Anthony Kay

A review of the physics and ecological implications of the thermal bar circulation

Following recent applications of numerical modelling and remote sensing to the thermal bar phenomenon, this paper seeks to review the current state of knowledge on the effect of its circulation on lacustrine plankton ecosystems. After summarising the literature on thermal bar hydrodynamics, a thorough review is made of all plankton observations taken in the presence of a thermal bar. Two distinct plankton growth regimes are found, one with production favoured throughout the inshore region and another with a maximum in plankton biomass near the position of the thermal bar. Possible explanations for the observed distributions are then discussed, with reference to numerical modelling studies, and the scope for future study of this interdisciplinary topic is outlined.

A model of the wind-driven circulation in Lake Baikal

Abstract A numerical model based on the Navier–Stokes equations is used to simulate the circulation produced by a strong wind in a cross-section of Lake Baikal. Temperature distributions have been obtained for different stages of the spring warming of the lake, using available measurements and simulating the faster warming of the near-shore areas in accordance with the local stability conditions. These have been used as initial conditions for the prediction of the wind-driven circulation. The results presented suggest that buoyancy forces have little impact on the magnitude of vertical currents descending towards the bottom of the lake, but the action of buoyancy forces could initiate additional motions that have been found to generate strong vertical currents far from the shores. Furthermore, there appears to be evidence in our data of local acceleration linked to changes in the bottom topography of the section.

A numerical study of plankton population dynamics in a deep lake during the passage of the Spring thermal bar

Abstract An N–P–Z plankton model has been included in a finite volume formulation of the Navier–Stokes equations and has been used to predict the effect of the spring warming and the thermal bar on the plankton ecosystem of a section of the Central Basin of Lake Baikal. The results presented show that the currents converging towards the thermal bar generate a maximum in the phytoplankton population at the location of the thermal bar, while the boundary between the unstable near-surface region and the stably stratified lower part of the lake acts as a barrier to the diffusion of the plankton population towards deeper regions. The enlargement of the unstable area during the warming of the lake has been found to have a major effect on the distribution of the phytoplankton, with enhanced vertical diffusion balancing the growth near the surface and preventing the phytoplankton population from reaching bloom values, and consequently inhibiting any development of the zooplankton population. It has also been found that the vertical component of the Coriolis force could allow the currents generated by the thermal bar to reach the deeper part of the lake.

A Numerical Study of the Dynamics of the Riverine Thermal Bar in a Deep Lake

A numerical model based on a Finite Volume formulation of the Navier–Stokes equations is used to simulate a range of scenarios leading to a thermal bar formed by a river inflow to an idealised deep lake. The results presented here show that small riverine salinity increases have a profound effect on the dynamics of the thermal bar, suppressing horizontal propagation of the plume and raising the possibility of a thermal bar which is capable of sinking to great depths. This finding is particularly relevant to Lake Baikal in Siberia, where the vigorous deep-water renewal is still not fully understood. An analysis of the buoyancy forces governing the depth of penetration of the thermal bar plume shows that realistic salinity gradients are an important factor in determining the circulation of Baikal waters. Observations of the saline curtailment of the thermal bars horizontal propagation also reveal a potential for reduced productivity in the ecosystem of any temperate river delta during the Spring renewal period.

Frontogenesis in gravity-driven flows with non-uniform density gradients

•A horizontal density gradient may be steepened to form a front if the horizontal flow which it drives is convergent. This convergence may be caused by an initial nonlinearity in the density gradient (as described by Simpson & Linden 1989). A quadratic density profile is analysed to illustrate the mechanism, and it is shown how the flow and the density profile interact to intensify and concentrate the front near a horizontal boundary. Linear and curved density profiles in a container of finite length are also studied : the most favourable location for frontogenesis is found to be where the flow emerges into a region of significant curvature after passing through a maximum of the density gradient.

Numerical modelling of the thermal bar and its ecological consequences in a river-dominated lake

Predictions from the first realistic model of the hydrodynamics of the riverine thermal bar in a medium-size lake are presented. Important features of field observations from Kamloops Lake, British Columbia are successfully reproduced, but the model adopts a generalised section, which is regarded as being representative of many other lakes. A study of the model sensitivity to various aspects of its formulation is also presented, particularly emphasising the important influence of Coriolis forcing on the thermal bar circulation. Plankton population dynamics within the thermal bar flow field is then studied by means of two ecological models of differing complexity. Differences between the predictions of the two models are explained with reference to intermediate simulations, and it is found that the simple ecosystem formulation used in previous work may give misleading results. The flow and stability conditions of the riverine thermal bar have a profound influence on ecosystem development, and support greater phytoplankton growth than in thermal bars resulting purely from radiative effects.

Numerical Modelling of Pollutant Propagation in Lake Baikal during the Spring Thermal Bar

Abstract In this paper, the phenomenon of the thermal bar in Lake Baikal and the propagation of pollutants from the Selenga River are studied with a nonhydrostatic mathematical model. An unsteady flow is simulated by solving numerically a system of thermal convection equations in the Boussinesq approximation using second-order implicit difference schemes in both space and time. To calculate the velocity and pressure fields in the model, an original procedure for buoyant flows, SIMPLED, which is a modification of the well-known Patankar and Spaldings SIMPLE algorithm, has been developed. The simulation results have shown that the thermal bar plays a key role in propagation of pollution in the area of Selenga River inflow into Lake Baikal.

Warm discharges in cold fresh water. Part 1. Line plumes in a uniform ambient

Turbulent buoyant plumes in cold fresh water are analysed, assuming a quadratic dependence of density on temperature. The model is based on the assumption that entrainment velocity is proportional to vertical velocity in the plume. Numerical and asymptotic solutions are obtained for both rising and descending plumes from virtual sources with all possible combinations of buoyancy, volume and momentum fluxes. Physical sources can be identified as points on trajectories of plumes from virtual sources. The zero-buoyancy condition, at which the plume and the ambient have equal densities but their temperatures are on opposite sides of the temperature of maximum density, is of particular importance. If an upwardly buoyant plume rising through a body of water reaches the surface before passing through its zero-buoyancy level, it will form a surface gravity current; otherwise, the plume water will return to the source as a fountain. The height at which zero buoyancy is attained generally decreases as the source momentum flux increases: greater plume velocity produces greater entrainment and hence more rapid temperature change. Descending plumes, if ejected downwards against upward buoyancy, may be classified as strongly or weakly forced according to whether they reach the zero-buoyancy condition before being brought to rest. If they do, they continue to descend with favourable buoyancy; otherwise, they may form an inverted fountain. Once a descending plume has attained downward buoyancy, it can continue to descend indefinitely, ultimately behaving like a plume in a fluid with a linear equation of state. In contrast, a rising plume will eventually come to rest, however large its initial upward buoyancy and momentum fluxes are.

Warm discharges in cold fresh water: 2. Numerical simulation of laminar line plumes

The behaviour of a discharge of warm water upwards into a homogeneous body of cold fresh water was investigated by means of a numerical model. The discharge has a parabolic velocity profile, with Reynolds number