Residual circulation due to internal waves shoaling on a slope

Abstract

We describe the residual circulation induced in a two-layer system when internal waves, with a wave length equal to or longer than the slope length, propagate over a sloping bottom and either reflect or break. For the case of no wave breaking, scaling is used to derive Boussinesq-type equations, the solution of which leads to an expression for the residual circulation adjacent to the sloping bottom. This residual circulation is maintained by a weak slope on the density interface. For breaking waves, laboratory experiments and numerical modeling were used to ascertain the details of the residual circulation arising from the formation of gravitational intrusions. Results from these three investigative tools were used to determine, as a function of bottom slope and incident wave amplitude, the internal wave reflection coefficient and the strength of the residual circulation pattern with and without wave breaking.

Bubbles emerging from a submerged granular bed

“…Marti & Imberger (2006) showed that a baroclinic density volume flux is set-up in the benthic boundary layer whenever a nonlinear density stratification exists in the lake, a condition that is nearly always present. Recently, Nakayama & Imberger (2010) have clarified this volume flux and showed that it may be sustained not only by a nonlinear density gradient, but also by differential mixing in the benthic boundary layer and nonlinear basin-scale internal wave breaking over a shoaling lake bottom. The current work has thus supplied the limiting link in the availability of re-generated nutrients.…”

Three-dimensional Numerical Modeling of Water Temperature and Internal Waves in a Large Stratified Lake

“…그러나 최근에는 컴퓨터의 발전과 함께 3차원 모델을 이용 하여 복잡한 지형과 경계조건을 고려한 성층 호수의 수리동 력학적 모의 연구가 가능해졌다 (Antenucci et al, 2000;Bernhardt and Kirillin, 2013;Chung et al, 2011;Hodges et al, 2000;Nakayama and Imberger, 2010;Shimizu et al, 2007). 본 연구의 목적은 Lake Tahoe에서 …”

The importance of nonlinear internal waves in a deep subalpine lake: Lake Iseo, Italy

“…Field observations show basin-scale internal waves can interact with sloping topography where they shoal, reflect, and possibly break into a number of smaller scale waves as they adjust to the new environment (Helfrich and Melville 2006;Filatov et al 2012). Whether internal waves will shoal and break nearshore depends on the ratio of the boundary slope to wave slope, known as the internal Iribarren number j (Boegman et al 2005b;Aghsaee et al 2010;Nakayama and Imberger 2010). The magnitude of the internal Iribarren number is useful in the prediction of energy loss and mixing efficiency during breaking.…”

“…This intensifies the benthic boundary layer updraft (Imberger and Ivey 1993) that plays a central role in the transport of nutrients and biological material from the hypolimnion to the euphotic zone (Marti and Imberger 2006;Bruce et al 2008). Moreover, the intrusion transports dissolved and resuspended material from the boundary to the center of the lake (Marti and Imberger 2006;Nakayama and Imberger 2010;Nakayama et al 2012).…”

“…Shoaling and breaking of high-frequency internal waves occurs along sloping boundaries (Boegman et al 2005b), enhancing dissipation and mixing across the pycnocline (Boegman et al 2003) and leading to sediment resuspension (Bonnin et al 2006) and augmented mass fluxes from internal wave-induced interfacial setup (Nakayama and Imberger 2010;Nakayma et al 2012). In this work, the possibility of wave breaking was inferred by calculating the internal Iribarren number j (Boegman et al 2005b;Aghsaee et al 2010).…”