Seasonality of density currents induced by differential cooling

Abstract

Abstract. When lakes experience surface cooling, the shallow littoral region cools faster than the deep pelagic waters. The lateral density gradient resulting from this differential cooling can trigger a cold downslope density current that intrudes at the base of the mixed layer during stratified conditions. This process is known as a thermal siphon (TS). TSs flush the littoral region and increase water exchange between nearshore and pelagic zones; thus, they may potentially impact the lake ecosystem. Past observations of TSs in lakes are limited to specific cooling events. Here, we focus on the seasonality of TS-induced lateral transport and investigate how seasonally varying forcing conditions control the occurrence and intensity of TSs. This research interprets 1-year-long TS observations from Rotsee (Switzerland), a small wind-sheltered temperate lake with an elongated shallow region. We demonstrate that TSs occur for more than 50 % of the days from late summer to winter and efficiently flush the littoral region within ∼10 h. We further quantify the occurrence, intensity, and timing of TSs over seasonal timescales. The conditions for TS formation become optimal in autumn when the duration of the cooling phase is longer than the time necessary to initiate a TS. The decrease in surface cooling by 1 order of magnitude from summer to winter reduces the lateral transport by a factor of 2. We interpret this transport seasonality with scaling relationships relating the daily averaged cross-shore velocity, unit-width discharge, and flushing timescale to the surface buoyancy flux, mixed-layer depth, and lake bathymetry. The timing and duration of diurnal flushing by TSs relate to daily heating and cooling phases. The longer cooling phase in autumn increases the flushing duration and delays the time of maximal flushing relative to the summer diurnal cycle. Given their scalability, the results reported here can be used to assess the relevance of TSs in other lakes and reservoirs.

Flushing the Lake Littoral Region: The Interaction of Differential Cooling and Mild Winds

“…Nearshore slopes of O(10 -2 ) are commonly found in lakes and depths of O(10) m are characteristic of shallow lakes. Our idealized basin holds these features and its geometry is, for example, similar to Lake Rotsee, a small temperate Swiss lake where TSs have been observed (Doda et al, 2022). The lake's total length and width are 1800 m and 190 m, respectively.…”

“…The flow, discharge per unit width, from the littoral region due to differential cooling depends on the magnitude of the surface buoyancy flux, B0, and the geometry of the littoral region, as shown for example in the laboratory experiments by Sturman & Ivey (1998) and Sturman et al (1999), and more recently in the theoretical and modeling study by Ulloa et al (2022). Specifically, Sturman & Ivey (1998) adapted the seminal Phillips (1966) similarity solution for convective turbulent flows driven by uniform buoyancy flow in the presence of side boundaries and proposed that the steady-state discharge qc could be estimated, as:…”

“…The colder littoral region triggers density-driven currents that transport littoral water downslope and intrude horizontally at the base of the surface mixed layer (e.g. Doda et al, 2022;Fer et al, 2001) or even at deeper depths for weak thermoclines, potentially contributing to deep water renewal (Biemond et al, 2021;Lemmin, 2020;Peeters et al, 2003). This particular type of density-driven flow is called thermal siphons (Monismith et al, 1990) and has been viewed as an important mechanism connecting the littoral and interior regions during calm conditions in lakes (Fer et al, 2001;Woodward et al, 2017) and oceanic coastal waters (e.g., Shapiro et al, 2003).…”

“…in which a is a proportionality coefficient varying from ≈ 0.1 to ≈ 0.4 (e.g., Doda et al, 2022;Harashima & Watanabe, 1986;Sturman & Ivey, 1998), hlit is the average depth of the littoral region and LSML is the length of the littoral region (Fig. 1a).…”

“…1a). This initial temperature profile is, for example, representative of late-autumn conditions in Rotsee (Doda et al, 2022). The progressive deepening of the surface mixed layer was tracked by fitting Eq.…”