Tidal flow over topography: effect of excursion number on wave energetics and turbulence

Abstract

The excursion number, Ex = U 0 /Ωl, is a parameter that characterizes the ratio of streamwise fluid advection during a tidal oscillation of amplitude U 0 and frequency Ω to the streamwise topographic length scale l. Direct numerical simulations are performed to study how internal gravity waves and turbulence change when Ex is varied from a low value (typical of a ridge in the deep ocean) to a value of unity (corresponding to energetic tides over a small topographic feature). An isolated obstacle having a smoothed triangular shape and 20 % of the streamwise length at critical slope is considered. With increasing values of Ex, the near field of the internal waves loses its beam-like character, the wave response becomes asymmetric with respect to the ridge centre, and transient lee waves form. Analysis of the baroclinic energy balance shows significant reduction in the radiated wave flux in the cases with higher Ex owing to a substantial rise in advection and baroclinic dissipation as well as a decrease in conversion. Turbulence changes qualitatively with increasing Ex. In the situation with Ex ∼ 0.1, turbulence is intensified at the near-critical regions of the slope, and is also significant in the internal wave beams above the ridge where there is intensified shear. At Ex = O(1), the transient lee waves overturn adjacent to the ridge flanks and, owing to convective instability, buoyancy acts as a source for turbulent kinetic energy. The size of the turbulent overturns has a non-monotonic dependence on excursion number: the largest overturns, as tall as twice the obstacle height, occur in the Ex = 0.4 case, but there is a substantial decrease of overturn size at larger values of Ex simulated here.

Large Eddy Simulation of Flow and Turbulence at the Steep Topography of Luzon Strait

“…Figure e shows TKE in the wave‐breaking region ( ) during flow reversal from down to upslope. The TKE and the isopycnal pattern are similar to those of case CEX04 shown in Figure 8c of Jalali et al () who simulated tidal flow over a triangular obstacle. The dynamically relevant excursion number (Winters & Armi, ) for topography that has low F r h (such as the Luzon topography) is E x i = U 0 /( ω l i ) where l i is the inner horizontal length scale of the unblocked flow at the top of the main subridge.…”

“…For the F r h = O (1) obstacle of case CEX04, the relevant parameter is the regular excursion number, E x . The values of E x i =0.55 in the present simulation and E x = 0.42 in case CEX04 of Jalali et al () are close, explaining the similarity in TKE pattern. The height of the turbulent patch is 3 L v , where L v = U 0 / N is the maximum vertical displacement of a fluid particle before all its kinetic energy is converted into potential energy.…”

“…The summed BC kinetic energy ( E k ) and potential energy ( E P ), using notation of Jalali et al (), satisfies The energy flux, ∇· F , in equation is the sum of the wave flux, M , and the advective flux, M adv . The conversion, C , from BT to BC components includes the linear theory term, C l , and an additional nonlinear part, C n l .…”

“…u bc , w bc , and p bc are BC components. The summed BC kinetic energy (E k ) and potential energy (E P ), using notation of Jalali et al (2014), satisfies…”

An immersed boundary method for direct and large eddy simulation of stratified flows in complex geometry

“…In section 9, internal tide generation and turbulence at a laboratory-scale obstacle are considered using the developed IBM solver in the direct numerical simulation (DNS) mode. The baroclinic energy budget and turbulence statistics are compared against the previous DNS studies of Rapaka et al (2013) and Jalali et al (2014) which utilized a body conforming grid. In section 10, internal tide generation is studied at a large scale topography using large eddy simulation (LES) along with a nonlinear bottom drag law.…”