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1.
A 3D non-hydrostatic model is developed to compute internal waves. A novel grid arrangement is incorporated in the model. This not only ensures the homogenous Dirichlet boundary condition for the non-hydrostatic pressure can be precisely and easily imposed but also renders the model relatively simple in its discretized form. The Perot scheme is employed to discretize horizontal advection terms in the horizontal momentum equations, which is based on staggered grids and has the conservative property. Based on previous water wave models, the main works of the present paper are to (1) utilize a semi-implicit, fractional step algorithm to solve the Navier-Stokes equations (NSE); (2) develop a second-order flux-limiter method satisfying the max–min property; (3) incorporate a density equation, which is solved by a high-resolution finite volume method ensuring mass conservation and max–min property based on a vertical boundary-fitted coordinate system; and (4) validate the developed model by using four tests including two internal seiche waves, lock-exchange flow, and internal solitary wave breaking. Comparisons of numerical results with analytical solutions or experimental data or other model results show reasonably good agreement, demonstrating the model’s capability to resolve internal waves relating to complex non-hydrostatic phenomena. 相似文献
2.
Numerical studies of flow over a sill: sensitivity of the non-hydrostatic effects to the grid size 总被引：1，自引：1，他引：0
A non-hydrostatic terrain-following model in cross sectional form is applied to study the processes in the lee of a sill in
an idealized stratified fjord during super-critical tidal inflow. A sequence of numerical studies with horizontal grid sizes
in the range from 100 to 1.5625 m are performed. All experiments are repeated using both hydrostatic and non-hydrostatic versions
of the model, allowing a systematic study of possible non-hydrostatic pressure effects and also of the sensitivity of these
effects to the horizontal grid size. The length scales and periods of the internal waves in the lee of the sill are gradually
reduced and the amplitudes of these waves are increased as the grid size is reduced from 100 down to 12.5 m. With a further
reduction in grid size, more short time and space scale motions become superimposed on the internal waves. Associated with
the internal wave activity, there is a deeper separation point that is fairly robust to all parameters investigated. Another
separation point nearer to the top of the sill appears in the numerical results from the high-resolution studies with the
non-hydrostatic model. Associated with this shallower separation point, an overturning vortex appears in the same set of numerical
solutions. This vortex grows in strength with reduced grid size in the non-hydrostatic experiments. The effects of the non-hydrostatic
pressure on the velocity and temperature fields grow with reduced grid size. In the experiments with horizontal grid sizes
equal to 100 or 50 m, the non-hydrostatic pressure effects are small. For smaller grid sizes, the time mean velocity and temperature
fields are also clearly affected by the non-hydrostatic pressure adjustments. 相似文献
3.
ABSTRACTThe generation processes and potential energy sources of internal solitary waves (ISWs) in the southern Taiwan Strait are investigated by driving a high resolution non-hydrostatic numerical model with realistic background conditions. Two main types of ISWs are clarified according to their different energy sources. One is generated by the nonlinear disintegration of remote internal tides emanating from Luzon Strait, and the other type is generated by local tide-topography interaction at the continental slope. The basic properties and evolution processes differ between these two kinds of ISWs. The waves originated from the remote internal tides at Luzon Strait have amplitudes comparable to previous field observations. In contrast, the ISWs generated locally are much weaker than observed waves, even in the presence of a steady offshore background current, which intensifies the generation of onshore ISWs. The ISWs induced by remotely generated M2 internal tides are stronger than those induced by K1 internal tides, and the fraction of internal wave energy transmitted onto the shelf is not significantly influenced by the intensity of remotely generated internal tides. 相似文献
4.
