By Jochen Kämpf

This ebook introduces the reader to complex tools utilized in the computer-based modelling of fluid tactics. This comprises nonhydrostatic methods akin to breaking inner waves and density-driven convection, however the version code is usually used to simulate an El-Niño occasion! The booklet includes 25 functional workouts, utilizing freely to be had Open-Source software program suites, that are everyday via the clinical group. during this booklet, the artwork of hydrodynamic modelling is made to be had and obvious to a much broader readership. an enticing byproduct of the booklet is that effects are animations instead of nonetheless pictures. version codes and animation scripts for all routines are provided on an internet site. The reader can undertake version codes for personal self sufficient studies

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**Sample text**

In a first consideration, the existence of a sea surface is ignored, assuming an ocean of infinite vertical extent. g. Cushman-Roisin, 1994): σ = 2π = ±N cos θ T where T is wave period and θ is the angle between the direction of wave propagation and the horizontal plane (Fig. 18). 8 Internal Waves 45 which implies purely horizontal propagation. This corresponds to the period of oscillations experienced by a buoyant object in a stratified fluid (see Sect. 10 of K¨ampf (2009)). Consequently, such internal waves propagate at a phase speed of: c= λN cos (θ) λ =± T 2π where λ is the wavelength.

In contrast to this, coordinate surfaces in σ -coordinate models follow the sea floor. The σ -coordinate is defined by: σ = ho + z ho + η where z is the Cartesian vertical coordinate, h o is undisturbed water depth, and η is sea-surface elevation. Accordingly, σ varies from zero at the sea floor to unity at the sea surface. Note that σ -coordinates respond to fluctuations of the sea level. Hydrodynamic models based on σ -coordinates are suitable for coastal applications, but steep bottom slopes can cause substantial truncation errors.

Both lateral boundaries are closed. 9 Exercise 5: Internal Waves 47 Fig. 20 Initial density distribution (shading and contours) and bathymetry for Exercise 5 near the left boundary (Fig. 20). 1 s−1 . Surface density is set to ρs = 1,028 kg/m3 . The minimum period of internal waves according to Eq. 54) is about 63 s. Such a strong density stratification does rarely exist in the ocean. The sole purpose here is to minimise the total simulation time whilst capturing about 10 wave periods. An initial density disturbance is added in the centre of the model domain over a width of 25 m (five adjacent grid cells).