Between Waves

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Between Waves is a Canadian psychological thriller film, directed by Virginia Abramovich and released in 2020.[1] The film stars Fiona Graham as Jamie, a photographer from Toronto whose partner Isaac (Luke Robinson), a quantum physicist who was researching the concept of travel between parallel dimensions, turns up dead, and Jamie then begins to see visions of him claiming that he succeeded in his research and imploring her to go through with their planned trip to São Miguel Island so that she can join him.[2]

To understand tsunamis, it is helpful to understand how they are different from the familiar ocean waves one might see when standing on a beach. Even though tsunamis and these other ocean waves have the same basic anatomy, they are really quite different.

One key difference is that tsunamis move through the entire water column, the full depth of the ocean - from the ocean surface to the ocean floor - while other ocean waves only affect the near-surface layer of the ocean. This is because of how they are generated.

Waves are caused by the transfer of energy from their source to the ocean.Tsunamis are generated by large and sudden displacements of the ocean, usually caused by an earthquake below or near the ocean floor. Most other ocean waves are caused by wind blowing over the water (wind waves). Typical tsunami sources, like earthquakes, can generate more energy than the wind.

Waves are typically described based on three basic characteristics: wavelength (horizontal distance between wave crests), period (time between wave crests), and speed. Additional differences between tsunamis and wind waves can be seen by examining these characteristics for the two types of waves.

Wind waves have short wavelengths, which are measured in feet, and they can be seen arriving at the shore every few seconds. In contrast, tsunamis have very long wavelengths that are measured in miles, and individual waves arrive minutes to hours apart. Tsunamis are also faster than wind waves.

The longer the wave, the greater the volume of water involved. Though they appear smaller in height (distance between trough and crest) in the deep ocean than some wind waves, tsunamis can grow to much greater heights and cause much more destruction than wind waves at the coast.

Waves are generated by wind moving over water; they indicate the speed of the wind in that area. Swell are waves (usually with smooth tops) that have moved beyond the area where they were generated. The distance between the crests, or tops, of the waves that make up swell is usually much greater than the distance between waves being actively generated by wind blowing over the water. Seas (usually described by the term combined seas) refers to wind waves and swell working together. Waves and seas are described by the height from trough to crest; swell also is described by the direction it's coming from.

These pictures were taken from the right hand (starboard) side of an aircraft on final approach to the airport. The waves will usually be heading in the opposite direction to any aircraft on final approach, since it will be landing into wind.

At the coast, swell meets land and the shallower water means that swell starts to rear up and break, forming waves. A headland sometimes gives us a chance to look at the different appearance of each at the same location.

In addition to non-turbulent motions, the atmospheric flows over complex terrain are known to be in a weak but continuous state of turbulence due to the breakdown of critical internal waves. This process is less effective over flat terrain, where turbulence remains highly intermittent and patchy (Fernando 2010). The coexistence of turbulence and submesoscale motions in the SBL has been inferred from the bimodal shape of the power spectra of the velocity and temperature variances (Vickers and Mahrt 2006; Hiscox et al. 2010; Liang et al. 2014; Stiperski et al. 2019). In the presence of turbulence and submesoscale motions, the power spectra are typically subdivided into two ranges of frequencies by a spectral gap ranging between 60 s and 450 s depending on the atmospheric stability, the geographical location, and the terrain complexity. Considering an SBL, characteristic spectral-gap times close to 60 s were found over vegetated canopies (Campos et al. 2009) and complex terrains (Stiperski et al. 2019), while reaching 450 s under intense shear over arid deserts (Liang et al. 2014). An estimation of the spectral-gap scale can be obtained from the inverse of the Ozmidov scale, which is physically interpreted as the size of the largest eddy unaffected by buoyancy (Mater et al. 2013); as such, it can be used to separate the buoyancy subrange from the inertial subrange, and thus the submesoscale motions from the turbulence contributions. A more direct method involves the estimation of a cut-off frequency on the observed spectra, as directly evaluated from measurements.