Field observations of tidally driven stratified flow in the sill area of Knight Inlet (British Columbia) revealed a very complicated structure, which includes solitary waves, upstream bifurcation, hydraulic jump and mixing processes. Recent observations suggest that the flow instabilities on the plunging pycnocline at the lee side of the sill may contribute to solitary wave generation through a subharmonic interaction. The present study reports on a series of numerical experiments of stratified tidal flow in Knight Inlet performed with the help of a fine resolution fully non-linear non-hydrostatic numerical model. The model reproduces all important stages of the baroclinic tidal dynamics observed in Knight Inlet. Results demonstrate that solitary waves are generated apart from the area of hydrodynamic instability. Accelerating tidal flux forms a baroclinic hydraulic jump just above the top of the sill, whereas the bifurcations and zones of shear instabilities are formed downstream of the sill. The first baroclinic mode having the largest velocity escapes from the generation area and propagates upstream, disintegrating further into a packet of solitary waves reviling the classical “non-subharmonic” mechanism of generation. The remaining part of the disturbance (slow baroclinic modes) is arrested by tidal flow and carried away to the lee side of the obstacle, where shear instability, billows and mixing processes are developed. Some sensitivity runs were performed for different value of tidal velocity. 相似文献
5.
Numerical model experiments have been performed to analyze the low-latitude baroclinic continental shelf response to a tropical cyclone. The theory of coastally trapped waves suggests that, provided appropriate slope, latitude, stratification and wind stress, bottom-intensified topographic Rossby waves can be generated by the storm. Based on a scale analysis, the Nicaragua Shelf is chosen to study propagating topographic waves excited by a storm, and a model domain is configured with simplified but similar geometry. The model is forced with wind stress representative of a hurricane translating slowly over the region at 6 km h−1. Scale analysis leads to the assumption that baroclinic Kelvin wave modes have minimal effect on the low-frequency wave motions along the slope, and coastal-trapped waves are restricted to topographic Rossby waves. Analysis of the simulated motions suggests that the shallow part of the continental slope is under the influence of barotropic topographic wave motions and at the deeper part of the slope baroclinic topographic Rossby waves dominate the low-frequency motions. Numerical solutions are in a good agreement with theoretical scale analysis. Characteristics of the simulated baroclinic waves are calculated based on linear theory of bottom-intensified topographic Rossby waves. Simulated waves have periods ranging from 153 to 203 h. The length scale of the waves is from 59 to 87 km. Analysis of energy fluxes for a fixed volume on the slope reveals predominantly along-isobath energy propagation in the direction of the group velocity of a topographic Rossby wave. Another model experiment forced with a faster translating hurricane demonstrates that fast moving tropical cyclones do not excite energetic baroclinic topographic Rossby waves. Instead, robust inertial oscillations are identified over the slope. 相似文献
6.
We present detailed observations of internally generated turbulence in a sheared, stratified natural flow, as well as an analysis of the external factors leading to its generation and temporal variability. Multi-month time series of vertical profiles of velocity, acoustic backscatter (0.5 Hz), and turbulence parameters were collected with two moored acoustic Doppler current profilers (ADCPs) in the Hudson River estuary, and estuary-long transects of water density were collected 30 times. ADCP backscatter is used for visualization of coherent turbulent structures and evaluation of surface wave biases to the turbulence measurements. Benefits of the continuous long-term turbulence record include our capturing: (1) the seasonality of turbulence due to changing riverflow, (2) hysteresis in stratification and turbulence over the fortnightly cycle of tidal range, and (3) intermittent events such as breaking internal waves. Internal mixing layers (IMLs) are defined as turbulent regions above the logarithmic velocity layer, and the bottom boundary layer (BBL) is defined as the continuously turbulent range of heights above the bed. A cross-correlation analysis reveals how IML and BBL turbulence vary with stratification and external forcing from tidal range, river flow, and winds. Turbulence in both layers is maximal at spring tide and minimal when most stratified, with one exception—IML turbulence at a site with changing channel depth and width is maximal at times of maximum stratification and freshwater input. 相似文献
7.
Starting out with two interacting Rossby-Haurwitz waves, the generation of zonal flow is discussed. It is shown that zonal flow cannot be generated by first or second order interactions between two such waves, unless they are exchanging energy with a third wave within a resonant triad. The generation of zonal flow at second order through resonant triad interactions is subsequently established and studied. 相似文献
8.
