Energetics and mixing of stratified, rotating flow over abyssal hills

Mapping Intimacies ◽

10.31223/x5xc8m ◽

2021 ◽

Author(s):

Varvara Zemskova ◽

Nicolas Grisouard

Keyword(s):

Energy Transfer ◽

Energy Loss ◽

Linear Theory ◽

Internal Waves ◽

Mixing Efficiency ◽

Mean Flow ◽

Diapycnal Mixing ◽

Transfer Rates ◽

Non Linear ◽

Mixing Rates

One of the proposed mechanisms for energy loss in the ocean is through dissipation of internal waves, in particular above rough topography where internal lee waves are generated. Rates of dissipation and diapycnal mixing are often estimated using linear theory and a constant value for mixing efficiency. However, previous oceanographic measurements found that non-linear dynamics may be important close to topography. In order to investigate the role of non-linear interactions, we conduct idealized 3D numerical simulations of steady flow over 1D topography and vary the topographic height, which correlates to the degree of flow non-linearity. We analyze spatial distribution of energy transfer rates between internal waves and the non-geostrophic portion of time-mean flow, and of dissipation and diapycnal mixing rates. In our simulations with taller, more non-linear topographies, energy transfer rates are similar to previously unexplained oceanographic observations near topography: internal waves gain energy from time-mean flow through horizontal straining and lose energy through vertical shearing. In the tall topography simulations, buoyancy fluxes also play a significant role, consistent with observations but contrary to linear wave theory, suggesting that quasigeostrophy-based approximations and linear theory may not hold in some regions above rough topography. Both dissipation and mixing rates increase with topographic height, but their vertical distributions differ between topographic regimes. As such, vertical profile of mixing efficiency is different for linear and non-linear topographic regimes, which may need to be incorporated into parameterizations of small-scale processes in models and estimates of ocean energy loss.

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A non-linear investigation of critical levels for internal atmospheric gravity waves

Journal of Fluid Mechanics ◽

10.1017/s0022112071002751 ◽

1971 ◽

Vol 50 (3) ◽

pp. 545-563 ◽

Cited By ~ 56

Author(s):

R. J. Breeding

Keyword(s):

Steady State ◽

Linear Theory ◽

Gravity Waves ◽

Incident Wave ◽

Critical Level ◽

Internal Gravity Waves ◽

Mean Flow ◽

Non Linear ◽

Energy And Momentum ◽

Almost All

The behaviour of internal gravity waves near a critical level is investigated by means of a transient two dimensional finite difference model. All the important non-linear, viscosity and thermal conduction terms are included, but the rotational terms are omitted and the perturbations are assumed to be incompressible. For Richardson numbers greater than 2·0 the interaction of the incident wave and the mean flow is largely as predicted by the linear theory–very little of the incident wave penetrates through the critical level and almost all of the wave's energy and momentum are absorbed by changes in the original wind. However, these changes in the wind are centred above the critical level, so that the change in the wind has only a small effect on the height of the critical level. For Richardson numbers less than 2·0 and greater than 0·25 a significant fraction of the incident wave is reflected, part of which could have been predicted by the linear theory. For these stable Richardson numbers a steady state is apparently reached where the maximum wind change continues to grow slowly, but the minimum Richardson number and wave magnitudes remain constant. This condition represents a balance between the diffusion outward of the added momentum and the rate at which it is absorbed. For Richardson numbers less than 0·25, over-reflexion, predicted from the linear theory, is observed, but because the system is dynamically unstable no over-reflecting steady state is ever reached.

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Energetics and mixing in buoyancy-driven near-bottom stratified flow

Journal of Fluid Mechanics ◽

10.1017/jfm.2019.184 ◽

2019 ◽

Vol 869 ◽

pp. 214-237

Author(s):

Pranav Puthan ◽

Masoud Jalali ◽

Vamsi K. Chalamalla ◽

Sutanu Sarkar

Keyword(s):

Kinetic Energy ◽

Potential Energy ◽

Energy Loss ◽

Convective Instability ◽

Mixing Efficiency ◽

Time Interval ◽

Mean Flow ◽

Available Potential Energy ◽

Long Time ◽

The Mean

Turbulence and mixing in a near-bottom convectively driven flow are examined by numerical simulations of a model problem: a statically unstable disturbance at a slope with inclination $\unicode[STIX]{x1D6FD}$ in a stable background with buoyancy frequency $N$ . The influence of slope angle and initial disturbance amplitude are quantified in a parametric study. The flow evolution involves energy exchange between four energy reservoirs, namely the mean and turbulent components of kinetic energy (KE) and available potential energy (APE). In contrast to the zero-slope case where the mean flow is negligible, the presence of a slope leads to a current that oscillates with $\unicode[STIX]{x1D714}=N\sin \unicode[STIX]{x1D6FD}$ and qualitatively changes the subsequent evolution of the initial density disturbance. The frequency, $N\sin \unicode[STIX]{x1D6FD}$ , and the initial speed of the current are predicted using linear theory. The energy transfer in the sloping cases is dominated by an oscillatory exchange between mean APE and mean KE with a transfer to turbulence at specific phases. In all simulated cases, the positive buoyancy flux during episodes of convective instability at the zero-velocity phase is the dominant contributor to turbulent kinetic energy (TKE) although the shear production becomes increasingly important with increasing $\unicode[STIX]{x1D6FD}$ . Energy that initially resides wholly in mean available potential energy is lost through conversion to turbulence and the subsequent dissipation of TKE and turbulent available potential energy. A key result is that, in contrast to the explosive loss of energy during the initial convective instability in the non-sloping case, the sloping cases exhibit a more gradual energy loss that is sustained over a long time interval. The slope-parallel oscillation introduces a new flow time scale $T=2\unicode[STIX]{x03C0}/(N\sin \unicode[STIX]{x1D6FD})$ and, consequently, the fraction of initial APE that is converted to turbulence during convective instability progressively decreases with increasing $\unicode[STIX]{x1D6FD}$ . For moderate slopes with $\unicode[STIX]{x1D6FD}<10^{\circ }$ , most of the net energy loss takes place during an initial, short ( $Nt\approx 20$ ) interval with periodic convective overturns. For steeper slopes, most of the energy loss takes place during a later, long ( $Nt>100$ ) interval when both shear and convective instability occur, and the energy loss rate is approximately constant. The mixing efficiency during the initial period dominated by convectively driven turbulence is found to be substantially higher (exceeds 0.5) than the widely used value of 0.2. The mixing efficiency at long time in the present problem of a convective overturn at a boundary varies between 0.24 and 0.3.

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