The interaction between buoyancy and inertial subranges is the key to understand how submesoscale motions drive turbulence and how turbulence influences the evolution of the submesoscale motions (Staquet and Sommeria 2002). Laboratory experiments (Dohan and Sutherland 2003) and numerical investigations (Renfrew 2004; Largeron et al. 2013) have detected the formation of submesoscale waves in katabatic flows caused by turbulent jets breaking into it. Sun et al. (2012), and more recently Cava et al. (2015, 2019), observed a degradation of buoyancy waves close to the terrain caused by turbulence mixing due to shear. Conversely, it is undeniable that submesoscale motions can cause sufficient shear for generating local turbulence patches (Baklanov et al. 2011; Mahrt et al. 2012). The vorticity waves can trigger intermittent turbulence driving turbulent events embedded in each transverse vorticity roll (Sun et al. 2015b). The buoyancy waves can generate intermittent turbulence in time and space after their breakdown (Einaudi et al. 1978; Sun et al. 2015a) and by periodically reducing the near-surface Richardson number of very stable flows below its critical value (Finnigan 1999).

Below, Sect. 2 describes the theoretical framework adopted to compute the energy budgets in the presence of waves. Section 3 describes the measurement site, the equipment, the data processing, and the methods used to evaluate the wave activity and turbulence contributions. Section 4 is devoted to the discussion of the potency of the wave contributions in the near-surface budgets. Finally, Sect. 5 draws the conclusions.

The formal theory of the Reynolds decomposition suggests the use of ensemble averages to separate the fluctuations from the mean. Practical application to field measurements often uses a time average due to the limitation of the instrumental apparati, choosing an averaging time interval long enough to include all the possible realizations. For the current investigation, we adopt this last formulation using different averaging time intervals in order to disaggregate the fluctuations and filter the wave from the small-scale turbulence. Using a single averaging interval prevents the separation between wave and small-scale turbulence because conventional averaging times (as 5 or 30 min) include the contribution of the waves (Smedman 1988).

The identification of the averaging intervals is described as follows. We use a conventional 30-min average to define the quantities related to the mean flow \(\langle A\rangle \). As suggested by Smedman (1988), the fluctuation resulting from \(a=A-\langle A\rangle \) (as resulting from a Reynolds decomposition) are indeed the sum of wave and turbulence contributions. To filter the wave, a second averaging interval is identified from the power spectra. The presence of a spectral gap in the power spectra is a common feature of the equilibrium between wave and small-scale turbulence. The characteristic frequency of the spectral gap is used as the cutting time between wave and small-scale turbulence, leading to the identification of the small-scale turbulence averaging interval as we discuss in Sect. 3.2. Therefore, we apply a 2-min average to the measurements in order to filter the wave from the small-scale turbulence, followed by a second average of the obtained 15 values to get the 30-min average of the small-scale turbulent quantities \(\langle a'b'\rangle \). The 2-min average used to filter the waves is in line with the spectral-gap time scales within nocturnal SBLs introduced in Sect. 1. Finally, by taking the difference between the total fluctuations \(\langle a\rangle \) obtained from the Reynolds decomposition and the small-scale turbulence \(\langle a^\prime \rangle \) from the double time average, we have an estimation of the contribution associated with the wave activity \(\langle {\tilde{a}}\rangle \). Although less formal, this practical approach is more suitable for field-experiment applications as it releases the evaluation of the wave activity from the specific wave type, which makes it preferable in this context.

Both equations show a total derivative (terms I), transport (terms II), pressure covariance divergence (terms III), shear production (terms IV), and buoyancy (terms V) of kinetic energy associated with the wave (Eq. 3) and the small-scale turbulence (Eq. 4). The viscous term associated with the wave kinetic energy is neglected in Eq. 3, assuming a large Reynolds number, while the TKE dissipation \(\epsilon _T\) is directly computed as in term VIII of Eq. 4. Terms VI and VII in both equations couple the wave and small-scale turbulence contributions as mutual interactions between the processes. Specifically, terms VII appear with opposite signs in the wave and small-scale turbulence equations, similarly to the shear production associated to the mean flow. Therefore, terms VII can be interpreted as wave-shear production,

It appears evident that even in the absence of the small-scale turbulence heat flux, the waves can feed the temperature variance of the small-scale turbulence. Again, both equations depend on the total derivative (terms I), transport (terms II), and transfer from the mean flow (terms III) of the potential-temperature variance associated with the wave (Eq. 9) and the small-scale turbulence (Eq. 10), respectively. The viscosity associated with the wave is neglected, while the turbulent potential-temperature dissipation \(\epsilon _{\Theta }\) is directly computed as term VI of Eq. 10. Once again, terms IV and V in both equations couple the wave with the small-scale turbulence, describing exchange processes between them. Terms V appear with an opposite sign in the equations, representing the small-scale turbulence potential-temperature productions subtracted from the wave. Defining these terms as 781b155fdc