Atsushi Kubokawa 《地球物理与天体物理流体动力学》2013,107(2):119-137
Although the study of topographic effects on the Rossby waves in a stratified ocean has a long history, the wave property over a periodic bottom topography whose lateral scale is comparable to the wavelength is still not clear. The present paper treats this problem in a two-layer ocean with one-dimensional periodic bottom topography by a simple numerical method, in which no restriction on the wavelength and/or the horizontal scale of the topography is required. The dispersion diagram is obtained for a wavenumber range of [?π/L b , π/L b ], where L b is the periodic length of the topography. When the topographic?β?is not negligible compared to the planetary β, the Rossby wave solutions around the wavenumbers which satisfy the resonant condition among the waves and topography disappear and separate into an infinite number of discrete modes. For convenience, each mode is numbered in order of frequency. As topographic height is increased, the high frequency barotropic Rossby wave (mode 1) becomes a topographic mode which can exist even on the f plane, and the highfrequency baroclinic mode (mode 2) becomes a surface intensified mode. Behaviors of low frequency modes are somewhat complicated. When the topographic amplitude is small, the low frequency baroclinic modes tend to be bottom trapped and the low frequency barotropic modes tend to be surface intensified. As topographic amplitude further increases, the relation between the mode number and vertical structure changes. This change can be attributed to the increase of the frequency of the topographic mode with the topographic amplitude. 相似文献
9.
Hans van Haren 《Ocean Dynamics》2012,62(8):1123-1137
During a period of 3?days, an accurate bottom-pressure sensor and a four-beam acoustic Doppler current profiler (ADCP) were mounted in a bottom frame at 23?m in a narrow sea strait with dominant near-rectilinear tidal currents exceeding 1?m?s?1 in magnitude. The pressure record distinguishes small and short surface waves, wind- and ferry-induced near-surface turbulence and waves, large turbulent overturns and high-frequency internal waves. Typical low-frequency turbulent motions have amplitudes of 50?N?m?2 and periods of about 50?s. Such amplitudes are also found in independent estimates of non-hydrostatic pressure using ADCP data, but phase relationships between these data sets are ambiguous probably due to the averaging over the spread of the slanted acoustic beams. ADCP's echo amplitudes that are observed in individual beams show much better phase correspondence with near-bottom pressure, whether they are generated near the surface (mainly air bubbles) or near the bottom (mainly suspended sediment). These 50-s motions are a mix of turbulence and internal waves, but they are not due to surface wave interactions, and they are not directly related to the main tidal flow. Internal waves are supported by stratification varying between extremely strong thin layer and very weak near-homogeneous stratification. They are driven by the main flow over 2-m amplitude sand-wave topography, with typical wavelengths of 150?m. 相似文献
10.
In this paper, we address the question of energy leakage from turbulence to internal waves (IWs) in the oceanic mixed layer
(OML). If this leakage is substantial, then not only does this have profound implications as far as the dynamics of the OML
is concerned, but it also means that the equation for the turbulence kinetic energy (TKE) used in OML models must include
an appropriate sink term, and traditional models must be modified accordingly. Through comparison with the experimental data
on grid-generated turbulence in a stably stratified fluid, we show that a conventional two-equation turbulence model without
any IW sink term can explain these observations quite well, provided that the fluctuating motions that persist long after
the decay of grid-generated turbulence are interpreted as being due to IW motions generated by the initial passage of the
grid through the stably stratified fluid and not during turbulence decay. We conclude that there is no need to postulate an
IW sink term in the TKE equation, and conventional models suffice to model mixing in the OML. 相似文献
11.
Two-layer equatorial primitive equations for the free troposphere in the presence of a thin atmospheric boundary layer and thermal dissipation are developed here. An asymptotic theory for the resonant nonlinear interaction of long equatorial baroclinic and barotropic Rossby waves is derived in the presence of such dissipation. In this model, a self-consistent asymptotic derivation establishes that boundary layer flows are generated by meridional pressure gradients in the lower troposphere and give rise to degenerate equatorial Ekman friction. That is to say, the asymptotic model has the property that the dissipation matrix has one eigenvalue which is nearly zero: therefore the dynamics rapidly dissipates flows with pressure at the base of the troposphere and creates barotropic/baroclinic spin up/spin down. The simplified asymptotic equations for the amplitudes of the dissipative equatorial barotropic and baroclinic waves are studied by linear theory and integrated numerically. The results indicate that although the dissipation slightly weakens the tropics to midlatitude connection, strong localized wave packets are nonetheless able to exchange energy between barotropic and baroclinic waves on intraseasonal timescales in the presence of baroclinic mean shear. Interesting dissipation balanced wave-mean flow states are discovered through numerical simulations. In general, the boundary layer dissipation is very efficient for flows in which the barotropic and baroclinic components are of the same sign at the base of the free troposphere whereas the boundary layer dissipation is less efficient for flows whose barotropic and baroclinic components are of opposite sign at the base of the free troposphere. 相似文献
12.
