Tidal Synchronization of Lee Vortices in Geophysical Wakes

Abstract

Wake vortices in tidally modulated currents past a conical hill in a stratified fluid are investigated using large‐eddy‐simulation. The vortex shedding frequency is altered from its natural steady‐current value leading to synchronization of wake vortices with the tide. The relative frequency (f*), defined as the ratio of natural shedding frequency (fs,c) in a current without tides to the tidal frequency (ft), is varied to expose different regimes of tidal synchronization. When f* increases and approaches 0.25, vortex shedding at the body changes from a classical asymmetric Kármán vortex street. The wake evolves downstream to restore the Kármán vortex‐street asymmetry but the discrete spectral peak, associated with wake vortices, is found to differ from both ft and fs,c, a novel result. The spectral peak occurs at the first subharmonic of the tidal frequency when 0.5 ≤ f* < 1 and at the second subharmonic when 0.25 ≤ f* < 0.5.

Wake Vortices and Dissipation in a Tidally Modulated Flow Past a Three‐Dimensional Topography

“…When $$\overline{S}\ll 1$$, the tide‐associated momentum loss is negligible and the influence of tidal forcing on the shed wake vortices may be insignificant. At R = 1, tidal synchronization is observed (Puthan et al., 2021). The behavior at lower values of R (and $$\overline{S}$$) remains to be ascertained.…”

“…Thus, we focus on the role of varying the relative amplitude of tidal velocity (R) in the emergence of transient eddies in Section 4, and the attendant dissipation in the wake and the hydraulic response region in Section 5. Puthan et al (2021) showed that in a tidally modulated flow with R = 1 and Ω s,c /Ω t = 5/6, downstream wake vortices are found at frequencies that differ from both the tidal frequency Ω t and the natural shedding value Ω s,c . Instead, the frequency of the wake vortices was found to be Ω t /2, a value smaller than both Ω t and Ω s,c .…”

“…The flow is illustrated with instantaneous snapshots of the velocity field in the midcenter plane (Figure 1a) and vertical vorticity in the horizontal plane (Figure 1b). The flow features such as transient lee waves (Jalali & Sarkar, 2017; Jalali et al., 2014; Legg & Klymak, 2008), downstream wake (Dong et al., 2006; Perfect et al., 2020a; Puthan et al., 2020), blocked fluid upstream (Baines, 1987, 1995), and coherent lee vortices (Perfect et al., 2018; Puthan et al., 2021) are prominent. These features must be resolved in simulations to quantify the contribution from the turbulent processes accurately.…”

“…Ritchet et al (2019) showed that mean current induces a Doppler-shift of internal tide frequencies which weakens the parametric subharmonic instability induced dissipation at critical latitude (∼29°). Recently Puthan et al (2021) considered the special case of mean velocity equaling the oscillation amplitude and performed a parametric study by varying the ratio between natural shedding frequency (Ω s,c ) and tidal frequency (Ω t ) from 0.1 to 1 and found tidal synchronization of lee vortices behind a conical hill in a stratified flow. Thus, it is evident from previous work that tidally modulated stratified flow over obstacles exhibits qualitative changes in internal wave energy flux, boundary layer turbulence, and wake dynamics, relative to the classical case of steady flow past obstacles.…”

Analysis of coherence in turbulent stratified wakes using spectral proper orthogonal decomposition

“…Turbulent wakes are ubiquitous both in nature and man-made devices. From flow past moving vehicles (Grandemange et al 2015) to flow past topographic features (Puthan, Sarkar & Pawlak 2021) in oceans, they play an important role in transporting momentum and energy across large distances from the wake generator. In the ocean and the atmosphere, the background density often has a stable density stratification.…”