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Table 2 The horizontal wavenumber, wavelength, and group speed for the M2 constituent (period = 12.42 h; ω = 1.405 × 10−4 s−1) in a water depth of 500 m and an upper layer thickness of 200 m at 32.5° N, following the equations in Table 1

From: An evaluation of the performance of vertical mixing parameterizations for tidal mixing in the Regional Ocean Modeling System (ROMS)

Wave type

Mode

k (m−1)

λH (km)

cg (m s−1)

Two-layer interfacial wave: over

1.6 × 106

618

43

Two-layer interfacial wave: finite over : barotropic

2.0 × 10−9

490,000

34,900

Two-layer interfacial wave: finite over : baroclinic shallow water

6.4 × 10−5

16

2.2

Continuous stratification without rotation

1

5.7 × 10−5

18

2.5

2

1.1 × 10−4

9

1.2

Continuous stratification with rotation

1

4.7 × 10−5

21

2.1

2

9.4 × 10−5

11

1.0

Barotropic Kelvin wave

2.0 × 10−6

498

70

Baroclinic Kelvin wave

6.3 × 10−5

16

2.2

Barotropic Poincaré wave

1.7 × 10−6

600

58

Baroclinic Poincaré wave

1

4.7 × 10−5

21

2.1

2

9.4 × 10−5

11

1.0

Shallow water surface gravity wave

2.0 × 10−6

498

70

Deep water surface gravity wave

2.1 × 10−9

496,000

34,900

  1. The mode 1 wavelength is 1000 m and the mode 2 is 500 m. Italics numbers indicate wavelengths that are resolvable in the simulations. Unrealistic waves due to wavelengths exceeding Earth’s circumference have been struck through