Asymptotic methods and numerical simulations are used to examine the evolution of an internal gravity wave packet comprising a continuous spectrum of horizontal wavenumbers and propagating upwards in a continuously stratified shear flow. In the multiple-scale framework for a horizontally localized wave packet generated by stratified flow over a localized mountain range with multiple peaks, there are in general two horizontal scales: the “fast” scale which is defined by the oscillations within the packet, i.e. the number of peaks, and the “slow scale” which is defined by the horizontal extent of the packet, i.e. the width of the mountain range. The focus here is on the specific case of an isolated mountain where the spectrum of horizontal wavenumbers is centred at zero and the multiple-scaling procedure is thus simplified by the absence of the fast spatial scale. The background flow is vertically sheared and critical-level interactions occur. The time frame within which non-linear critical-level effects become significant is determined by the magnitude of the non-linear terms in the governing equations. With the isolated mountain forcing this time frame is significantly longer than in the case of a multiple-peak mountain range forcing and it depends on the horizontal scale of the forcing, as well as on the amplitude. At leading-order, the non-linear asymptotic solution approaches a steady state in the outer region at late time, but the zero-wavenumber component of the solution continues to evolve with time in the vicinity of the critical level. 相似文献
13.
If convection in the Earth's liquid outer core is disrupted, degrades to turbulence and begins to behave in a chaotic manner, it will destabilize the Earth's magnetic field and provide the seeds for kimberlite melts via turbulent jets of silicate rich core material which invade the lower mantle. These (proto-) melts may then be captured by extreme amplitude solitary nonlinear waves generated through interaction of the outer core surface with the base of the mantle. A pressure differential behind the wave front then provides a mechanism for the captured melt to ascend to the upper mantle and crust so quickly that emplacement may indirectly promote a type of impact fracture cone within the relatively brittle crust. These waves are very rare but of finite probability. The assumption of turbulence transmission between layers is justified using a simple three-layer liquid model. The core derived melts eventually become frozen in place as localised topographic highs in the Mohorovicic discontinuity (Moho), or as deep rooted intrusive events. The intrusion's final composition is a function of melt contamination by two separate sources: the core contaminated mantle base and subducted Archean crust. The mega-wave hypothesis offers a plausible vehicle for early stage emplacement of kimberlite pipes and explains the age association of diamondiferous kimberlites with magnetic reversals and tectonic plate rearrangements. 相似文献
14.
Gregory M. Zhikharev 《地球物理与天体物理流体动力学》2013,107(3-4):259-279
Abstract A spectral low-order model is proposed in order to investigate some effects of bottom corrugation on the dynamics of forced and free Rossby waves. The analysis of the interaction between the waves and the topographic modes in the linear version of the model shows that the natural frequencies lie between the corresponding Rossby wave frequencies for a flat bottom and those applying in the “topographic limit” when the beta-effect is zero. There is a possibility of standing or eastward-travelling free waves when the integrated topograhic effect exceeds the planetary beta-effect. The nonlinear interactions between forced waves in the presence of topography and the beta-effect give rise to a steady dynamical mode correlated to the topographic mode. The periodic solution that includes this steady wave is stable when the forcing field moves to the West with relatively large phase speed. The energy of this solution may be transferred to the steady zonal shear flow if the spatial scale of this zonal mode exceeds the scale of the directly forced large-scale dynamical mode. 相似文献
15.
