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small - scale ocean motions have an important effect on oceanic flows several orders of magnitude larger than them .
the best - known bulk effect of small - scale processes is a substantial contribution to the transport of heat , salt , momentum , and passive tracers in all parts in the world s oceans .
this effect is usually included in ocean circulation models by modifying the transport and mixing properties of the fluid from their molecular values to larger ones , giving rise to eddy - diffusion approaches of increasing sophistication and predictive power @xcite .
the transport processes parametrized by these effective changes of the diffusive fluid properties have been shown to control important aspects of the earth s climate @xcite .    beyond eddy diffusion approaches , physical effects of small - scale activity are still poorly understood .
for this reason , the nature and variability of small - scale oceanic motions have been exhaustively examined in different oceanographic contexts @xcite .
given the nature of small - scale activity  disordered , fluctuating and turbulent  a contribution to diffusion and dispersion effects is obvious on physical grounds . but a more coherent influence of processes occurring at small - scales on large scales motions is unexpected unless some oceanographic factor is able to get a significant mean component out of the fluctuating behavior .
bottom topography is one of such factors breaking the symmetry of the fluctuation statistics , and thus provides a dynamical link for energy transfer from the small to the large scale .
evidence has been accumulated in the last decade showing that mean flows following the topographic contours are often found in the vicinity of topographic features of different scales @xcite .
these topographically generated currents have been shown to influence both local and global aspects of the earth s climate @xcite .
for example , large - scale motions related to topographic anomalies have been found in the north and south atlantic playing a major role in determining regional circulation and climatic characteristics @xcite .
coriolis force , topography and fluctuations have been pointed out as the main ingredients to generate these along - isobaths coherent motions @xcite .
briefly , coriolis force links topography to the dynamics of ocean vorticity .
thus changes in ocean depth provide a symmetry breaking factor distinguishing according to their vorticity content otherwise isotropic mesoscale fluctuations .
the result is that the mean effect of small - scale fluctuations does not average to zero yielding the existence of mean flows .
finally , the topographic structure determines the circulation patterns of the originated currents .    on the basis of present knowledge ,
anticyclonic ( cyclonic ) tendencies are expected over bumps ( depressions ) for generated mean flows over topography .
however , [ 1998 ] pointed out that these circulations tendencies could be strongly dependent on the properties of the small - scale variability .
they theoretically addressed the possibility that the above mentioned circulation pattern could be even reversed ( cyclonic ( anticyclonic ) circulations over bumps ( depressions ) ) by the action of the small scales .
the same effect is predicted when considering bottom friction instead of viscosity as the damping mechanism @xcite .
the present letter attempts to elucidate , by means of computer simulations , if the direction of these mean flows is sensitive to the statistical characteristics of the small - scale , as it was argued on theoretical grounds .
to explore in detail the possible relations between large and small scales in the presence of topography an ideal ocean represented by a single layer of fluid subjected to quasigeostrophic dynamics will be considered .
baroclinic effects which in real oceans give rise to meso - small scale activity are modeled here by an explicit stochastic forcing with prescribed statistical properties @xcite .
this term might also be considered as representing any high frequency wind forcing components and other processes below the resolution considered in the numerical model .
this random forcing , in combination with viscous dissipation , will bring the ocean model to a statistically steady state . while highly idealized , the simplifying modeling assumptions above arise from our interest in isolating just the essential processes by which small - scale variability leads to topography - generated currents .    within our approximations ,
the full ocean dynamics can be described by @xcite :    @xmath0 = \nu \nabla^4 \psi + f \ , \ ] ]    the ocean dynamics described by eq .
( [ eq ] ) is an f - plane quasigeostrophic model where @xmath1 is the streamfunction , @xmath2 is the above mentioned stochastic vorticity input , @xmath3 is the viscosity parameter and @xmath4 , with @xmath5 the coriolis parameter , @xmath6 the mean depth , and @xmath7 the local topographic height over the mean depth .
the poisson bracket or jacobian is defined as @xmath8= { \partial a \over \partial x } { \partial b \over \partial y } - { \partial b \over \partial x}{\partial a \over \partial y}\ .\ ] ]    a set of numerical simulations has been carried out to determine the dependence of the large scale pattern circulation on the structure and variability of the small - scales .
the description of the numerical model and different parameters employed in the simulations are summarized in appendix a. a randomly generated bottom topography is used in all the cases . as a way of changing in a continuous manner the statistical properties of the forcing @xmath2 we assume it to be a gaussian stochastic process of zero mean , white in time , and spatial spectrum given by @xmath9 , where @xmath10 is the wavenumber .
a positive exponent @xmath11 represents relative - vorticity fluctuations more dominant at the large scales , whereas negative @xmath11 represents fluctuations dominant at the smaller scales .
the distribution of fluctuation variance among the scales can thus be controlled by varying @xmath11 .
the spectrum of the energy input corresponding to the above stochastic vorticity forcing is also white in time , with a wavenumber dependence given by the relation @xmath12 .
we have started first considering a situation where the small - scale variability is described by @xmath13 .
this power - law has been observed for vorticity forcing induced by winds in the pacific ocean @xcite .
the model has been integrated until a stationary state is achieved .
figure 1b shows the mean currents obtained from this specific simulation . in the mean state
the currents do not average to zero , despite the isotropy of the fluctuations and dissipation .
instead the final mean state is characterized by the existence of large - scale mean currents strongly correlated with bottom topography . the spatial correlation coefficient between the streamfunction and the bottom topography is for this case @xmath14 .
