Practical Guide to Measurement of these Waves

On the basis of the aforementioned disucssion, a step-by-step guide is provided on the method that should be applied when investigating these waves-Gravity Waves:

1. Compute inertial frequency for the latitude of the lake in question using eqn. [1].

2. Make a simple two-layer approximation to the stratification, and compute the equivalent water depth He using eqn. [4].

3. Compute the internal wave speed using c = VgHe. Typically this value will be between 0.1 and 0.3ms-1.

4. Compute the internal Rossby radius using eqn. [5].

5. Based on the dimension of the lake, compute the Burger number using eqn. [6]. If the lake is approximately circular, use the radius for the length-scale L. If the lake is approximately elliptical, use the major axes half-length for the length-scale L. If the Burger number is greater than 2, rotational effects will be minimal. If the Burger number is less than 1, rotational effects will be very important.

6. From Figure 4(a), read off the nondimensional frequency m/f for both the fundamental (lowest horizontal mode) cyclonic and anticyclonic wave for the aspect ratio of your lake.

7. Compute the angular frequency m from the non-dimensional frequency m/f and the inertial frequency f for each of these two fundamental modes.

8. Compute the period T of these two waves from T = 2 p/m.

9. Install measuring equipment (thermistor chain and/ or current meters) for a sufficient period to measure more than 10 cycles of each wave. For example, if T = 2 days, at least 20 days of measurement will be required to achieve significant confidence in the data analysis. The location of these instruments should be carefully selected and is nontrivial. Typically the best location is halfway between the lake center and the lake boundary. Multiple sampling points are generally necessary -if two stations are deployed they should not be placed 180° apart as the direction of propagation can not be determined. It is best to orient stations such that they are 45-135° offset.

10. Compute spectra of temperature signals, isotherm depths, or integrated potential energy to determine the dominant frequencies in the field.

11. Compute rotary spectra of currents to determine the dominant rotation direction.

12. Compute phase and coherence between stations to assist in determining rotation direction and spatial structure. This can be done graphically by simply overlaying signals from the two stations or by using spectral analysis techniques.

Vorticity Waves:

1. Compute inertial frequency for the latitude of the lake in question using eqn. [1].

2. Deploy current meters for many periods longer than the inertial period, typically several months of record will be required. Two stations are required at the minimum, as with gravity waves they should not be placed 180° apart. Current meters should be placed in both the upper and lower layer, away from the thermocline.

3. Compute spectra of current signals to determine dominant frequencies, whether these frequencies change as a function of stratification, and whether the upper and lower layer current structure differs.

Armed with this information, it should be possible to determine which waves are dominating the temperature and current signals. Going into greater detail would typically require the reader to conduct further reading.

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