In the present paper zonal mean flow excitation by inertial waves is studied in analogy to mean flow excitation by gravity waves that plays an important role for the quasi-biennial oscillation in the equatorial atmosphere. In geophysical flows that are stratified and rotating, pure gravity and inertial waves correspond to the two limiting cases: gravity waves neglect rotation, inertial waves neglect stratification. The former are more relevant for fluids like the atmosphere, where stratification is dominant, the latter for the deep oceans or planet cores, where rotation dominates. In the present study a hierarchy of simple analytical and numerical models of zonally symmetric inertial wave-mean flow interactions is considered and the results are compared with data from a laboratory experiment. The main findings can be summarised as follows: (i) when the waves are decoupled from the mean flow they just drive a retrograde (eastward) zonal mean flow, independent of the sign of the meridional phase speed; (ii) when coupling is present and the zonal mean flow is assumed to be steady, the waves can drive vertically alternating jets, but still, in contrast to the gravity wave case, the structure is independent of the sign of the meridional phase speed; (iii) when coupling is present and time-dependent zonal mean flows are considered the waves can drive vertically and temporarily oscillating mean flows. The comparison with laboratory data from a rotating annulus experiment shows a qualitative agreement. It appears that the experiment captures the basic elements of the inertial wave mean flow coupling. The results might be relevant to understand how the Equatorial Deep Jets can be maintained against dissipation, a process currently discussed controversially. 相似文献
16.
The nonhydrostatic pressure effects on the generation and propagation of wind-forced internal waves are studied with a two-dimensional
numerical ocean model. A one-way directed wind pulse over a stratified ocean initiates surface and internal waves in a closed
basin. The studies are performed with horizontal grid sizes in the range from 1 km to 62.5 m. The experiments are performed
with both a hydrostatic and a nonhydrostatic model, facilitating systematic studies of the sensitivity of the numerical model
results to the grid size and to the nonhydrostatic pressure adjustments. The results show that the nonhydrostatic pressure
effects are highly dependent on the grid size and grow with increased resolution. In the internal depression wave, the horizontal
nonhydrostatic pressure gradients reach the same order of magnitude as the hydrostatic gradients in the high-resolution nonhydrostatic
studies. In these studies, the nonhydrostatic pressure gradients approximately balance the corresponding hydrostatic pressure
gradients in the internal depression wave, and the wave degenerates into a train of soliton waves. The time for the soliton
form to develop agrees with the steepening timescale calculated from Korteweg-de Vries theory. In the high-resolution hydrostatic
model, the internal depression wave takes the form of a single wave front. When the internal waves are generated in the boundary
layers, the nonhydrostatic pressure gradients are much smaller than the hydrostatic gradients and the generation processes
are not effected by the nonhydrostatic pressure with the present range of grid sizes. 相似文献
17.
A three-dimensional non-hydrostatic numerical model for simulation of the free-surface stratified flows is presented. The model is a non-hydrostatic extension of free-surface primitive equation model with a general vertical coordinate and horizontal orthogonal curvilinear coordinates. The model equations are integrated with mode-splitting technique and decomposition of pressure and velocity fields on hydrostatic and non-hydrostatic components. The model was tested against laboratory experiments on the steep wave transformation over the longshore bar, solitary wave impact on the vertical wall, the collapse of the mixed region in the thin pycnocline, mixing in the lock-exchange flows and water exchange through the sea strait. The agreement is generally fair.Responsible Editor: Hans Burchard 相似文献
18.
Contemporary hydrodynamics and morphological change are examined in a shallow microtidal estuary, located on a wave-dominated coast (Port Stephens, NSW, Australia). Process-based numerical modelling is undertaken by combining modules for hydrodynamics, waves, sediment transport and bathymetry updates. Model results suggest that the complex estuarine bathymetry and geometry give rise to spatial variations in the tidal currents and a marked asymmetry between ebb and flood flows. Sediment transport paths correspond with tidal asymmetry patterns. The SE storms significantly enhance the quantities of sediment transport, while locally generated waves by the westerly strong winds also are capable of causing sediment entrainment and contribute to the delta morphological change. The wave/wind-induced currents are not uniform with flow over shoals driven in the same direction as waves/winds while a reverse flow occurring in the adjacent channel. The conceptual sediment transport model developed in this study shows flood-directed transport occurs on the flood ramp while ebb-directed net transport occurs in the tidal channels and at the estuary entrance. Accretion of the intertidal sand shoals and deepening of tidal channels, as revealed by the model, suggest that sediment-infilling becomes advanced, which may lead to an ebb-dominated estuary. It is likely that a switch from flood- to ebb-dominance occurs during the estuary evolution, and the present-day estuary acts as a sediment source rather than sediment sink to the coastal system. This is conflictive to the expectation drawn from the estuarine morphology; however, it is consistent with previous research suggesting that, in an infilling estuary, an increase in build-up of intertidal flats/shoals can eventually shift an estuary towards ebb dominance. Thus, field data are needed to validate the result presented here, and further study is required to investigate a variety of estuaries in the Australian area. 相似文献
19.
