Empirical relation between Hs and Tav

[aboobacker]

Hi,

Is there any relation between Significant wave height(Hs) and Mean wave period (Tav)?

If anybody knows, please give me the formulae and its reference.

Thank you

[bpkumar]

Dear Aboobacker:

The following answers to your query:

In the later stage of the first generation and mid of second generation wave modeling efforts, numerous empirical relations based on nomograms were generated, notably manual methods of SMB and PNJ in wave prediction were routinely used. Apart from these, formulation by Bretschneider and Wilson were also being used. However the non-dimensional fetch (X) could be expressed as function of wave parameters. As these nomograms could not provide basic information on wave direction, which was considered essentially useful the applicability of these methods were out of limelight. These methods were used as thumbrules to derive the wave parameters related to wave height and period (where fetch limited and duration limited cases were taken into consideration).

After the advent of the spectral energy balance equation, where wave energy could be expressed conveniently as function of frequency, direction both of which are dependent variables; position and time are independent variables, all essential wave information could be derived based on statistics. As wave energy is a function of frequency, area under the one-dimensional wave spectrum (viz; P-M, JONSWAP,.... etc) essentially is an integrated way of representing energy as a function of frequency. Models like WAM, SWAN etc. computes the net energy (contribution resulting from combination of wind-waves and swells) which can be later used to derive essential wave parameters like sig. wave height, mean wave period etc.

Since you are looking into an empirical related formulation, hope the following helps. There is an attachment file named "relation.pdf" where different formulations are given for finite depth.


Fitzpatrick proposed a wind wave height relation of the form:

H_s=(0.283U)/g)*(tanh(0.530(gd/U)0.75))*(tanh((0.0125(gF/_U)0.42)/(tanh(0.530(gd/U)0.75))))

where Hs is the significant wave height, U the wind speed, F the fetch length, d the water depth, and g the acc. due to gravity. The units are in FPS system.

Using the SMB approach, the period T can be estimated : gT/2*pi*U

Using this method, the result matches close with the SMB formulation.

Hope this helps.

Prasad K. Bhaskaran
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Dr.Prasad Kumar Bhaskaran
Assistant Professor
Dept. of Ocean Engineering & Naval Architecture
Indian Institute of Technology, Kharagpur
Kharagpur - 721 302
INDIA

Tel: +91-3222-283772 (work)
+91-3222-283773 (home)
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Seymour, R.J. "Estimating Wave Generation in Restricted Fetches", J. ASME WW2, May 1977, pp251-263