The tidally induced bottom boundary layer in the rotating frame: development of the turbulent mixed layer under stratification

Abstract

To investigate turbulent properties and the developing mechanisms of the tidally induced bottom boundary layer in the linearly stratified ocean, numerical experiments have been executed with a non-hydrostatic three-dimensional model in the rotating frame, changing the temporal Rossby number Rot = |σ/f|, i.e. the ratio of the tidal frequency σ to the Coriolis parameter f. After the flow transitions to turbulence, the entire water column can be characterized by three layers: the mixed layer where density is homogenized and the flow is turbulent (z < zm); the stratified layer where the initial stratification remains and the flow is laminar (z > zt); and the interfacial layer between them where the flow is turbulent but the stratification remains (zm < z < zt). Turbulence is scaled by the frictional velocity uτ and the mixed-layer thickness zm (uτ and uτ/N where N is the buoyancy frequency) in the mixed (interfacial) layer, and has similarity. The mixed layer is thickened by the process where light water of the upper stratified layer is mixed with the lower unstratified layer water through the interfacial layer. As Rot approaches unity, i.e. near the critical latitude, the mixed layer develops more rapidly according to the following mechanism. As becomes Rot closer to unity, the current shear in the interfacial layer is intensified, since the difference of velocity becomes larger between the lower turbulent mixed and upper laminar stratified layers, and this leads to thickening of the interfacial layer. As a result, density deviation of the water entrained from above becomes larger, and this causes more rapid development of the mixed layer. In terms of the energy conversion from the eddy kinetic energy (EKE) to the potential energy (PE), the efficiency factor β which is the ratio of the conversion rate from EKE to PE to that from the tidal shear to EKE increased from 0.25% for Rot = 0.5 to 3.5% for Rot = 1.05 on average. When the time is normalized by the period required for the mixed layer to be thickened to the unstratified turbulent boundary layer δ = uτ/|f+σ|, the mixed layer development occurred in a similar manner in all cases. This similarity suggests the possibility of universal formulation for the turbulent tidal mixing under stratification.

Can neap-spring tidal cycles modulate biogeochemical fluxes in the abyssal near-seafloor water column?

“…To better understand the effects of an oscillating (tidal) flow component on aspects of BBL fluid dynamics, we revisited the data sets of Sakamoto and Akitomo (2009) who used a numerical model to investigate a tidally induced BBL in a rotating frame. The initial water column was weakly mass-density-stratified (the Richardson number Ri = / was only 47.5, where N ∞ is the initial buoyancy frequency in the free-stream waters above the boundary layer and  is the frequency of the tidal oscillations).…”

“…It turned out that the boundary layer in case D was almost 14 times thicker than in case Ek. Although an explicit model run for a counter-rotating scenario was not carried out by Sakamoto and Akitomo (2009), it was speculated that the boundary layer in case D could be more than 40 times thicker than in the counter-rotating case (and it would seem that the boundary layer in the counter-rotating case would then be ~ 3 times thinner than in the pure Ek case) (Fig. 5a).…”

“…5a). For a given tidal current-speed amplitude, co-rotation almost always leads to a thickening of the BBL compared to a corresponding non-oscillating Ekman layer (exceptions occur near / at the equator for semidiurnal and diurnal oscillations; Sakamoto and Akitomo, 2009). It is very important to note that these very significant differences in boundarylayer thickness occur for the same tidal current-speed amplitude and are entirely dependent on the effects of the rotational behaviour of the boundary layer on turbulence intensities within the boundary layer.…”

“…In this context, the study of Sakamoto and Akitomo (2009) showed that a key effect of co-rotational tidal oscillation is a significant increase of absolute turbulence intensities across a very large part of the upper BBL (i.e., above the log layer), leading to the aforementioned thickening of the BBL and BML ( Effects of tidal oscillation on boundary shear stress ---As outlined in Section 1, nearseafloor particle dynamics in the deep sea are partly driven by rebound and / or even resuspension. Within this context, it is, therefore, also important to note that Weatherly et al (1980) related different combinations of co-and counter-rotation to effects on the average 'boundary shear stress',  0 , at the seafloor.…”

“…The increased residence times of the particulate matter are thought to be due to increased turbulence intensities near the seafloor (Fig. 1a) (e.g., Wimbush and Munk, 1970;Gust and Weatherly, 1985;Gross et al, 1986;Taylor and Sarkar, 2007;Sakamoto and Akitomo, 2009). This is because turbulent overturns might have a direct 'suspending' effect on the particle aggregates and / or an indirect effect through gradual breakdown of larger faster settling aggregates into smaller more slowly settling aggregates or even primary particles, thereby reducing net settling speeds.…”