Large-scale zonal flow driven across submarine topography establishes standing Rossby waves. In the presence of stratification,
the wave pattern can be represented by barotropic and baroclinic Rossby waves of mixed planetary topographic nature, which
are locked to the topography. In the balance of momentum, the wave pattern manifests itself as topographic formstress. This
wave-induced formstress has the net effect of braking the flow and reducing the zonal transport. Locally, it may lead to acceleration,
and the parts induced by the barotropic and baroclinic waves may have opposing effects. This flow regime occurs in the circumpolar
flow around Antarctica. The different roles that the wave-induced formstress plays in homogeneous and stratified flows through
a zonal channel are analyzed with the BARBI (BARotropic-Baroclinic-Interaction ocean model, Olbers and Eden, J Phys Oceanogr 33:2719–2737, 2003) model. It is used in complete form and in a low-order version to clarify the different regimes. It is shown that the barotropic
formstress arises by topographic locking due to viscous friction and the baroclinic one due to eddy-induced density advection.
For the sinusoidal topography used in this study, the transport obeys a law in which friction and wave-induced formstress
act as additive resistances, and windstress, the effect of Ekman pumping on the density stratification, and the buoyancy forcing
(diapycnal mixing of the stratified water column) of the potential energy stored in the stratification act as additive forcing
functions. The dependence of the resistance on the system parameters (lateral viscosity ε, lateral diffusivity κ of eddy density advection, Rossby radius λ, and topography height δ) as well as the dependence of transport on the forcing functions are determined. While the current intensity in a channel
with homogeneous density decreases from the viscous flat bottom case in an inverse quadratic law ~δ
–2 with increasing topography height and always depends on ε, a stratified system runs into a saturated state in which the transport becomes independent of δ and ε and is determined by the density diffusivity κ rather than the viscosity: κ/λ
2 acts as a vertical eddy viscosity, and the transport is λ
2/κ times the applied forcing. Critical values for the topographic heights in these regimes are identified. 相似文献
20.
The differentially heated rotating annulus is a laboratory experiment historically designed for modelling large-scale features of the mid-latitude atmosphere. In the present study, we investigate a modified version of the classic baroclinic experiment in which a juxtaposition of convective and motionless stratified layers is created by introducing a vertical salt stratification. The thermal convective motions are suppressed in a central region at mid-depth of the rotating tank, therefore double-diffusive convection rolls can develop only in thin layers located at top and bottom, where the salt stratification is weakest. For high enough rotation rates, the baroclinic instability destabilises the flow in the top and the bottom shallow convective layers, generating cyclonic and anticyclonic eddies separated by the stable stratified layer. Thanks to this alternation of layers resembling the convective and radiative layers of stars, the planetary’s atmospheric troposphere and stratosphere or turbulent layers at the sea surface above stratified waters, this new laboratory setup is of interest for both astrophysics and geophysical sciences. More specifically, it allows to study the exchange of momentum and energy between the layers, primarily by the propagation of internal gravity waves (IGW). PIV velocity maps are used to describe the wavy flow pattern at different heights. Using a co-rotating laser and camera, the wave field is well resolved and different wave types can be found: baroclinic waves, Kelvin and Poincaré type waves. The signature of small-scale IGW can also be observed attached to the baroclinic jet. The baroclinic waves occur at the thin convectively active layer at the surface and the bottom of the tank, though decoupled they show different manifestation of nonlinear interactions. The inertial Kelvin and Poincaré waves seem to be mechanically forced. The small-scale wave trains attached to the meandering jet point to an imbalance of the large-scale flow. For the first time, the simultaneous occurrence of different wave types is reported in detail for a differentially heated rotating annulus experiment. 相似文献