this positive spatial correlation implies the existence of mean anticyclonic ( cyclonic ) circulations over bumps ( depressions ) . as a next step ,
we have modeled the action of small - scales as a noisy process with a correlation described by the power - law @xmath15 .
this spectrum describes a situation where the small - scale variability is more energetic than the one induced by the previous @xmath16 power - law .
the response of the system is drastically changed by this small - scale activity . as shown in figure 1c
the mean state of the ocean displays a pattern of circulation practically uncorrelated with bottom topography .
specifically , the spatial correlation coefficient is @xmath17 .
increasing again the exponent of the power law to @xmath18 , we obtain the generation of mean currents anticorrelated with bottom topography , as it can be observed from figure 1d .
the spatial correlation coefficient is @xmath19 in this case of high small - scale activity , indicating the existence of mean cyclonic ( anticyclonic ) motions over bumps ( depressions ) .
note that figures 1c and d display topography - generated currents much weaker than those obtained for the @xmath16 power - law case , figure 1b .
this feature comes from the scale - selective character of the viscosity , more efficient at small scales where the forcing energy is most localized in the @xmath15 and @xmath20 cases . besides this effect
, it should also be mentioned that forcing with a @xmath16 spectral power - law directly provides more energy input to the large - scale components than the @xmath15 and @xmath20 forcings .
additional numerical simulations , for different initial conditions and noise and topography realizations , consistently confirm the results of the simulations presented in fig .  1 , that is the sensibility of the large - scale circulations not only to the particular structure of the underlying topography but also to the characteristics of the small - scale variability of the environment .
in particular , as the small - scale content in the vorticity forcing is augmented with respect to the large - scale one , mean currents are always seen to reverse direction .
on the basis of the property of potential - vorticity conservation , anticyclonic ( cyclonic ) motions are traditionally expected over topographic bumps ( depressions ) @xcite .
if potential vorticity is not preserved because of the presence of some kind of forcing mechanism , then different circulation patterns can be generated .
small - scale activity constitutes a systematic and persistent forcing of the circulation in the whole ocean . due to the relatively small and fast space and time scales that characterize this variability ,
the physical characteristics of this forcing are usually described in terms of their statistical properties @xcite . in other words ,
small - scale activity can be considered as a fluctuating background in which the large - scale motions are embedded .
the relevance of the role played by this fluctuating environment in modifying the transport and viscous properties of the large scales is widely recognized . beyond these diffusive and viscous effect of the small - scale activity ,
the numerical results presented in this letter show that in the presence of bottom topography , statistical details of the variability of the small - scales can induce different large - scale oceanic circulations .
the strength of this effect will be affected by the spectral characteristics of the topographic and forcing fields as well as by the real baroclinic nature of the ocean .
preliminary computer simulations indicate that the strength of the mean currents increases when the topography contains more proportion of large - scale features .
this effect and the dependence of the current direction on the forcing spectral exponent , presented in fig .
1 , nicely validates the theoretical results in @xcite .
extension of the theoretical methods to the baroclinic case is in progress .
however , a complete analysis of the influence of different forcings and topography shapes can only be addressed numerically .
the shape of the topography was already shown to play a fundamental role in the energy transfer between different scales in baroclinic quasigeostrophic turbulence @xcite .
finally , the results shown in this letter stress the need for a better observational characterization of the space and time variability of oceans at small - scales in order to achieve a complete understanding of the large - scale ocean circulation .
numerical simulations of eq .
( [ eq ] ) have been conducted in a parameter regime of geophysical interest .
a value of @xmath21 was chosen as appropriate for the coriolis effect at mean latitudes on earth and @xmath22 for the viscosity , a value usual for the eddy viscosity in ocean models .
we use the numerical scheme developed in [ 1992 ] on a grid of @xmath23 points .
the distance between grid points corresponds to 20 km , so that the total system size is @xmath24 km .
the algorithm , based on arakawa finite differences and the leap - frog algorithm , keeps the value of energy and enstrophy constant when it is run in the inviscid and unforced case .
the consistent way of introducing the stochastic term into the leap - frog scheme can be found in [ 1997 ] .
the amplitude of the forcing has been chosen in order to obtain final velocities of several centimeters per second .
the topographic field is randomly generated from a isotropic spectrum containing , with equal amplitude and random phases , all the fourier modes corresponding to scales between 80 km and 300 km .
the model was run for @xmath25 time steps ( corresponding to 206 years ) after a statistically stationary state was reached .
the streamfunction is then averaged during this last interval of time .    financial support from cicyt ( amb95 - 0901-c02 - 01-cp and mar98 - 0840 ) , and from the mast program matter mas3-ct96 - 0051 ( ec ) is greatly acknowledged .
comments of two anonymous referees are also greatly appreciated .
alvarez , a. , and j. tintor , topographic stress : importance and parameterization , _ ocean modeling and parameterization , _ edited by e. p. chassignet and j. verron , kluwer academic publishers , netherlands , 1998 .
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oceanogr . , _ _ 37 , _ 167 - 192 , 1991 .
small - scale oceanic motions , in combination with bottom topography , induce mean large - scale along - isobaths flows . 
 the direction of these mean flows is usually found to be anticyclonic ( cyclonic ) over bumps ( depressions ) . 
 here we employ a quasigeostrophic model to show that the current direction of these topographically induced large - scale flows can be reversed by the small - scale variability . 
 this result addresses the existence of a new bulk effect from the small - scale activity that could have strong consequences on the circulation of the world s ocean .