit: kHz

Note: Value should be greater than 0.

Formulas to find Wave Frequency

Frequency at Spectral Peak

Frequency at Spectral Peak is the number of occurrences of a repeating event per unit of time.

Symbol: f_p

Measurement: FrequencyUnit: kHz

Note: Value can be positive or negative.

Formulas to find Frequency at Spectral Peak

Peak Enhancement Factor

Peak Enhancement Factor is a ratio used to quantify the increase in force or load experienced by a structure during extreme events, such as storms or earthquakes.

Symbol: γ

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Peak Enhancement Factor

Standard Deviation

Standard Deviation is a statistical measure used to quantify the amount of variation or dispersion of a set of data points from the mean (average).

Symbol: σ

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Standard Deviation

Gravitational acceleration on Earth

Gravitational acceleration on Earth means that the velocity of an object in free fall will increase by 9.8 m/s2 every second.

Symbol: [g]

Value: 9.80665 m/s²

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

exp

n an exponential function, the value of the function changes by a constant factor for every unit change in the independent variable.

Syntax: exp(Number)

Other formulas in Parametric Spectrum Models category

Go Phillip's Equilibrium Range of Spectrum for Fully Developed Sea in Deep Water

E ω = b \cdot {[g]}^{2} \cdot ω^{- 5}

Go Frequency at Spectral Peak

f p = 3.5 \cdot {(\frac{{[g]}^{2} \cdot F l}{{V 10}^{3}})}^{- 0.33}

Go Fetch Length given Frequency at Spectral Peak

F l = \frac{({V 10}^{3}) \cdot ({(\frac{f p}{3.5})}^{- (\frac{1}{0.33})})}{{[g]}^{2}}

Go Wind Speed at Elevation 10m above Sea Surface given Frequency at Spectral Peak

V = {(\frac{F l \cdot {[g]}^{2}}{{(\frac{f p}{3.5})}^{- (\frac{1}{0.33})}})}^{\frac{1}{3}}

How to Evaluate JONSWAP Spectrum for Fetch-limited Seas?

JONSWAP Spectrum for Fetch-limited Seas evaluator uses Frequency Energy Spectrum = ((Dimensionless Scaling Parameter*[g]^2)/((2*pi)^4*Wave Frequency^5))*(exp(-1.25*(Wave Frequency/Frequency at Spectral Peak)^-4)*Peak Enhancement Factor)^exp(-((Wave Frequency/Frequency at Spectral Peak)-1)^2/(2*Standard Deviation^2)) to evaluate the Frequency Energy Spectrum, The JONSWAP Spectrum for Fetch-limited Seas is defined as a situation in which wave energy (or wave height) is limited by the size of the wave generation area (fetch). Frequency Energy Spectrum is denoted by E_f symbol.

How to evaluate JONSWAP Spectrum for Fetch-limited Seas using this online evaluator? To use this online evaluator for JONSWAP Spectrum for Fetch-limited Seas, enter Dimensionless Scaling Parameter (α), Wave Frequency (f), Frequency at Spectral Peak (f_p), Peak Enhancement Factor (γ) & Standard Deviation (σ) and hit the calculate button.

FAQs on JONSWAP Spectrum for Fetch-limited Seas

What is the formula to find JONSWAP Spectrum for Fetch-limited Seas?

The formula of JONSWAP Spectrum for Fetch-limited Seas is expressed as Frequency Energy Spectrum = ((Dimensionless Scaling Parameter*[g]^2)/((2*pi)^4*Wave Frequency^5))*(exp(-1.25*(Wave Frequency/Frequency at Spectral Peak)^-4)*Peak Enhancement Factor)^exp(-((Wave Frequency/Frequency at Spectral Peak)-1)^2/(2*Standard Deviation^2)). Here is an example- 2.9E-22 = ((0.1538*[g]^2)/((2*pi)^4*8000^5))*(exp(-1.25*(8000/13.162)^-4)*5)^exp(-((8000/13.162)-1)^2/(2*1.33^2)).

How to calculate JONSWAP Spectrum for Fetch-limited Seas?

With Dimensionless Scaling Parameter (α), Wave Frequency (f), Frequency at Spectral Peak (f_p), Peak Enhancement Factor (γ) & Standard Deviation (σ) we can find JONSWAP Spectrum for Fetch-limited Seas using the formula - Frequency Energy Spectrum = ((Dimensionless Scaling Parameter*[g]^2)/((2*pi)^4*Wave Frequency^5))*(exp(-1.25*(Wave Frequency/Frequency at Spectral Peak)^-4)*Peak Enhancement Factor)^exp(-((Wave Frequency/Frequency at Spectral Peak)-1)^2/(2*Standard Deviation^2)). This formula also uses Gravitational acceleration on Earth, Archimedes' constant and Exponential Growth (exp) function(s).

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JONSWAP Spectrum for Fetch-limited Seas Formula

JONSWAP Spectrum for Fetch-limited Seas Example

JONSWAP Spectrum for Fetch-limited Seas Solution

JONSWAP Spectrum for Fetch-limited Seas Formula Elements

Other formulas in Parametric Spectrum Models category

How to Evaluate JONSWAP Spectrum for Fetch-limited Seas?

FAQs on JONSWAP Spectrum for Fetch-limited Seas

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